texlive[72842] Master/texmf-dist: curve2e (13nov24)
commits+karl at tug.org
commits+karl at tug.org
Wed Nov 13 22:11:45 CET 2024
Revision: 72842
https://tug.org/svn/texlive?view=revision&revision=72842
Author: karl
Date: 2024-11-13 22:11:45 +0100 (Wed, 13 Nov 2024)
Log Message:
-----------
curve2e (13nov24)
Modified Paths:
--------------
trunk/Master/texmf-dist/doc/latex/curve2e/README.txt
trunk/Master/texmf-dist/doc/latex/curve2e/curve2e-manual.pdf
trunk/Master/texmf-dist/doc/latex/curve2e/curve2e-manual.tex
trunk/Master/texmf-dist/doc/latex/curve2e/curve2e.pdf
trunk/Master/texmf-dist/source/latex/curve2e/curve2e.dtx
trunk/Master/texmf-dist/tex/latex/curve2e/curve2e-v161.sty
trunk/Master/texmf-dist/tex/latex/curve2e/curve2e.sty
Modified: trunk/Master/texmf-dist/doc/latex/curve2e/README.txt
===================================================================
--- trunk/Master/texmf-dist/doc/latex/curve2e/README.txt 2024-11-13 21:11:32 UTC (rev 72841)
+++ trunk/Master/texmf-dist/doc/latex/curve2e/README.txt 2024-11-13 21:11:45 UTC (rev 72842)
@@ -1,16 +1,22 @@
%%
%% This is file `README.txt',
+%% generated with the docstrip utility.
%%
-%% Copyright (C) 2005--2023 Claudio Beccari all rights reserved.
+%% The original source files were:
+%%
+%% curve2e.dtx (with options: `readme')
+%%
+%% Copyright (C) 2005--2024 Claudio Beccari all
+%% rights reserved.
%% License information appended
%%
File README.txt for package curve2e
- [2023-01-01 v.2.3.1 Extension package for pict2e]
+[2024-11-13 v.2.6.0 Extension package for pict2e]
+
The package bundle curve2e is composed of the following files
curve2e.dtx
curve2e-manual.tex
-README.txt
The derived files are
@@ -18,9 +24,12 @@
curve2e-v161.sty
curve2e.pdf
curve2e-manual.pdf
+README.txt
+If you install curve2e without using your TeX system package handler,
Compile curve2e.dtx and curve2e-manual.tex two or three times until
-all labels and citation keys are completely resolved.
+all labels and citation keys are completely resolved. Then move the
+primary and derived files as follows:
Move curve2e.dtx and curve2e-manual.tex to ROOT/source/latex/curve2e/
Move curve2e.pdf and curve2e-manual.pdf to ROOT/doc/latex/curve2e/
@@ -28,80 +37,72 @@
Move README.txt to ROOT/doc/latex/curve2e/
curve2e.dtx is the documented TeX source file of the derived files
-curve2e.sty, and curve2e-v161.sty.
+curve2e.sty, curve2e.pdf, curve2e-v161.sty and README.txt.
-You get curve2e.sty, curve2e.pdf, and curve2e-v161.sty by running
-pdflatex on curve2e.dtx.
+You get curve2e.sty, curve2e.pdf, curve2e-v161.sty, and README.txt
+by running pdflatex on curve2e.dtx.
-The curve2e-manual file contains the user manual; in this way the long
-preliminary descriptive part has been transferred to a shorter dedicated
-file, where the “normal” user should find enough information to use the
-package. The curve2e.pdf file, extracted from the .dtx one, contains the
-code documentation and is intended for developers, or for curious
-advanced users. For what concerns curve2e-v161.sty, it is a previous
-fall back version of this package; see below why the older version might
-become necessary to the end user.
+The curve2e-manual files contains the user manual; in
+this way the long preliminary descriptive part of the previous versions
+curve2e.pdf file has been transferred to a shorter dedicated file, and the
+"normal" user should have enough information to use the package. The
+curve2e.pdf file, extracted from the .dtx one, contains the code
+documentation and is intended for the developers, or for the curious
+advanced users. For what concerns curve2e-v161.sty, it is a previous
+version of this package; see below why the older version might become
+necessary to the end user.
README.txt, this file, contains general information.
-Curve2e.sty is an extension of the package pict2e.sty which initially
-extended the standard picture LaTeX environment according to what Leslie
-Lamport specified in the second edition of his LaTeX manual (1994); in
-time pict2e.sty evolved to contain further enhancements to what Leslie
-Lamport announced in 1994.
+This bundle contains also package curve2e-v161.sty, a roll-back
+version needed in certain rare cases.
+Curve2e.sty is an extension of the package pict2e.sty which extends the
+standard picture LaTeX environment according to what Leslie Lamport
+specified in the second edition of his LaTeX manual (1994).
+
This further extension curve2e.sty to pict2e.sty allows to draw lines
-and vectors with any non integer slope parameters, to draw dashed and
-dotted lines of any slope, to draw arcs and curved vectors, to draw
-curves where just the interpolating nodes are specified together with
-the slopes at such nodes; closed paths of any shape can be filled with
-color; all coordinates are treated as ordered pairs, i.e. 'complex
-numbers'; coordinates may be expressed also in polar form. Coordinates
-may be specified with macros, so that editing any drawing is rendered
-much simpler: any point specified with a macro may be modified only
-once in its macro definition.
+and vectors with any non integer slope parameters, to draw dashed and
+dotted lines of any slope, to draw arcs and curved vectors, to draw
+curves where just the interpolating nodes are specified together with
+the tangent directions at such nodes; closed paths of any shape can be
+filled with color; all coordinates are treated as ordered pairs, i.e. "complex
+numbers"; coordinates may be expressed also in polar form. Coordinates
+may be specified with macros, so that editing any drawing is rendered
+much simpler: any point specified with a macro is modified only once
+in its macro definition.
Some of these features have been incorporated in the 2009 version of
pict2e; therefore this package avoids any modification to the original
-pict2e commands. In any case this version of curve2e is compatible with
+pict2e commands. In any case the version of curve2e is compatible with
later versions of pict2e; see below.
-As said above, curve2e now accepts polar coordinates in addition to the
-usual cartesian ones; several macros have been upgraded; a new macro for
-tracing cubic Bezier splines with their control nodes specified in polar
-form is available. The same applies to quadratic Bezier splines. The
-\multiput command has been completely modified in a backwards compatible
-way; the new version allows to manipulate the increment components in a
-configurable way. A new \xmultiput command has been defined that is more
-configurable than the original one; both commands \multiput and \xmultiput
-are backwards compatible with the original picture environment definition.
+Curve2e now accepts polar coordinates in addition to the usual cartesian
+ones; several macros have been upgraded; a new macro for tracing cubic
+Bezier splines with their control nodes specified in polar form is
+available. The same applies to quadratic Bezier splines. The multiput
+command has been completely modified in a backwards compatible way; the
+new version allows to manipulate the increment components in a configurable
+way. A new xmultiput command has been defined that is more configurable
+than the original one; both commands multiput and xmultiput are backwards
+compatible with the original picture environment definition.
Curve2e solves a conflict with package eso-pic.
-This version of curve2e is almost fully compatible with pict2e dated
-2014/01/12 version 0.2z and later; as of today the last pct2e revision
-is version 0.4b dated 2020, and curve2e has been tested also with this
-revision confirming that it performs as expected.
-Pay attention, though, that in 2020 also the \LaTeX kernel segment dealing
-with the picture environment has been upgraded; since then, the picture
-environment opening and internal commands can handle explicit dimensions
-and accepts dimensional expressions as those that can be processed by the
-eTeX command \dimexpr. Such functionalities should be avoided when using
-curve2e; at least when dealing with coordinates that curve2e assumes to
-be real possibly floating point numbers, not dimensions.
+This version of curve2e is almost fully compatible with pict2e version 0.4z and later.
-If you specify:
+If you specify
\usepackage[<pict2e options>]{curve2e}
-package pict2e is loaded and curve2e options are automatically passed on to pict2e.
+the package pict2e is automatically invoked with the specified options.
The -almost fully compatible- phrase is necessary to explain that this
-version of curve2e uses some `functions' of the LaTeX3 language that were
-made available to the LaTeX developers by mid October 2018. Should the
-user have an older or a basic/incomplete installation of the TeX system,
+version of curve2e uses some "functions" of the LaTeX3 language that were
+made available to the LaTeX developers by mid October 2018. Should the user
+have an older or a basic/incomplete installation of the TeX system,
such L3 functions might not be available. This is why this
package checks the presence of the developer interface; in case
-such interface is not available it falls back to the previous version
+such interface is not available it rolls back to the previous version
renamed curve2e-v161.sty, which is part of this bundle; this roll-back
file name must not be modified in any way. The compatibility mentioned
above implies that the user macros remain the same, but their
@@ -109,13 +110,13 @@
rely totally on the xfp package functionalities, but legacy documents
source files should compile correctly.
-This package has the LPPL status of maintained.
+The package has the LPPL status of maintained.
According to the LPPL licence, you are entitled to modify this package,
as long as you fulfil the few conditions set forth by the Licence.
-Nevertheless this package is an extension to the standard LaTeX pict2e
-(2014 and 2020) package. Therefore any change must be controlled on the
+Nevertheless this package is an extension to the standard LaTeX
+pict2e (2014) package. Therefore any change must be controlled on the
parent package pict2e, so as to avoid redefining or interfering with
what is already contained in that package.
@@ -128,5 +129,18 @@
claudio dot beccari at gmail dot com
+%%
+%% Distributable under the LaTeX Project Public
+%% License, version 1.3c or higher (your choice).
+%% The latest version of this license is at:
+%% http://www.latex-project.org/lppl.txt
+%%
+%% This work is "maintained"
+%%
+%% This work consists of file curve2e.dtx, and the
+%% derived files curve2e.sty and curve2e.pdf, plus
+%% the auxiliary derived files README.txt and
+%% curve2e-v161.sty.
+%%
%%
%% End of file `README.txt'.
Modified: trunk/Master/texmf-dist/doc/latex/curve2e/curve2e-manual.pdf
===================================================================
(Binary files differ)
Modified: trunk/Master/texmf-dist/doc/latex/curve2e/curve2e-manual.tex
===================================================================
--- trunk/Master/texmf-dist/doc/latex/curve2e/curve2e-manual.tex 2024-11-13 21:11:32 UTC (rev 72841)
+++ trunk/Master/texmf-dist/doc/latex/curve2e/curve2e-manual.tex 2024-11-13 21:11:45 UTC (rev 72842)
@@ -1,12 +1,13 @@
% !TEX TS-program = pdflatex
% !TEX encoding = UTF-8 Unicode
\documentclass[a4paper]{article}\errorcontextlines=100
+\ProvidesFile{curve2e-manual.tex}[2024-11-13 v.2.6.0 curve2e user manual]
\hfuzz 10pt
-\usepackage[utf8]{inputenc}
+%\usepackage[utf8]{inputenc}
\usepackage{lmodern,textcomp}
\usepackage{mflogo}
\usepackage{multicol,amsmath,fancyvrb,graphics,shortvrb}
-\usepackage{xcolor,verbatim,enumitem,trace}
+\usepackage{xcolor,verbatim,enumitem,FramedSyntax,trace}
\usepackage{curve2e}
\MakeShortVerb{\|}
\providecommand*\diff{\mathop{}\!\mathrm{d}}
@@ -67,16 +68,20 @@
\ProvideDocumentEnvironment{Esempio}{ O{\footnotesize} D(){0.50}}
% All definitions and assignments are local
% #1 := Latex font size command or \setfontsize{<size>}
-% %2 := \textwidth percentage for the code box; the complement, less the
-% column gap for the compiled result
+% %2 := \textwidth percentage for the code box; the
+% complement, less the column gap for the compiled
+% result
%
-% Syntax: \begin{Esempio}[<size command>](<code box percentage width>)
+% Syntax: \begin{Esempio}[<size command>](<code box
+% percentage width>)
%
-% Warning: No extra space is put before and/or after the display; this
-% environment is assumed to be used within a figure environment
-% that already provides its own vertical spaces. Should this
-% environment be used between paragraphs, the user should manually
-% provide a convenient amount of space above and below it.
+% Warning: No extra space is put before and/or after the
+% display; this environment is assumed to be used
+% within a figure environment that already provides
+% its own vertical spaces. Should this environment
+% be used between paragraphs, the user should
+% manually provide a convenient amount of space
+% above and below it.
% Remember: This environment sets itself in vertical mode
{\par\dimendef\Wboxu=2570 \dimendef\Wboxd=2572
\Wboxu=#2\linewidth\relax
@@ -151,7 +156,7 @@
\begin{document}
-\author{Claudio Beccari\\{\small\texttt{claudio dot beccari at gmail dot com}}}
+\author{Claudio Beccari\\{\small\texttt{claudio(dot)beccari(at)gmail(dot)com}}}
\title{Package \pack{curve2e} user manual}
\GetFileInfo{curve2e.sty}
\date{Version \fileversion~--~Last revised \filedate}
@@ -162,20 +167,20 @@
\end{multicols}
\begin{abstract}\setfontsize{9.5}
-This file contains the user manual of the \pack{curve2e} extension package to the \pack{pict2e} bundle; the latter was described by Lamport himself in the 1994 second edition of his \LaTeX\ handbook.
+This file contains the user manual of the \pack{curve2e} extension package to the \pack{pict2e} bundle; the latter was described by Lamport himself in the 1994 second edition of his \LaTeX\ handbook.
-Please take notice that on April 2011 a package \pack{pict2e} upgraded version has been released that incorporates some of the commands defined in early versions of this package \pack{curve2e}; apparently there are no conflicts, because this package contains only the advanced features that extend the above package.
+Please take notice that on April 2011 a package \pack{pict2e} upgraded version has been released that incorporates some of the commands defined in early versions of this package \pack{curve2e}; apparently there are no conflicts, because this package contains only the advanced features that extend the above package.
-Since this extension redefines some commands and introduces some more drawing facilities (that allow to draw circular arcs and arbitrary curves with the minimum of user intervention) the user needs a user manual that contains several actual examples; this auxiliary manual is contained in file |curve2e-manual.pdf|. The software available to show the drawing code and its result after compilation is incompatible with the usual
-\LaTeX\ |ltxdoc| class for code documentation, therefore a separate user manual has been made available. If the user wants to explore the \pack{curve2e} code and its documentation s/he has available the |curve2e.pdf| file. Either file is readable by entering in a terminal window the command |texdoc curve2e-manual| or |texdoc curve2e.pdf|; please do not forget the extension when you want to read the code documentation.
+Since this extension redefines some commands and introduces some more drawing facilities (that allow to draw circular arcs and arbitrary curves with the minimum of user intervention) users need a user manual that contains several actual examples; this auxiliary manual is contained in file
+|curve2e-manual.pdf|. The software available to show the drawing code and its result after compilation is incompatible with the usual \LaTeX\ |ltxdoc| class for code documentation, therefore a separate user manual has been made available. If users want to explore the \pack{curve2e} code and its documentation they have available the |curve2e.pdf| file. Either file is readable by entering in a terminal window the command |texdoc curve2e-manual| or |texdoc curve2e.pdf|; please do not forget the extension when you want to read the code documentation.
\end{abstract}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Installation}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-If \TeX\ system was installed with a \TeX~Live or a MiK\TeX\ complete and updated distribution this package is already installed; in order to verify open a terminal or command prompt window and use it to enter the \texttt{texdoc curve2e-manual}; as soon as the command is executed a screen window should open displaying this manual. If this does not happen, either you misspelt the command (it happens more often than not), or your installation is not complete and updated.
+If \TeX\ system was installed with a \TeX~Live or a MiK\TeX\ complete and updated distribution this package is already installed; in order to verify open a terminal or command prompt window and use it to enter the \texttt{texdoc curve2e-manual} command; as soon as the command is executed a screen window should open displaying this manual. If this does not happen, either you misspelt the command (it happens more often than not), or your installation is not complete and updated.
-I suggest you to use your computer installation facilities to install this bundle. Otherwise, download this curve2e.zip package from one of the CTAN (Comprehensive TeX Archive Network) archives, to your downloads folder.
+I suggest you to use your computer installation facilities to install this bundle. Otherwise, download this curve2e.zip package from one of the CTAN (Comprehensive TeX Archive Network) archives, to your downloads folder.
Before doing anything else verify if you have a \emph{personal} \texttt{texmf} tree; if not, create one reading you distribution instruction; let us assume that your personal |texmf| archive is in |HOME/texmf| (on Windows change the slash with a backslash) and |HOME| is a path starting from the root of you hard disk and going though several other folders. On Windows~10 it might be |C:\Users\YourName|; on Linux it might simply be |~|; on Mac it would be |~/\Library|, but sometimes the |HOME| might be different, especially on Windows platforms. Create the following subfolders:
\begin{enumerate}[noitemsep]
\item |HOME/texmf/source/latex/curve2e/|
@@ -183,13 +188,13 @@
\item |HOME/texmf/tex/latex/curve2e/|
\end{enumerate}
-Now move file \file{curve2e.zip} to the |.../source/latex/curve2e/| folder; then decompress the |.zip| file with the software you have available on your platform. Run |pdflatex| on the |.dtx| file; then do the same with the |curve2e-manual.tex|. You might need to repeat these compilations two or three times in order to have the table of contents and all the references correctly connected.
+Now move file \file{curve2e.zip} to the |.../source/latex/curve2e/| folder; then decompress the |.zip| file with the software you have available on your platform. Run |pdflatex| on the |.dtx| file; then compile the |curve2e-manual.tex| file. You might need to repeat these compilations two or three times in order to have the table of contents and all the references correctly connected.
-This done move the |.pdf| files to the |.../doc/latex/curve2e/| folder. and move the |.sty| files to the |.../tex/latex/curve2e/| folder.
+This done, move the |.pdf| files to the |.../doc/latex/curve2e/| folder. and move the |.sty| files to the |.../tex/latex/curve2e/| folder.
Clear the |.../source/latex/curve2e/| folder from the auxiliary files, all those remaining in the folder except those that have the extensions |.zip|, |.dtx|, |.tex|, and |.txt|. Read the \file{README.txt} file.
-If your \TeX\ system is correctly set up, your files in your personal tree should be immediately usable; probably you have to create the file-name database with MiK\TeX; in this case read the documentation of your MiK\TeX\ installation to discover how to~do~it.
+If your \TeX\ system is correctly set up, your files in your personal tree should be immediately usable; probably you have to create or update the file-name database with MiK\TeX; in this case read the documentation of your MiK\TeX\ installation to discover how to~do~it.
Remember to delete all these subfolders if you decide to install a complete updated version of your favourite distribution, and you'd better keep it updated approximately once every 7 or 10 days. This is much simpler than to struggle with these manual operations.
@@ -197,18 +202,20 @@
\section{Package \pack{pict2e} and this extension \pack{curve2e}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- Package \pack{pict2e} was announced in issue 15 of \file{latexnews}
- around December 2003; it was declared that the new package would
- replace the dummy one that had been accompanying every release of
- \LaTeXe\ since its beginnings in 1994. The dummy package was just
- issuing an info message that simply announced the temporary
- unavailability of the real package.
+ Package \pack{pict2e} was announced in issue 15 of
+ \file{latexnews} around December 2003; it was declared that
+ the new package would replace the dummy one that had been
+ accompanying every release of \LaTeXe\ since its beginnings
+ in 1994. The dummy package was just issuing an info message
+ that simply announced the temporary unavailability of the
+ real package.
- Eventually Gäßlein and Niepraschk implemented what Lamport himself had
- already documented in the second edition of his \LaTeX\ handbook, it was
- a \LaTeX\ package that contained the macros capable of removing all
- the limitations contained in the standard commands of the original
- \texttt{picture} environment; specifically what follows.
+ Eventually Gäßlein and Niepraschk implemented what Lamport
+ himself had already documented in the second edition of his
+ \LaTeX\ handbook, it was a \LaTeX\ package that contained
+ the macros capable of removing all the limitations contained
+ in the standard commands of the original \texttt{picture}
+ environment; specifically what follows.
\begin{enumerate}[noitemsep]
\item The line and vector slopes were limited to the ratios of relative
@@ -482,11 +489,11 @@
package, it has to load it \emph{before} \pack{curve2e}.
%%
\item Since they are used very much in the following examples, we recall some commands to label certain drawing elements, such as points, lines, arcs, and similar lines, and to insert legends in some figures. They are \cs{legenda}, \cs{Zbox} and \cs{Pbox}; their syntax is the following:
-\begin{sintassi}\ttfamily\obeylines
+\begin{Sintassi}[9.75]\ttfamily
|\legenda|\parg{coordinates}\marg{formula}
|\Zbox|\parg{coordinates}\oarg{position}\marg{formula}\oarg{dot diameter}
|\Pbox|\parg{coordinates}\oarg{position}\marg{text}\oarg{dot diameter}\meta{\texttt{*}}\aarg{angle}
-\end{sintassi}
+\end{Sintassi}
They are described in any up to date documentation of \pack{curve2e}.
%%
\item The user is offered new commands in order to control the line
@@ -505,12 +512,12 @@
not have any influence on these commands.
%%
\item The commands
- \begin{sintassi}\obeylines
+ \begin{Sintassi}
|\linethickness|\marg{thickness}
|\thicklines|
|\thinlines|
|\defaultlinethickness|\marg{thickness}
- \end{sintassi}
+ \end{Sintassi}
always redefine the internal |\@wholewidth| and |\@halfwidth| so that the
latter ones always refer to a full width and to a half of it in this way
if you issue the command {\setfontsize{8.75}|\defaultlinethickness{2pt}|}
@@ -542,29 +549,30 @@
is just for internal usage, rather than a user command. Now
\pack{curve2e} has available also the “arc vectors” with the arrow tips
at one or at both ends. The |\segment| syntax is
- \begin{sintassi}\obeylines
+ \begin{Sintassi}
\cs{segment}\parg{starting point}\parg{ending point}
- \end{sintassi}
+ \end{Sintassi}
The same applies to the vector commands |\Vector| and |\VECTOR| and
|\VVECTOR|; the latter command behaves as |\VECTOR| but draws a vector
with arrow tips at both ends; furthermore this command is available
only with main versions~2 or higher of \pack{curve2e}.
- \begin{sintassi}\obeylines
- |\put|\parg{starting point}\Marg{\cs{Vector}\meta{vector cartesian or polar components}}
+ \begin{Sintassi}\small
+ |\put|\parg{starting point}\Marg{\cs{Vector}\parg{vector cartesian or polar components}}
|\VECTOR|\parg{starting point}\parg{ending point}
|\VVECTOR|\parg{starting point}\parg{ending point}
- \end{sintassi}
+ \end{Sintassi}
- Experience has shown that the commands intended to join two specified
- points are particularly useful; see figure~\ref{fig:vectors}.
+ Experience has shown that the commands intended
+ to join two specified points are particularly
+ useful; see figure~\ref{fig:vectors}.
\begin{figure}[!hb]
\begin{Esempio}[\small](0.60)
\unitlength=0.01\linewidth
\begin{picture}(80,20)
-\AutoGrid
+\AutoGrid[red]
\put(0,0){\vector(1.5,2.3){10}}
\put(20,0){\Vector(10,15.33333)}
\VECTOR(40,0)(50,15.33333)
@@ -571,15 +579,18 @@
\ifdefined\VVECTOR \VVECTOR(60,0)(80,10)\fi
\end{picture}
\end{Esempio}
- \caption{Three (displaced) identical vectors obtained with the three
- vector macros\ifdefined\VVECTOR; a double tipped vector is
- also shown\fi.}\label{fig:vectors}
+\caption{Three (displaced) identical vectors
+ obtained with the three
+ vector macros\ifdefined\VVECTOR; a double
+ tipped vector is also shown\fi. The darker
+ cyan color is an usage example optional grid
+ coloring }\label{fig:vectors}
\end{figure}
-%%
+%
\item The |\polyline| command has already been introduced in \pack{pict2e}: in \pack{curve2e} it is redefined so as to accept also polar coordinates; this new version of |\polyline| accepts also an optional argument to specify how two consecutive segments join together; it accepts an unlimited list of point coordinates, possibly stored in macros, enclosed within round parentheses; the command draws a sequence of connected segments that join in order the specified points; the syntax is:
- \begin{sintassi}
+ \begin{Sintassi}
\cs{polyline}\oarg{optional join style}\parg{$P_1$}\parg{$P_2$}\texttt{...}\parg{$P_n$}
- \end{sintassi}
+ \end{Sintassi}
See figure~\ref{fig:polyline} where a regular pentagon is drawn; usage
of polar coordinates is also shown; please notice how polar
coordinates act in this figure.
@@ -596,8 +607,9 @@
\label{fig:polyline}
\end{figure}
- Examples of using polar and cartesian coordinates are shown in
- figure~\ref{fig:polar}. Notice the |\AutoGrid| macro that draws the grid of mesh lines that are very useful to seti objects at the right positions. The lines are |10\unitlenght| apart.
+Examples of using polar and cartesian coordinates are shown in figure~\ref{fig:polar}. Notice the
+|\AutoGrid| macro that draws the grid of mesh lines that are very useful to set objects at the right positions. The main lines are
+\verb|10\unitlength| apart so that the main squares are clearly visible; if the squares are too small only the median lines are traced with thinner lines; if the squares are not so small thin lines are traced \verb|2\unitlength| apart; otherwise the thin median lines and the thinner \verb|1\unitlength| apart are traced as in regular millimetre drawing paper. The rendering on the screen depends very much on its pixel density, nevertheless we think that e nicely thick grid is very helpful while drawing geometric graphs. When the drawing is completed the \verb|\AutoGrid| command may be commented out so that the grid does not appear in the final document.
\begin{figure}[htb]
\begin{Esempio}[\normalsize]%
@@ -638,9 +650,9 @@
%
\item The new command |\Dashline| (alias: |\Dline| for backwards
compatibility):
- \begin{sintassi}
+ \begin{Sintassi}
|\Dashline|\parg{first point}\parg{second point}\marg{dash and gap length}
- \end{sintassi}
+ \end{Sintassi}
draws a dashed line containing as many dashes as possible, just as long
as specified, and separated by a gap exactly the same size; actually,
in order to make an even gap-dash sequence, the desired dash length is
@@ -678,7 +690,9 @@
\begin{Esempio}[\normalsize]%
\unitlength=0.025\textwidth
\begin{picture}(40,30)
-\AutoGrid(40,30)
+\noinnerlines % <-------- !
+\AutoGrid(40,30)\thicklines
+\color{red}%
\Dashline(0,0)(40,10){2}
\Dashline(0,0)(40,20){2}
\Dashline(0,0)(40,30){2}
@@ -685,11 +699,10 @@
\Dashline(0,0)(30,30){2}
\Dashline(0,0)(20,30){2}
\Dashline(0,0)(10,30){2}
-{\color{blue}%
\Dashline(40,0)(108:30){2}
\Dashline(40,0)(126:30){2}
\Dashline(40,0)(144:30){2}
-\Dashline(40,0)(162:30){2}}
+\Dashline(40,0)(162:30){2}
\end{picture}
\end{Esempio}
\caption{Different length dashed lines with the same nominal dash
@@ -739,10 +752,10 @@
the nearest multiple of 10, while the point coordinates specified to
|\put| are not rounded at all; therefore some care should be used to
place the working grid on the drawing canvas.
- \begin{sintassi}
+ \begin{Sintassi}
|\GraphicGrid|\parg{grad base, grid height}
|\AutoGrid|
- \end{sintassi}
+ \end{Sintassi}
This grid is intended as an aid while drawing; even if you sketch your
drawing on millimetre paper, the drawing grid turns out to be very
useful; one must only delete or comment out the command when the drawing
@@ -764,23 +777,22 @@
These trigonometric functions are used within the complex number
macros; but if the user wants to use them the syntax is the following:
-\begin{sintassi}
+\begin{Sintassi}
\cs{SinOf}\meta{angle}\texttt{to}\meta{control sequence}
\cs{CosOf}\meta{angle}\texttt{to}\meta{control sequence}
\cs{TanOf}\meta{angle}\texttt{to}\meta{control sequence}
-\end{sintassi}
+\end{Sintassi}
The \meta{control sequence} may then be used, for example, as a
multiplying factor of a length.
-
%%
\item Arcs can be drawn as simple circular arcs, or with one or two
arrows at their ends (curved vectors); the syntax is:
-\begin{sintassi}
+\begin{Sintassi}
\cs{Arc}\parg{center}\parg{starting point}\marg{angle}
\cs{VectorArc}\parg{center}\parg{starting point}\marg{angle}
\cs{VectorARC}\parg{center}\parg{starting point}\marg{angle}
\cs{VVectorArc}\parg{center}\parg{starting point}\marg{angle}
-\end{sintassi}
+\end{Sintassi}
If the angle is specified numerically it must be enclosed in braces,
while if it is specified with a control sequence the braces (curly
brackets) are not necessary. The above macro |\Arc| draws a simple
@@ -832,7 +844,7 @@
\thinlines
\polyline(0,0)(0,-50)(50,-50)(50,0)
\Pbox(0,0)[r]{C}[0.75ex]
-\Pbox(18,0)[tr]{H}[0.75ex]
+\Pbox(18,0)[bl]{H}[0.75ex]
\Pbox(50,0)[l]{B}[0.75ex]
\Pbox(18,24)[b]{A}[0.75ex]
\Pbox(0,-50)[br]{E}[0.75ex]
@@ -852,7 +864,7 @@
\caption{Geometrical construction to prove Pitagora's theorem}
\label{fig:pitagora}
\end{figure}
-
+%%
\item A multitude of commands have been defined in order to manage
complex numbers; actually complex numbers are represented as a comma
separated pair of fractional numbers; internally these macros use
@@ -873,7 +885,7 @@
counterclockwise direction, as it is used in the
Euler formula $ \vec{v} = M\eu^{\mathrm{j}\varphi}$.
-\begin{sintassi}
+\begin{Sintassi}
|\MakeVectorFrom|\meta{numeric macro}\meta{numeric macro}|to|\meta{vector macro}
|\CopyVect|\meta{first vector}|to|\meta{second vector macro}
|\ModOfVect|\meta{vector}|to|\meta{modulus macro}
@@ -884,10 +896,10 @@
\qquad\qquad|to|\meta{distance macro} |and|\meta{versor macro}}
|\XpartOfVect|\meta{vector}|to|\meta{macro}
|\YpartOfVect|\meta{vector}|to|\meta{macro}
-\end{sintassi}
+\end{Sintassi}
-\begin{sintassi}
+\begin{Sintassi}
|\DirFromAngle|\meta{angle}|to|\meta{versor macro}
|\ArgOfVect|\meta{vector}|to|\meta{angle macro}
|\ScaleVect|\meta{vector}|by|\meta{scaling factor}|to|\meta{vector macro}
@@ -901,10 +913,11 @@
\qquad\qquad (\textcolor{red}{discouraged; maintained for backwards compatibility})
|\MultVect|\meta{first vector}|by*|\meta{second vector}|to|\meta{vector macro}
\qquad\qquad (\textcolor{red}{discouraged; maintained for backwards compatibility})
- |\Divvect|\marg{dividend vector}\marg{divisor vector}\marg{vector macro}
+ |\Divvect|\marg{dividend vector}\marg{divisor vector}\marg{vector macro} {\color{blue}notice
+ \qquad\qquad that this new command warns the user if the divisor is zero}
|\DivVect|\meta{dividend vector}|by|\meta{divisor vector}|to|\meta{vector macro}
\qquad\qquad (\textcolor{red}{discouraged: maintained for backwards compatibility})
-\end{sintassi}
+\end{Sintassi}
%%
\item General curves can be drawn with the \pack{pict2e} macro
|\curve| but it requires the specification of the third-order
@@ -925,11 +938,11 @@
but the driver between this code and the physical representation on
paper or screen) assumes a straight line closure of the whole path.
The syntax offers several variants but it is substantially the following:
- \begin{sintassi}
+ \begin{Sintassi}
|\Curve|\parg{node}\aarg{direction}\dots\parg{node}\aarg{direction}
|\Curve*|\parg{node}\aarg{direction}\dots\parg{node}\aarg{direction}
\qquad\qquad\dots\aarg{direction}\oarg{new direction}\parg{node}\dots
- \end{sintassi}
+ \end{Sintassi}
See some more explanation below.
\item \cs{Qurve} is similar to |\Curve|, but with second order
@@ -1039,68 +1052,74 @@
construction contains many of the commands described so far.
\begin{figure}[p]
-\begin{minipage}{\linewidth}\small
-\begin{verbatim}
-\unitlength=0.007\textwidth
-\begin{picture}(100,90)(-50,-50)
-\put(-50,0){\vector(1,0){100}}\put(50,1){\makebox(0,0)[br]{$x$}}%
-\put(20,-1){\makebox(0,0)[t]{$s$}}%
-\put(0,0){\circle*{2}}\put(-1,-1){\makebox(0,0)[tr]{$M$}}%
-\legenda(12,-45){s=\overline{MP_2}=R\sin\theta}%
-\put(0,-50){\vector(0,1){90}}%
-\put(1,40){\makebox(0,0)[tl]{$y$}}%
-\put(0,-40){\circle*{2}}\put(1,-41){\makebox(0,0)[lt]{$C$}}%
-\segment(0,-40)(-40,0)\segment(0,-40)(40,0)%
-\put(-41,1){\makebox(0,0)[br]{$P_1$}}\put(-40,0){\circle*{2}}%
-\put(41,1){\makebox(0,0)[bl]{$P_2$}}\put(40,0){\circle*{2}}%
-\put(0,0){\linethickness{1pt}\Arc(0,-40)(40,0){90}}%
-\segment(-40,0)(-20,20)\put(-20,20){\circle*{2}}%
-\put(-20,21.5){\makebox(0,0)[b]{$C_1$}}%
-\segment(40,0)(20,20)\put(20,20){\circle*{2}}%
-\put(20,21.5){\makebox(0,0)[b]{$C_2$}}%
-\put(0,-40){\put(0,56.5685){\circle*{2}}%
-\put(1,58){\makebox(0,0)[bl]{$P$}}}%
-\VectorARC(0,-40)(15,-25){45}\put(10,-18){\makebox(0,0)[c]{$\theta$}}%
-\VectorARC(40,0)(20,0){-45}\put(19,5){\makebox(0,0)[r]{$\theta$}}%
-\VectorARC(-40,0)(-20,0){45}\put(-19,5){\makebox(0,0)[l]{$\theta$}}%
-\put(-20,-18){\makebox(0,0)[bl]{$R$}}%
-\put(-32,13){\makebox(0,0)[bl]{$K$}}%
-\put(32,13){\makebox(0,0)[br]{$K$}}%
-\end{picture}
-\end{verbatim}
-\end{minipage}\vspace{\stretch{1}}
-
-\begin{minipage}{\linewidth}\centering
-\unitlength=0.007\textwidth
-\begin{picture}(100,90)(-50,-50)
-\put(-50,0){\vector(1,0){100}}\put(50,1){\makebox(0,0)[br]{$x$}}%
-\put(20,-1){\makebox(0,0)[t]{$s$}}%
-\put(0,0){\circle*{2}}\put(-1,-1){\makebox(0,0)[tr]{$M$}}%
-\legenda(12,-45){s=\overline{MP_2}=R\sin\theta}%
-\put(0,-50){\vector(0,1){90}}%
-\put(1,40){\makebox(0,0)[tl]{$y$}}%
-\put(0,-40){\circle*{2}}\put(1,-41){\makebox(0,0)[lt]{$C$}}%
-\segment(0,-40)(-40,0)\segment(0,-40)(40,0)%
-\put(-41,1){\makebox(0,0)[br]{$P_1$}}\put(-40,0){\circle*{2}}%
-\put(41,1){\makebox(0,0)[bl]{$P_2$}}\put(40,0){\circle*{2}}%
-\put(0,0){\linethickness{1pt}\Arc(0,-40)(40,0){90}}%
-\segment(-40,0)(-20,20)\put(-20,20){\circle*{2}}%
-\put(-20,21.5){\makebox(0,0)[b]{$C_1$}}%
-\segment(40,0)(20,20)\put(20,20){\circle*{2}}%
-\put(20,21.5){\makebox(0,0)[b]{$C_2$}}%
-\put(0,-40){\put(0,56.5685){\circle*{2}}%
-\put(1,58){\makebox(0,0)[bl]{$P$}}}%
-\VectorARC(0,-40)(15,-25){45}\put(10,-18){\makebox(0,0)[c]{$\theta$}}%
-\VectorARC(40,0)(20,0){-45}\put(19,5){\makebox(0,0)[r]{$\theta$}}%
-\VectorARC(-40,0)(-20,0){45}\put(-19,5){\makebox(0,0)[l]{$\theta$}}%
-\put(-20,-18){\makebox(0,0)[bl]{$R$}}%
-\put(-32,13){\makebox(0,0)[bl]{$K$}}%
-\put(32,13){\makebox(0,0)[br]{$K$}}%
-\end{picture}
-\end{minipage}
-\caption{The code to display the nodes and control points for an arc to
- be approximated with a cubic Bézier spline}
-\label{fig:arcspline}
+ \begin{minipage}{\linewidth}\small
+ \begin{verbatim}
+ \unitlength=0.007\textwidth
+ \begin{picture}(100,90)(-50,-50)
+ \put(-50,0){\vector(1,0){100}}\put(50,1){\makebox(0,0)[br]{$x$}}%
+ \put(20,-1){\makebox(0,0)[t]{$s$}}%
+ \put(0,0){\circle*{2}}\put(-1,-1){\makebox(0,0)[tr]{$M$}}%
+ \legenda(12,-45){s=\overline{MP_2}=R\sin\theta}%
+ \put(0,-50){\vector(0,1){90}}%
+ \put(1,40){\makebox(0,0)[tl]{$y$}}%
+ \put(0,-40){\circle*{2}}\put(1,-41){\makebox(0,0)[lt]{$C$}}%
+ \segment(0,-40)(-40,0)\segment(0,-40)(40,0)%
+ \put(-41,1){\makebox(0,0)[br]{$P_1$}}\put(-40,0){\circle*{2}}%
+ \put(41,1){\makebox(0,0)[bl]{$P_2$}}\put(40,0){\circle*{2}}%
+ \put(0,0){\linethickness{1pt}\Arc(0,-40)(40,0){90}}%
+ \segment(-40,0)(-20,20)\put(-20,20){\circle*{2}}%
+ \put(-20,21.5){\makebox(0,0)[b]{$C_1$}}%
+ \segment(40,0)(20,20)\put(20,20){\circle*{2}}%
+ \put(20,21.5){\makebox(0,0)[b]{$C_2$}}%
+ \put(0,-40){\put(0,56.5685){\circle*{2}}%
+ \put(1,58){\makebox(0,0)[bl]{$P$}}}%
+ \VectorARC(0,-40)(15,-25){45}\put(10,-18){\makebox(0,0)[c]{$\theta$}}%
+ \VectorARC(40,0)(20,0){-45}\put(19,5){\makebox(0,0)[r]{$\theta$}}%
+ \VectorARC(-40,0)(-20,0){45}\put(-19,5){\makebox(0,0)[l]{$\theta$}}%
+ \put(-20,-18){\makebox(0,0)[bl]{$R$}}%
+ \put(-32,13){\makebox(0,0)[bl]{$K$}}%
+ \put(32,13){\makebox(0,0)[br]{$K$}}%
+ \end{picture}
+ \end{verbatim}
+ \end{minipage}
+\par
+\vspace*{\stretch{1}}
+\par
+ \begin{minipage}{\linewidth}\centering
+% \unitlength=0.007\textwidth
+% \begin{picture}(100,90)(-50,-50)
+% \put(-50,0){\vector(1,0){100}}\put(50,1){\makebox(0,0)[br]{$x$}}%
+% \put(20,-1){\makebox(0,0)[t]{$s$}}%
+% \put(0,0){\circle*{2}}\put(-1,-1){\makebox(0,0)[tr]{$M$}}%
+% \legenda(12,-45){s=\overline{MP_2}=R\sin\theta}%
+% \put(0,-50){\vector(0,1){90}}%
+% \put(1,40){\makebox(0,0)[tl]{$y$}}%
+% \put(0,-40){\circle*{2}}\put(1,-41){\makebox(0,0)[lt]{$C$}}%
+% \segment(0,-40)(-40,0)\segment(0,-40)(40,0)%
+% \put(-41,1){\makebox(0,0)[br]{$P_1$}}\put(-40,0){\circle*{2}}%
+% \put(41,1){\makebox(0,0)[bl]{$P_2$}}\put(40,0){\circle*{2}}%
+% \put(0,0){\linethickness{1pt}\Arc(0,-40)(40,0){90}}%
+% \segment(-40,0)(-20,20)\put(-20,20){\circle*{2}}%
+% \put(-20,21.5){\makebox(0,0)[b]{$C_1$}}%
+% \segment(40,0)(20,20)\put(20,20){\circle*{2}}%
+% \put(20,21.5){\makebox(0,0)[b]{$C_2$}}%
+% \put(0,-40){\put(0,56.5685){\circle*{2}}%
+% \put(1,58){\makebox(0,0)[bl]{$P$}}}%
+% \VectorARC(0,-40)(15,-25){45}
+% \put(10,-18){\makebox(0,0)[c]{$\theta$}}%
+% \VectorARC(40,0)(20,0){-45}
+% \put(19,5){\makebox(0,0)[r]{$\theta$}}%
+% \VectorARC(-40,0)(-20,0){45}
+% \put(-19,5){\makebox(0,0)[l]{$\theta$}}%
+% \put(-20,-18){\makebox(0,0)[bl]{$R$}}%
+% \put(-32,13){\makebox(0,0)[bl]{$K$}}%
+% \put(32,13){\makebox(0,0)[br]{$K$}}%
+% \end{picture}
+ \end{minipage}
+ \caption{The code to display the nodes and
+ control points for an arc to be approximated
+ with a cubic Bézier spline}
+ \label{fig:arcspline}
\end{figure}
@@ -1148,15 +1167,16 @@
\caption{Curves between two points with different start and end slopes}\label{fig:curva-due-punti}
\end{figure}
- A little more complicated is the use of the |\CBezierBetween| macro,
- figure~\ref{fig:Cbezier}. The directions are specified with unit
- vectors in polar form; the control points are specified by adding their
- distances from their neighbouring nodes; actually the right distance
- is maintained to the value~1, while the left one increases from~4
- to~10.
- The black line corresponds to the standard |\CurveBetween| where the
- default distance is computed to trace an arc of a circle and
- is approximately~3.5.
+ A little more complicated is the use of the
+ |\CBezierBetween| macro, figure~\ref{fig:Cbezier}. The
+ directions are specified with unit vectors in polar form;
+ the control points are specified by adding their distances
+ from their neighbouring nodes; actually the right distance
+ is maintained to the value~1, while the left one increases
+ from~4 to~10.
+ The black line corresponds to the standard |\CurveBetween|
+ where the default distance is computed to trace an arc of a
+ circle and is approximately~3.5.
\begin{figure}[!tb]
\begin{minipage}[t]{0.52\textwidth}\small
@@ -1191,22 +1211,24 @@
\label{fig:Cbezier}
\end{figure}
- In figure~\ref{fig:tensions} the effect of tension specification is
- shown. The red line corresponds to the default tension, since the
- tension values are not specified. The black lines correspond to the
- various values used in the various commands to the |\Curve| macro.
- With a tension of zero, the spline is almost coincident with the
- horizontal base line of the frame. Increasing the parameter value
- to~4.5, the curved becomes taller and taller, until it wraps itself
- displaying an evident loop. We would say that the value of ~2 is a
- reasonable maximum one and that increasing that value is just to
- obtain special effects.
+ In figure~\ref{fig:tensions} the effect of tension
+ specification is shown. The red line corresponds to the
+ default tension, since the tension values are not specified.
+ The black lines correspond to the various values used in the
+ various commands to the |\Curve| macro.
+ With a tension of zero, the spline is almost coincident
+ with the horizontal base line of the frame. Increasing the
+ parameter value to~4.5, the curved becomes taller and
+ taller, until it wraps itself displaying an evident loop.
+ We would say that the value of ~2 is a reasonable maximum
+ one and that increasing that value is just to obtain special
+ effects.
\begin{figure}[!htb]\centering
\begin{Esempio}[\setfontsize{8.5}]%
\unitlength=0.01\textwidth
\begin{picture}(70,70)
-\put(0,0){\color{blue}\framebox(70,70){}}
+\put(0,0){\color{black}\framebox(70,70){}}
\put(0,0){\color{red}%
\Curve(0,0)<1,1>(70,0)<1,-1>}
\Curve(0,0)<1,1>(70,0)<1,-1;0,0>
@@ -1220,17 +1242,19 @@
\caption{The effects of tension factors}\label{fig:tensions}
\end{figure}
- Figure~\ref{fig:sinewave} displays two approximations of a sine wave;
- Bézier splines can approximate transcendental curves, but the
- approximation may be a poor one, depending on the approximated curve,
- when few arcs are used to draw it. With arcs specified with more
- complicated macros the approximation is better even with a lower number
- of arcs. With many arcs it is possible to approximate almost anything.
- On the left side of figure~\ref{fig:sinewave} a modest approximation is
- obtained with just three standard arcs obtained with |\Curve| and four
- node specifications; on the right we have just two arcs created with
- |\CBezierBetween| with tension specification and control point
- distances; this drawing is almost undistinguishable from a real
+ Figure~\ref{fig:sinewave} displays two approximations of
+ a sine wave; Bézier splines can approximate transcendental
+ curves, but the approximation may be a poor one, depending
+ on the approximated curve, when few arcs are used to draw
+ it. With arcs specified with more complicated macros the
+ approximation is better even with a lower number of arcs.
+ With many arcs it is possible to approximate almost nything.
+ On the left side of figure~\ref{fig:sinewave} a modest
+ approximation is obtained with just three standard arcs
+ obtained with |\Curve| and four node specifications; on the
+ right we have just two arcs created with |\CBezierBetween|
+ with tension specification and control point distances;
+ this drawing is almost undistinguishable from a real
sinusoid.
\begin{figure}[!htb]
@@ -1273,17 +1297,19 @@
\label{fig:sinewave}
\end{figure}
- In figure~\ref{fig:quadratic-arcs} some lines are shown; they are
- drawn with quadratic splines by means of the |\Qurve| macro. In the
- left there are some open and closed curves inscribed within a square.
- On the right a “real" circle is compared to a quadratic spline circle;
- the word “real” is emphasised because it actually is an approximation
- with four quarter-circle cubic splines that, in spite of being drawn
- with third degree parametric polynomials, approximate very well a real
- circle; on the opposite the quadratic spline circle is clearly a poor
- approximation even if the maximum radial error amounts just to about
- 6\% of the radius.
-
+ In figure~\ref{fig:quadratic-arcs} some lines are shown;
+ they are drawn with quadratic splines by means of the
+ |\Qurve| macro. In the left there are some open and closed
+ curves inscribed within a square.
+ On the right a “real" circle is compared to a quadratic
+ spline circle; the word “real” is emphasised because it
+ actually is an approximation with four quarter-circle cubic
+ splines that, in spite of being drawn with third degree
+ parametric polynomials, approximate very well a real circle;
+ on the opposite the quadratic spline circle is clearly a
+ poor approximation even if the maximum radial error amounts
+ just to about 6\% of the radius.
+
\begin{figure}[!htb]
\begin{minipage}{\linewidth}
\begin{Verbatim}[fontsize=\setfontsize{7.75}]
@@ -1331,31 +1357,66 @@
\put(0,0){\framebox(100,100){}}
\put(50,50){\Qurve(0,-50)<1,0>(50,0)<0,1>(0,50)<-1,0>(-50,0)<0,-1>(0,-50)<1,0>
\Curve(0,-50)<1,0>(50,0)<0,1>(0,50)<-1,0>(-50,0)<0,-1>(0,-50)<1,0>}
-\Zbox(50,50)[t]{O}\Pall[2](50,50)\put(50,50){\Vector(45:50)}\Zbox(67,70)[tl]{R}
+\Zbox(50,50)[t]{O}\Pall[2](50,50)\put(50,50){\Vector(45:50)}\Zbox(67,70)[tl]{R}[0]
\end{picture}
\end{minipage}
-\caption{\rule{0pt}{4ex}Several graphs drawn with quadratic Bézier
- splines. On the right a quadratic spline circle is compared with a
- cubic line circle.}
+\caption{\rule{0pt}{4ex}Several graphs drawn with quadratic
+ Bézier splines. On the right a quadratic spline circle is
+ compared with a cubic line circle.}
\label{fig:quadratic-arcs}
\end{figure}
- Notice that the previous version of \pack{curve2e} contained an error
- and would color the outside of the green four-pointed star.
- The |curve2e-v161| package, attached to this bundle, has been corrected;
- therefore it is not actually identical to the previous version,
- although the latter one performed correctly for everything else except
- for color filled quadratic paths.
- %%
- \item The new version of |\multiput| is backwards compatibile with
+ Notice that the previous version of \pack{curve2e} contained
+ an error and would color the outside of the green four-pointed
+ star. The |curve2e-v161| package, attached to this bundle, has
+ been corrected; therefore it is not actually identical to the
+ previous version, although the latter one performed correctly
+ for everything else except for color filled quadratic paths.
+
+The “real” circle, even if rendered with quarter circles, is visually very similar to a true circumference, but any Bézier circle arc that approximates a circumference arc of the same amplitude, displays a small error at an angle of 1/4 and 3/4 the total arc amplitude; this error diminishes as the total arc amplitude diminishes, nevertheless the error is there. If the arc amplitude amounts to 180°, the maximum error is at 45° and at 135° angular distances from the staring point. It amounts to 2\% of the arc radius; see figure~\ref{fig:halfcircle}, where a half circle is compared with a sequence of four arcs of 45° each, drawn by means of the \cs{Curve} macro; the code is the following:
+\begin{verbatim}
+\unitlength=0.005\linewidth
+\begin{picture}(100,50)(-50,0)
+ \AutoGrid
+ \Zbox(0,0)[t]{\textsf{O}}[1]
+ \Arc(0,0)(50,0){180}
+ \VECTOR(0,0)(45:50)\Zbox(45:25)[br]{R}[0]
+ \Curve(50,0)<0,1>(45:50)<135:1>(0,50)<-1,0>%
+ (135:50)<225:1>(-50,0)<0,-1>
+% \Arc(0,0)(50,0){90}\Arc(0,0)(0,50){90}
+% \Curve(50,0)<0,1>(0,50)<-1,0>(-50,0)<0,-1>
+\end{picture}
+\end{verbatim}
+
+\begin{figure}\centering
+ \unitlength=0.005\linewidth
+ \begin{picture}(100,50)(-50,0)
+ \AutoGrid
+ \Zbox(0,0)[t]{\textsf{O}}[1]
+ \Arc(0,0)(50,0){180}
+ \VECTOR(0,0)(45:50)\Zbox(45:25)[br]{R}[0]
+ \Curve(50,0)<0,1>(45:50)<135:1>(0,50)<-1,0>%
+ (135:50)<225:1>(-50,0)<0,-1>
+% \Arc(0,0)(50,0){90}\Arc(0,0)(0,50){90}
+% \Curve(50,0)<0,1>(0,50)<-1,0>(-50,0)<0,-1>
+ \end{picture}
+\caption{Comparison between a 180° arc (red) drawn with the \cs{Arc} macro, and a comparable half circle (blaxk) drawn with four 45° \cs{Curve} arcs}\label{fig:halfcircle}
+\end{figure}
+
+The circle radius amounts to $R=50$\cs{unitlength}, while the external line, drawn with \cs{Arc}, at 45° displays the maximum distance from the circle center \textsf{O}; it amounts to $51$\cs{unitlength}, 2\% larger than the correct value. In most circumstances this error is negligible, but sometimes the drawing by means of \cs{Curve} is more appropriate.
+
+An alternative solution consists in tracing two consecutive arcs of 90° each drawn with \cs{Arc}, instead of four arcs of 45° each drawn with \cs{Curve} or with \cs{Arc}. The code above contains also the other solutions; they are commented out but the user can copy the code and paste it in a personal \texttt{.tex} file, so that each solution can be tested individually, so as to remark the (invisible) differences.
+
+%
+\item The new version of |\multiput| is backwards compatibile with
the original version contained in the \LaTeX\ kernel. The new macro
adds the handling of the coordinate increments from one position to
the next for the \meta{object} to include in the drawing.
The syntax is the following:
- \begin{sintassi}\setfontsize{8.5}
+ \begin{Sintassi}\setfontsize{8}
|\multiput|\parg{initial point}\parg{increment}\marg{number of items}\marg{object}\oarg{handler}
- \end{sintassi}
+ \end{Sintassi}
The only small change is the addition of the last optional argument that allows to do several interesting actions on the sequence o objects to be repeated, for example, to set them on a curved line, instead of on a straight line, as shown in figure~\ref{pag:multiput}.
In this figure we show the code for the picture shown there. The red grid
@@ -1433,9 +1494,9 @@
Th |\xmultiput| syntax is the is similar to that of |\multiput| but besides the stepping up or down of the iteration counter, it can access and modify certain internal with the commands that appear in the \meta{handler} argument. Actually this \meta{handler} is available also with |\multiput|. In both cases the handler can be defined to modify some internals, including the iteration counter only for |\xmultipot|, but also the |\R| and |\D| internals; |\R| contains the coordinates where to put the \meta{object}, while |\D|, if set, contains the angle of rotation of the object. The code and picture examples in figures~\ref{pag:multiput} and~\ref{pag:orologio} show some examples of usage through tis \meta{handler} code.
.
-\begin{sintassi}\small
+\begin{Sintassi}\small
|\xmultiput|\parg{initial point}\parg{increment}\marg{iterations}\marg{object}\oarg{handler}
-\end{sintassi}
+\end{Sintassi}
\begin{figure}[!htb]
@@ -1463,7 +1524,7 @@
\GraphGrid(100,100)
\put(50,50){\thicklines\circle{100}}
\xmultiput[50,50](60:40)(-30:1){12}%
- {\makebox(0,0){\circle*{2}}}[\MultVect\R by\D to\R]%
+ {\makebox(0,0){\circle*{2}}}[\Multvect{\R}{\D}{\R}]%
\xmultiput[50,50](60:43)(-30:1){12}%
{\ArgOfVect\R to\Ang\rotatebox{\fpeval{\Ang-90}}%
{\makebox(0,0)[b]{\Roman{multicnt}}}}%
@@ -1479,11 +1540,11 @@
|\fptest|, |\fpdowhile|, |\fpwhiledo| to the two already contained and
documented in the latter package. The syntax of such new commands
is the following
- \begin{sintassi}\obeylines
+ \begin{Sintassi}
\cs{fptest}\marg{test}\marg{true}\marg{false}
\cs{fpdowhile}\marg{test}\marg{operations to be repeated}
\cs{fpwhiledo}\marg{test}\marg{operations to be repeated}
- \end{sintassi}
+ \end{Sintassi}
The macro |\fptest| requires two further arguments that contain
what to do if the \meta{test} is true, and what to do if the
\meta{test} is false.
@@ -1573,9 +1634,9 @@
\end{verbatim}
The syntax is the following:
-\begin{sintassi}\obeylines
+\begin{Sintassi}
\cs{Lissajous}\marg{in}\Oarg{\meta{$A_1$},\meta{$N_1$},\meta{$\phi_1$},\meta{$A_2$},\meta{$N_2$},\meta{$\phi_2$}}\meta{$P_{\mathrm{out}}$}
-\end{sintassi}
+\end{Sintassi}
where \meta{$P_{\mathrm{out}}$} is a macro that gets
defined with the cartesian coordinates of the computed output
point. Arguments \meta{in} (the $t$ parameter) and \meta{$P_\mathrm{out}$} (the comput coordinates) need not be enclosed within braces if they are given as macros; actually the code shown in figure~\ref{fig:lissajous} shows such procedure that renders the input code simpler to read.
@@ -1617,9 +1678,9 @@
diagram.
%
\item Another useful application of |\fpdowhile| is the following: when making a diagram the axes should get suitable labeled ticks in order to show the graduations; the label of each tick should lay close to the axis on the other side than the tick. It is also necessary to know if the axis to be marked is horizontal or vertical, since in the former case each tick is vertical, while in the latter case it is horizontal. The example in figure~\ref{fig:ticks} shows both the code and its usage. The syntax of the |\Tbox| macro is the following.
-\begin{sintassi}
+\begin{Sintassi}
|\Tbox|\parg{coordinates}\oarg{reference}\marg{label}\oarg{size}\aarg{direction}
-\end{sintassi}
+\end{Sintassi}
where \meta{coordinates} indicates the position of the tick base along its axis; \meta{reference} is a letter, either |t| (if the axis is on top of the label) or |b|(if the axis is at the bottom of the label) for vertical ticks or either |r| (if the axis is at the right of the label) or |l| (if the axis is at the left of the label) for horizontal ticks; \meta{label} is the value of the scale or a literal label that by default is typeset in math mode, so that a math symbol may be used without the need of entering math mode, while in the unusual circumstance that a textual label is to be used, users should use the |\text| macro; the \meta{size} argument is the size of the tick: if such size is zero, just the label is set, but in this case the |\Tbox| macro behaves as the the |\Zbox| one, and accepts two reference codes in order to print the label the same as |\Zbox| would do when the dot size is zero; the \meta{direction} argument is the letter |V| for vertical ticks, and |H| for horizontal ticks. There is some redundancy because |\Tbox| may behave as |\Zbox|, but experience shows that this is not a problem.
The source preamble should contain the following code.
@@ -1650,11 +1711,12 @@
}\egroup\ignorespaces}%
\end{verbatim}
}
-If the code is contained in a personal |.sty| file the |\makeatletter| should be omitted.
+If the code is contained in a personal |.sty| file the
+|\makeatletter| should be omitted.
As it can be seen, the fifth argument code is preset to to |Z| so that if users forget to specify it, error messages pop op and can be seen in both the console window and in the log file, but no tick and label are typeset. This kind of commands to label in one way or another may be very useful depending on the users' kind of drawings. Figure~\ref{fig:labeled diagram} contains also the iterations to label the axes and are done with the
-|\fpdowhile| macro; it can be seen that the actual coordinate of each tick is transformed into the actual label that si put in its position by the
-|\Zbox| command' of course the diagram scale and the actual label are related to one another but do not have the same value.
+|\fpdowhile| macro; it can be seen that the actual coordinate of each tick is transformed into the actual label that is put in its position by the
+|\Zbox| command; of course the diagram scale and the actual label are related to one another but do not have the same value.
\begin{figure}
{\small\begin{verbatim}
@@ -1675,9 +1737,9 @@
}%
%
{\color{blue}\linethickness{1.5pt}%
-\Curve(-40,0)<1,0>(0,20)<45:1>% Parabola: y=0.25(x_2)^2
-\Curve(0,20)<1,0>(20,0)<0,-1>% Quarter circle: x^2+y^2=1
-\Curve(20,0)<0,1>(40,34.64)<49:1>}% Hyperbola:x^2-y^=1
+\Curve(-40,0)<1,0>(0,20)<45:1>% Parabola: y=0.25(x_2)^2
+\Curve(0,20)<1,0>(20,0)<0,-1>% Quarter circle: x^2+y^2=1
+\Curve(20,0)<0,1>(40,34.64)<49:1>}% Hyperbola:x^2-y^=1
\thinlines
\Dashline(0,0)(45,45){2}% asymptote
\end{picture}
@@ -1700,9 +1762,9 @@
\fpdowhile{\Coord<=50}{\edef\Y{\fpeval{round(\Coord/20,1)}}%
\Tbox(0,\Coord)[r]{\Y}[1ex]<H>\edef\Coord{\fpeval{\Coord+10}}}%
}%
-{\color{blue}\linethickness{1.5pt}%
-\Curve(-40,0)<1,0>(0,20)<45:1>% Parabola: y=0.25(x_2)^2
-\Curve(0,20)<1,0>(20,0)<0,-1>% Quarter circle: x^2+y^2=1
+{\color{red}\linethickness{1.5pt}%
+\Curve(-40,0)<1,0>(0,20)<45:1>% Parabola: y=0.25(x_2)^2
+\Curve(0,20)<1,0>(20,0)<0,-1>% Quarter circle: x^2+y^2=1
\Curve(20,0)<0,1>(40,34.64)<49:1>}% Hyperbola:x^2-y^2=1
\thinlines
\Dashline(0,0)(45,45){2}% asymptote
@@ -1786,35 +1848,33 @@
\section{Acknowledgements}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- I wish to express my deepest thanks to Michel Goosens who spotted some
- errors and very kindly submitted them to me so that I was able to
- correct them.
+I wish to express my deepest thanks to the many persons who submitted notices about bugs or inconsistencies.
+
+ Michel Goosens spotted some errors and very kindly submitted
+ them to me so that I was able to correct them.
I collaborated extensively with Josef Tkadlec in order to
- implement a better real long division so as to get correctly the
- quotient fractional part and to avoid as much as possible any numeric
- overflow; many Josef's ideas are incorporated in the macro that was
- implemented in the previous version of this package, although the
- macro used by Josef was slightly different. Both versions aim/aimed
- at a better accuracy and at widening the operand ranges. In this
- version of \pack{curve2e} I abandoned our long division macro, and
- substituted it with the floating point division provided by the |xfp|
- package functionalities that are now part of the \LaTeX\ kernel.
+ implement a better real long division so as to get correctly
+ the quotient fractional part and to avoid as much as
+ possible any numeric overflow; many Josef's ideas were
+ incorporated in the long division macro that was implemented
+ in the previous version of this package, although the macro
+ used by Josef was slightly different. Both versions
+ aim/aimed at a better accuracy and at widening the operand
+ ranges.
+ In this version of \pack{curve2e} I abandoned our long
+ division macro, and substituted it with the floating point
+ division provided by the |xfp| package functionalities that
+ are now part of the \LaTeX\ kernel.
-Daniele Degiorgi spotted a fault in the kernel definition of
-|\linethickness| that heavily influenced also \pack{curve2e}; see in
-the code documentation \file{curve2e.pdf} file.
+Daniele Degiorgi spotted a fault in the kernel definition of
+|\linethickness| that heavily influenced also \pack{curve2e}; see the code documentation \file{curve2e.pdf} file.
-Many thanks to Domenicus van der Wijst who spotted a sneaky bug in the updated |\Arc| macro; for arcs not wider that $180^\circ$ it worked properly, while for larger angle apertures it produced syntax errors. It was just a typo, but very sneaky.
+Domenicus van der Wijst spotted a sneaky bug in the updated |\Arc| macro; for arcs not wider than $180^\circ$ that macro worked properly, while for larger angle apertures it produced syntax errors. It was just a typo, but very sneaky.
-Thanks also to Jin-Hwan Cho and Juho Lee who suggested a small but
- crucial modification in order to have \pack{curve2e} work smoothly
- also with XeTeX (XeLaTeX). Actually if \pack{pict2e}, version 0.2x or
- later, dated 2009/08/05 or later, is being used, such modification is
- not necessary any more, but it is true that it becomes imperative when
- legacy versions were used.
+Jin-Hwan Cho and Juho Lee suggested a small but crucial modification in order to have \pack{curve2e} work smoothly also with XeTeX (XeLaTeX). Actually if \pack{pict2e}, version 0.2x or later, dated 2009/08/05 or later, is being used, such modification is not necessary any more, but it is true that it was imperative when legacy versions were used.
-Many thanks also to Ashish Kumar Das who spotted an inconsistency in the design of vectors with PostScript style arrow tips with large line width settings, that did not show up with \LaTeX\ styled ones.
+Ashish Kumar Das spotted an inconsistency in the design of vectors with PostScript style arrow tips with large line width settings, that did not show up with \LaTeX\ styled ones.
\end{document}
Modified: trunk/Master/texmf-dist/doc/latex/curve2e/curve2e.pdf
===================================================================
(Binary files differ)
Modified: trunk/Master/texmf-dist/source/latex/curve2e/curve2e.dtx
===================================================================
--- trunk/Master/texmf-dist/source/latex/curve2e/curve2e.dtx 2024-11-13 21:11:32 UTC (rev 72841)
+++ trunk/Master/texmf-dist/source/latex/curve2e/curve2e.dtx 2024-11-13 21:11:45 UTC (rev 72842)
@@ -6,7 +6,8 @@
\keepsilent
\preamble
- Copyright (C) 2005--2023 Claudio Beccari all rights reserved.
+ Copyright (C) 2005--2024 Claudio Beccari all
+ rights reserved.
License information appended
\endpreamble
@@ -13,21 +14,23 @@
\postamble
-Distributable under the LaTeX Project Public License,
-version 1.3c or higher (your choice). The latest version of
-this license is at: http://www.latex-project.org/lppl.txt
+Distributable under the LaTeX Project Public
+License, version 1.3c or higher (your choice).
+The latest version of this license is at:
+http://www.latex-project.org/lppl.txt
This work is "maintained"
-This work consists of file curve2e.dtx, and the derived files
-curve2e.sty and curve2e.pdf, plus the auxiliary derived files
-README.txt and curve2e-v161.sty.
+This work consists of file curve2e.dtx, and the
+derived files curve2e.sty and curve2e.pdf, plus
+the auxiliary derived files README.txt and
+curve2e-v161.sty.
\endpostamble
\askforoverwritefalse
\generate{\file{curve2e.sty}{\from{curve2e.dtx}{package}}}
-%\generate{\file{README.txt}{\from{curve2e.dtx}{readme}}}
+\generate{\file{README.txt}{\from{curve2e.dtx}{readme}}}
\generate{\file{curve2e-v161.sty}{\from{curve2e.dtx}{v161}}}
\def\tmpa{plain}
@@ -46,15 +49,15 @@
%<+package>\ProvidesPackage{curve2e}%
%<+readme>File README.txt for package curve2e
%<*package|readme>
- [2023-07-04 v.2.3.1 Extension package for pict2e]
+[2024-11-13 v.2.6.0 Extension package for pict2e]
%</package|readme>
%<*driver>
-\documentclass{ltxdoc}\errorcontextlines=9
+\documentclass{ltxdoc}\errorcontextlines=100
\hfuzz 10pt
\usepackage[utf8]{inputenc}
\usepackage{lmodern,textcomp}
\usepackage{mflogo}
-\usepackage{multicol,amsmath,fancyvrb,graphicx,verbatim,trace}
+\usepackage{multicol, amsmath, fancyvrb, graphicx, verbatim, FramedSyntax, trace}
\usepackage{xcolor,curve2e}
\GetFileInfo{curve2e.dtx}
\title{The extension package \textsf{curve2e}}
@@ -149,6 +152,7 @@
\par%\addvspace{3.0ex plus 0.8ex minus 0.5ex}\vskip -\parskip
}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}\errorcontextlines=100
\maketitle
@@ -160,25 +164,29 @@
\end{document}
%</driver>
% \fi
-%
-% \CheckSum{5678}
+% \CheckSum{5663}
% \begin{abstract}
-% This file documents the |curve2e| extension package to the |pict2e|
-% bundle implementation; the latter was described by Lamport
-% himself in the 1994 second edition of his \LaTeX\ handbook.
+% This file documents the |curve2e| extension package to the
+% |pict2e| bundle implementation; the latter was described by
+% Lamport himself in the 1994 second edition of his \LaTeX\
+% handbook.
%
-% Please take notice that on April 2011 a new updated version of the
-% package |pict2e| has been released that incorporates some of the
-% commands defined in early versions of this package; apparently there
-% are no conflicts, but only the advanced features of |curve2e| remain
-% available for extending the above improved package.
+% Please take notice that on April 2011 a new
+% updated version of the package |pict2e| has been
+% released that incorporates some of the commands
+% defined in early versions of this package;
+% apparently there are no conflicts, but only the
+% advanced features of |curve2e| remain available
+% for extending the above improved package.
%
-% This extension redefines some commands and introduces some more
-% drawing facilities that allow to draw circular arcs and arbitrary
-% curves with the minimum of user intervention. This version is open to
-% the contribution of other users as well as it may be incorporated in
-% other people's packages. Please cite the original author and the chain
-% of contributors.
+% This extension redefines some commands and
+% introduces some more drawing facilities that
+% allow to draw circular arcs and arbitrary curves
+% with the minimum of user intervention. This
+% version is open to the contribution of other
+% users as well as it may be incorporated in other
+% people's packages. Please cite the original
+% author and the chain of contributors.
% \end{abstract}
%
%
@@ -186,322 +194,384 @@
% \section{Introduction}
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
-% Package \texttt{pict2e} was announced in issue 15 of \texttt{latexnews}
-% around December 2003; it was specified that the new package would
-% replace the dummy one that was been accompanying every release of
-% \LaTeXe\ since its beginnings in 1994. The dummy package was just
-% issuing an info message that simply announced the temporary
+% Package \texttt{pict2e} was announced in issue 15 of
+% \texttt{latexnews} around December 2003; it was specified
+% that the new package would replace the dummy one that was
+% been accompanying every release of \LaTeXe\ since its
+% beginnings in 1994. The dummy package was just issuing an
+% info message that simply announced the temporary
% unavailability of the real package.
%
-% Eventually Gäßlein and Niepraschk implemented what Lamport himself had
-% already documented in the second edition of his \LaTeX\ handbook, that
-% is a \LaTeX\ package that contained the macros capable of removing all
-% the limitations contained in the standard commands of the original
-% \texttt{picture} environment; specifically what follows.
+% Eventually Gäßlein and Niepraschk implemented what Lamport
+% himself had already documented in the second edition of his
+% \LaTeX\ handbook, that is a \LaTeX\ package that contained
+% the macros capable of removing all the limitations contained
+% in the standard commands of the original \texttt{picture}
+% environment; specifically what follows.
% \begin{enumerate}
-% \item The line and vector slopes were limited to the ratios of relative
-% prime one-digit integers of magnitude not exceeding 6 for lines and 4
-% for vectors.
+% \item
+% The line and vector slopes were limited to the ratios of
+% relative prime one-digit integers of magnitude not exceeding 6
+% for lines and 4 for vectors.
%^^A
-% \item Filled and unfilled full circles were limited by the necessarily
-% limited number of specific glyphs contained in the special \LaTeX\
-% \texttt{picture} fonts.
+% \item
+% Filled and unfilled full circles were limited by the
+% necessarily limited number of specific glyphs contained in the
+% special \LaTeX\ \texttt{picture} fonts.
%^^A
-% \item Quarter circles were also limited in their radii for the same
+% \item
+% Quarter circles were also limited in their radii for the same
% reason.
%^^A
-% \item Ovals (rectangles with rounded corners) could not be too small
-% because of the unavailability of small radius quarter circles, nor
-% could be too large, in the sense that after a certain radius the
-% rounded corners remained the same and would not increase proportionally
-% to the oval size.
+% \item
+% Ovals (rectangles with rounded corners) could not be too
+% small because of the unavailability of small radius quarter
+% circles, nor could be too large, in the sense that after a
+% certain radius the rounded corners remained the same and
+% would not increase proportionally to the oval size.
%^^A
-% \item Vector arrows had only one possible shape and matched the limited
-% number of vector slopes.
+% \item
+% Vector arrows had only one possible shape and matched the
+% limited number of vector slopes.
%^^A
-% \item For circles and inclined lines and vectors just two possible
-% thicknesses were available.
+% \item
+% For circles and inclined lines and vectors just two possible
+% thicknesses were available.
% \end{enumerate}
%
% The package \texttt{pict2e} removes most if not all the above
% limitations.
% \begin{enumerate}
-% \item Line and vector slopes are virtually unlimited; the only
-% remaining limitation is that the direction coefficients must be
-% three-digit integer numbers (but see below); they need not be relatively
-% prime; with the 2009 upgrade even this limitation was removed and now
-% slope coefficients can be any fractional number whose magnitude does not
-% exceed 16\,384, the maximum dimension in points that \TeX\ can handle.
+% \item
+% Line and vector slopes are virtually unlimited; the only
+% remaining limitation is that the direction coefficients must
+% be three-digit integer numbers (but see below); they need not
+% be relatively prime; with the 2009 upgrade even this
+% limitation was removed and now slope coefficients can be any
+% fractional number whose magnitude does not exceed 16\,384,
+% the maximum dimension in points that \TeX\ can handle.
%^^A
-% \item Filled and unfilled circles can be of any size.
+% \item
+% Filled and unfilled circles can be of any size.
%^^A
-% \item Ovals can be designed with any specified corner curvature and
-% there is virtually no limitation to such curvatures; of course corner
-% radii should not exceed half the lower value between the base and the
-% height of the oval.
+% \item
+% Ovals can be designed with any specified corner curvature and
+% there is virtually no limitation to such curvatures; of
+% course corner radii should not exceed half the lower value
+% between the base and the height of the oval.
%^^A
-% \item There are two shapes for the arrow tips; the triangular one
-% traditional with \LaTeX\ vectors, or the arrow tip with PostScript
-% style.
+% \item
+% There are two shapes for the arrow tips; the triangular one
+% traditional with \LaTeX\ vectors, or the arrow tip with
+% PostScript style.
%^^A
-% \item The |\linethickness| command changes the thickness of all lines,
-% straight, curved, vertical, horizontal, arrow tipped, et cetera.
+% \item
+% The |\linethickness| command changes the thickness of all
+% lines, straight, curved, vertical, horizontal, arrow tipped,
+% et cetera.
% \end{enumerate}
%
-% This specific extension package |curve2e| adds the following features.
+% This specific extension package |curve2e| adds the following
+% features.
% \begin{enumerate}
-% \item Point coordinates my be specified in both cartesian and polar
-% form: internally they are handled as cartesian coordinates, but
-% users can specify their points also in polar form. In order to avoid
-% confusion with other graphic packages, |curve2e| uses the usual comma
-% separated couple \meta{$x,y$} of integer or fractional numbers for
-% cartesian coordinates, and the colon separated pair
-% \meta{$\theta$}:\meta{$\rho$} for polar coordinates (the angle preceding
-% the radius).
-% All graphic object commands accept polar or cartesian coordinates at
-% the choice of users who may use for each object the formalism they
-% prefers. Also the |put| and |\multiput| commands have been redefined so
-% as to accept cartesian or polar coordinates. The same holds true for the
-% low level |pict2e| commands \cs{moveto}, \cs{lineto}, and \cs{curveto}.
+% \item
+% Point coordinates my be specified in both cartesian and polar
+% form: internally they are handled as cartesian coordinates,
+% but users can specify their points also in polar form.
+% In order to avoid confusion with other graphic packages,
+% |curve2e| uses the usual comma separated couple \meta{$x,y$}
+% of integer or fractional numbers for cartesian coordinates,
+% and the colon separated pair \meta{$\theta$}:\meta{$\rho$}
+% for polar coordinates (the angle preceding the radius).
+% All graphic object commands accept polar or cartesian
+% coordinates at the choice of users who may use for each
+% object the formalism they prefer. Also the |put| and
+% |\multiput| commands have been redefined so as to accept
+% cartesian or polar coordinates. The same holds true for the
+% low level |pict2e| commands \cs{moveto}, \cs{lineto}, and
+% \cs{curveto}.
%
-% Of course the user must pay attention to the meaning of cartesian
-% vs. polar coordinates. Both imply a displacement with respect to the
-% actual origin of the axes. So when a circle is placed at coordinates
-% $a,b$ with a normal |\put| command, the circle center is placed exactly
-% is that point; with a normal |\put| command the same happens if
-% coordinates $\alpha{:}\rho$ are specified.
-% But if the |\put| command is nested into another |\put| command, the
-% current origin of the axes is displaced — this is obvious and the
-% purpose of nesting |\put| commands is exactly that. But if a segment
-% is specified so that its ending point is at a specific distance and in
-% specific direction from its starting point, polar coordinates appear to
-% be the most convenient to use; in this case, though, the origin of the
-% axes becomes the starting point of the segment, therefore the segment
-% might be drawn in a strange way. Attention has been
-% paid to avoid such misinterpretation, but maybe some unusual
-% situation may not have come to my mind; feedback is very welcome.
+% Of course the user must pay attention to the meaning of
+% cartesian vs.~polar coordinates. Both imply a displacement
+% with respect to the actual origin of the axes. So when a
+% circle is placed at coordinates $a,b$ with a normal |\put|
+% command, the circle center is placed exactly is that point;
+% with a normal |\put| command the same happens if coordinates
+% $\alpha{:}\rho$ are specified. But if the |\put| command is
+% nested into another |\put| command, the current origin of the
+% axes is displaced — this is obvious and the purpose of
+% nesting |\put| commands is exactly that. But if a segment is
+% specified so that its ending point is at a specific distance
+% and in a specific direction from its starting point, polar
+% coordinates appear to be the most convenient to use; in this
+% case, though, the origin of the axes becomes the starting
+% point of the segment, therefore the segment might be drawn
+% in a strange way. Attention has been paid to avoid such
+% misinterpretation, but maybe some unusual situation may not
+% have come to my mind; feedback is very welcome.
% Meanwhile pay attention when you use polar coordinates.
%^^A
-%\item Most if not all cartesian coordinate pairs and slope pairs are
-% treated as \emph{ordered pairs}, that is \emph{complex numbers}; in
-% practice users do not notice any difference from what they were
-% used to, but all the mathematical treatment to be applied to these
-% entities is coded as complex number operations, since complex numbers
-% may be viewed non only as ordered pairs, but also as vectors or as
-% roto-amplification operators.
+%\item
+% Most if not all cartesian coordinate pairs and polar pairs
+% are treated as \emph{ordered pairs}, that is \emph{complex
+% numbers}; in practice users do not notice any difference from
+% what they were used to, but all the mathematical treatment to
+% be applied to these entities is coded as complex number
+% operations, since complex numbers may be viewed non only as
+% ordered pairs, but also as vectors or as roto-amplification
+% operators.
%^^A
-% \item Commands for setting the line terminations were introduced; the
-% user can chose between square or round caps; the default is set to
-% round caps; now this feature is directly available with |pict2e|.
+% \item
+% Commands for setting the line terminations were introduced;
+% the user can chose between square or round caps; the default
+% is set to round caps; now this feature is directly available
+% with |pict2e|.
%^^A
-% \item Commands for specifying the way two lines or curves join to one
-% another.
+% \item
+% Commands for specifying the way two lines or curves join to
+% one another.
% ^^A
-% \item Originally the |\line| macro was redefined so as to allow large
-% (up to three digits) integer direction coefficients, but maintaining
-% the same syntax as in the original \texttt{picture} environment; now
-% |pict2e| removes the integer number limitations and allows fractional
-% values, initially implemented by |curve2e|, and then introduced directly
-% in |pict2e|.
+% \item
+% Originally the |\line| macro was redefined so as to allow
+% large (up to three digits) integer direction coefficients,
+% but maintaining the same syntax as in the original
+% \texttt{picture} environment; now |pict2e| removes the
+% integer number limitations and allows fractional values,
+% initially implemented by |curve2e|, and then introduced
+% directly in |pict2e|.
% ^^A
-% \item A new macro |\Line| was originally defined by |curve2e| so as to
-% avoid the need to specify the horizontal projection of inclined lines;
-% now this functionality is available directly with |pict2e|; but this
-% |curve2e| macro name now conflicts with |pict2e| 2009 version;
-% therefore its name is changed to |\LIne| and supposedly it will not be
-% used very often, if ever, by the end user (but it is used within this
-% package macros).
+% \item
+% A new macro |\Line| was originally defined by |curve2e| so as
+% to avoid the need to specify the horizontal projection of
+% inclined lines; now this functionality is available directly
+% with |pict2e|; but this |curve2e| macro name now conflicts
+% with |pict2e| 2009 version; therefore its name is changed to
+% |\LIne| and supposedly it will not be used very often, if
+% ever, by the end user (but it is used within this package
+% macros).
% ^^A
-% \item A new macro |\LINE| was defined in order to join two points
-% specified with their coordinates; this is now the normal behaviour of
-% the |\Line| macro of |pict2e| so that in this package |\LINE| is now
-% renamed |\segment|; there is no need to use the |\put| command with
-% this line specification.
+% \item A new macro |\LINE| was defined in order to join two
+% points specified with their coordinates; this is now the
+% normal behaviour of the |\Line| macro of |pict2e| so that in
+% this package |\LINE| is now renamed |\segment|; there is no
+% need to use the |\put| command with this line specification.
% ^^A
-% \item A new macro |\DashLine| (alias: |\Dline|) is defined in order to
-% draw dashed lines joining any two given points; the dash length and
-% gap (equal to one another) get specified through one of the macro
-% arguments. The starting point may be specified in cartesian or polar
-% form; the end point in cartesian format specifies the desired end
-% point; while if the second point is in polar form it is meant
-% \emph{relative to the starting point}, not as an absolute end point.
-% See the examples further on.
+% \item
+% A new macro |\DashLine| (alias: |\Dline|) is defined in order
+% to draw dashed lines joining any two given points; the dash
+% length and gap (equal to one another) get specified through
+% one of the macro arguments. The starting point may be
+% specified in cartesian or polar form; the end point in
+% cartesian format specifies the desired end point; while if
+% the second point is in polar form it is meant
+% \textcolor{red}{\emph{relative to the starting point}}, not
+% as an absolute end point. See the examples further on.
% ^^A
-% \item A similar new macro |\Dotline| is defined in order to draw dotted
-% straight lines as a sequence of equally spaced dots, where the gap can
-% be specified by the user; such straight line may have any inclination,
-% as well as the above dashed lines. Polar coordinates for the second
-% point have the same relative meaning as specified for the |\Dashline|
-% macro.
+% \item
+% A similar new macro |\Dotline| is defined in order to draw
+% dotted straight lines as a sequence of equally spaced dots,
+% where the gap can be specified by the user; such straight
+% line may have any inclination, as well as the above dashed
+% lines. Polar coordinates for the second point have the same
+% relative meaning as specified for the |\Dashline| macro.
% ^^A
-% \item Similar macros are redefined for vectors; |\vector| redefines the
-% original macro but with the vector slope limitations removed; |\Vector|
-% gets specified with its two horizontal and vertical components in
-% analogy with |\LIne|; |\VECTOR| joins two specified points (without
-% using the |\put| command) with the arrow pointing to the second point.
+% \item Similar macros are redefined for vectors; |\vector|
+% redefines the original macro but with the vector slope
+% limitations removed; |\Vector| gets specified with its two
+% horizontal and vertical components in analogy with |\LIne|;
+% |\VECTOR| joins two specified points (without using the
+% |\put| command) with the arrow pointing to the second point.
%^^A
-% \item A new macro |\polyline| for drawing polygonal lines is defined
-% that accepts from two vertices up to an arbitrary (reasonably limited)
-% number of them (available now also in |pict2e|); here it is redefined
-% so as to allow an optional specification of the way segments for the
-% polyline are joined to one another. Vertices may be specified with
-% polar coordinates.
+% \item
+% A new macro |\polyline| for drawing polygonal lines is
+% defined that accepts from two vertices up to an arbitrary
+% (reasonably limited) number of them (available now also in
+% |pict2e|); here it is redefined so as to allow an optional
+% specification of the way segments for the polyline are joined
+% to one another. Vertices may be specified with polar
+% coordinates.
%^^A
-% \item The |pict2e| |polygon| macro to draw closed polylines (in
-% practice general polygons) has been redefined in such a way that it
-% can accept the various vertices specified with polar coordinates.
-% The |polygon*| macro produces a color filled polygon; the default
-% color is black, but a different color may be specified with the
-% usual |\color| command given within the same group where |\polygon*| is
-% enclosed.
+% \item
+% The |pict2e| |polygon| macro to draw closed polylines (in
+% practice general polygons) has been redefined in such a way
+% that it can accept the various vertices specified with polar
+% coordinates. The |polygon*| macro produces a color filled
+% polygon; the default color is black, but a different color
+% may be specified with the usual |\color| command given within
+% the same group where |\polygon*| is enclosed.
%^^A
-% \item A new macro |\Arc| is defined in order to draw an arc with
-% arbitrary radius and arbitrary aperture (angle amplitude); this
-% amplitude is specified in sexagesimal degrees, not in radians; a
-% similar functionality is now achieved with the |\arc| macro of
-% |pict2e|, which provides also the starred version |\arc*| that fills
-% up the interior of the generated circular arc with the current color.
-% It must be noticed that the syntax is slightly different, so that it is
-% reasonable that these commands, in spite of producing identical arcs,
-% might be more comfortable with this or that syntax.
+% \item
+% A new macro |\Arc| is defined in order to draw an arc with
+% arbitrary radius and arbitrary aperture (angle amplitude);
+% this amplitude is specified in sexagesimal degrees, not in
+% radians; a similar functionality is now achieved with the
+% |\arc| macro of |pict2e|, which provides also the starred
+% version |\arc*| that fills up the interior of the generated
+% circular arc with the current color.
+% It must be noticed that the syntax is slightly different, so
+% that it is reasonable that these commands, in spite of
+% producing identical arcs, might be more comfortable with this
+% or that syntax.
%^^A
-% \item Two new macros |\VectorArc| and |\VectorARC| (alias
-% |\VVectorArc|) are defined in order to draw circular arcs with an
-% arrow at one or both ends.
+% \item
+% Two new macros |\VectorArc| and |\VectorARC| (alias
+% |\VVectorArc|) are defined in order to draw circular arcs
+% with an arrow at one or both ends.
%^^A
-% \item A new macro |\Curve| is defined so as to draw arbitrary curved
-% lines by means of cubic Bézier splines; the |\Curve| macro requires
-% only the curve nodes and the directions of the tangents at each
-% node. The starred version fills up the interior of the curve with the
-% current color.
+% \item
+% A new macro |\Curve| is defined so as to draw arbitrary
+% curved lines by means of cubic Bézier splines; the |\Curve|
+% macro requires only the curve nodes and the directions of the
+% tangents at each node. The starred version fills up the
+% interior of the curve with the current color.
%^^A
-% \item The above |\Curve| macro is recursive and it can draw an
-% unlimited (reasonably limited) number of connected Bézier spline arcs
-% with continuous tangents except for cusps; these arcs require only the
-% specification of the tangent direction at the interpolation nodes.
-% It is possible to use a lower level macro |\CbezierTo| that does the
-% same but lets the user specify the control points of each arc; it is
-% more difficult to use but it is more performant.
+% \item
+% The above |\Curve| macro is recursive and it can draw an
+% unlimited (reasonably limited) number of connected Bézier
+% spline arcs with continuous tangents except for cusps; these
+% arcs require only the specification of the tangent direction
+% at the interpolation nodes. It is possible to use a lower
+% level macro |\CbezierTo| that does the same but lets the user
+% specify the control points of each arc; it is more difficult
+% to use but it is more performant.
%^^A
-% \item The basic macros used within the cumulative |\Curve| macro can be
-% used individually in order to draw any curve, one cubic arc at the
-% time; but they are intended for internal use, even if it is not
-% prohibited to use them; by themselves such arcs are not different form
-% those used by |Curve|, but the final command, |\FillCurve|, should be
-% used in place of |\CurveFinish|, so as to fill up the closed path with
-% the locally specified color; see the documentation |curve2e-manual.pdf|
-% file. It is much more convenient to use the starred version of the
-% |\Curve| macro.
+% \item
+% The basic macros used within the cumulative |\Curve| macro
+% can be used individually in order to draw any curve, one
+% cubic arc at the time; but they are intended for internal
+% use, even if it is not prohibited to use them; by themselves
+% such arcs are not different from those used by |Curve|, but
+% the final command, |\FillCurve|, should be used in place of
+% |\CurveFinish|, so as to fill up the closed path with
+% the locally specified color; see the documentation
+% |curve2e-manual.pdf| file. It is much more convenient to use
+% the starred version of the |\Curve| macro.
% \end{enumerate}
%
-% The |pict2e| package already defines macros such as |\moveto|,
-% |\lineto|, |\curveto|, |\closepath|, |\fillpath|, and |\strokepath|;
-% of course these macros can be used by the end user, and sometimes they
-% perform better than the macros defined in this package, because the
-% user has a better control on the position of each Bézier-spline
-% control points, while here the control points are sort of rigid. It
-% would be very useful to resort to the |hobby| package, but its macros
-% are compatible with those of the |tikz| and |pgf| packages, not with
-% |curve2e|; an interface should be created in order to deal with the
-% |hobby| package, but this has not been done yet.
-% In any case they are redefined so as to accept symbolic names for the
-% point coordinates in both the cartesian and polar form.
+% The |pict2e| package already defines macros such as
+% |\moveto|, |\lineto|, |\curveto|, |\closepath|, |\fillpath|,
+% and |\strokepath|; of course these macros can be used by the
+% end user, and sometimes they perform better than the macros
+% defined in this package, because the user has a better
+% control on the position of each Bézier-spline control points,
+% while here the control points are sort of rigid. It would be
+% very useful to resort to the |hobby| package, but its macros
+% are compatible with those of the |tikz| and |pgf| packages,
+% not with |curve2e|; an interface should be created in order
+% to deal with the |hobby| package, but this has not been done
+% yet. In any case they are redefined so as to accept symbolic
+% names for the point coordinates in both the cartesian and
+% polar form.
%
-% In order to make the necessary calculations many macros have been
-% defined so as to use complex number arithmetics to manipulate point
-% coordinates, directions (unit vectors, also known as `versors'),
-% rotations and the like. In the first versions of this package the
-% trigonometric functions were also defined in a way that the author
-% believed to be more efficient than those defined by the |trig|
-% package; in any case the macro names were sufficiently different to
-% accommodate both definition sets in the same \LaTeX\ run. With the
-% progress of the \LaTeX\,3 language, the |xfp| has recently become
-% available, by which any sort of calculations can be done with floating
-% point decimal numbers; therefore the most common algebraic, irrational
-% and transcendental functions can be computed in the background with the
-% stable internal floating point facilities. We maintain some computation
-% with complex number algebra, but use the |xfp| functionalities to
-% implement them and to make other calculations. Most |xfp| code has been
-% included into the \LaTeX\ kernel, so that most of this package
-% functionality is already available without the need of loading the
-% package. Loading is necessary only when a small set of special
-% functionalities are needed, that have not made their way to the kernel.
+% In order to make the necessary calculations many macros have
+% been defined so as to use complex number arithmetics to
+% manipulate point coordinates, directions (unit vectors, also
+% known as `versors'), rotations and the like. In the first
+% versions of this package the trigonometric functions were
+% also defined in a way that the author believed to be more
+% efficient than those defined by the |trig| package; in any
+% case the macro names were sufficiently different to
+% accommodate both definition sets in the same \LaTeX\ run.
+% With the progress of the \LaTeX\,3 language, the |xfp|
+% package functionalities have recently become available
+% directly in the \LaTeXe\ kernel, by which any sort of
+% calculations can be done with floating point decimal numbers;
+% therefore the most common algebraic, irrational and
+% transcendental functions can be computed in the background
+% with the stable internal floating point facilities.
+% We maintain some computation with complex
+% number algebra, but use the |xfp| functionalities to
+% implement them and to make other calculations. Most |xfp|
+% code has been included into the \LaTeX\ kernel, so that most
+% of this package functionality is already available without
+% the need of loading that package. Loading is necessary only
+% when a small set of special functionalities are needed, that
+% have not made their way to the kernel.
%
% Many aspects of this extension could be fine tuned for better
-% performance; many new commands could be defined in order to further
-% extend this extension. If the new service macros are accepted by other
-% \TeX\ and \LaTeX\ programmers, this version could become the start for
-% a real extension of the |pict2e| package or even become a part of
-% it. Actually some macros have already been included in the |pict2e|
-% package. The |\Curve| algorithm, as said before, might be redefined
-% so as to use the macros introduced by the |hobby| package, that
-% implements for the |tikz| and |pgf| packages the same functionalities
-% that John Hobby implemented for the \MF\ and \MP\ programs.
+% performance; many new commands could be defined in order to
+% further extend this extension. If the new service macros are
+% accepted by other \TeX\ and \LaTeX\ programmers, this version
+% could become the start for a real extension of the |pict2e|
+% package or even become a part of it. Actually some macros
+% have already been included in the |pict2e| package. The
+% |\Curve| algorithm, as said before, might be redefined so as
+% to use the macros introduced by the |hobby| package, that
+% implements for the |tikz| and |pgf| packages the same
+% functionalities that John Hobby implemented for the \MF\ and
+% \MP\ programs.
%
-% For these reasons I suppose that every enhancement should be submitted
-% to Niepraschk, who is the maintainer of \texttt{pict2e}; he is the only
-% one who can decide whether or not to incorporate new macros in the
-% |pict2e| package.
+% For these reasons I suppose that every enhancement should be
+% submitted to Niepraschk, who is the maintainer of
+% \texttt{pict2e}; he is the only one who can decide whether or
+% not to incorporate new macros in the |pict2e| package.
%
-% \textbf{Warning}\quad In 2020 the \LaTeX\ Project Team upgraded the
-% \LaTeX\ native |picture| environment so that all information concerning
-% lengths (line and vector lengths, coordinates, et cetera) may be
-% expressed with dimension expressions such as |0.71\textwidth|,
-% |\parindent + 5mm|, |\circle{1ex}|, and so on. With such dimensional
-% specifications, the information does not depend anymore on
-% |\unitlength|; therefore such dimensional forms do not scale by
-% changing the value of |\unitlength|.
-% |pict2e| in 2020-09-30 was correspondingly upgraded to version~0.4b.
-% Apparently such upgrades do not have any influence on |curve2e|
-% workings, or, at least, when no explicit dimensions are used; this
-% applies in particular when the |\AutoGrid| or the |GraphGrid| macros
-% are used; also he coordinates processing should be done with real
-% numbers, not with dimensions. Nevertheless feedback is welcome if
-% some corrections are needed.
+% \textbf{Warning}\quad{\color{red} In 2020 the \LaTeX\ Project
+% Team upgraded the \LaTeX\ native |picture| environment so
+% that all information concerning lengths (line and vector
+% lengths, coordinates, et cetera) may be expressed with
+% dimension expressions such as |0.71\textwidth|,
+% |\parindent + 5mm|, |\circle{1ex}|, and so on. With such
+% dimensional specifications, the information does not depend
+% anymore on |\unitlength|; therefore such dimensional forms do
+% not scale by changing the value of |\unitlength|. |pict2e| in
+% 2020-09-30 was correspondingly upgraded to version~0.4b.
+% Apparently such upgrades do not have any influence on
+% |curve2e| workings, or, at least, when no explicit dimensions
+% are used; this applies in particular when the |\AutoGrid| or
+% the |GraphGrid| macros are used; also he coordinates
+% processing should be done with real numbers, not with
+% dimensions. Nevertheless feedback is welcome if some
+% corrections are needed}.
%
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \section{Acknowledgements}
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
-% I wish to express my deepest thanks to Michel Goosens who spotted some
-% errors and very kindly submitted them to me so that I was able to
-% correct them.
+% I wish to express my deepest thanks to the various
+% individuals who spotted some errors and notified them to me;
+% Many, many thanks to all of them.
+
+% Michel Goosens spotted some errors and very kindly submitted
+% them to me so that I was able to correct them.
%
-% Josef Tkadlec and the author collaborated extensively in order to make
-% a better real long-division so as to get correctly the quotient
-% fractional part and to avoid as much as possible any numeric overflow;
-% many Josef's ideas are incorporated in the macro that was implemented
-% in the previous versions of this package, although the macro used by
-% Josef was slightly different. Both versions aim/aimed at a better
-% accuracy and at widening the operand ranges. In this version we
-% abandoned our long-division macro, and substituted it with the
-% floating point division provided by the |xfp| package.
+% Josef Tkadlec and the author collaborated extensively in
+% order to make a better real long-division so as to get
+% correctly the quotient fractional part and to avoid as much
+% as possible any numeric overflow; many Josef's ideas are
+% incorporated in the macro that was implemented in the
+% previous versions of this package, although the macro used by
+% Josef was slightly different. Both versions aim/aimed at a
+% better accuracy and at widening the operand ranges. In this
+% version we abandoned our long-division macro, and substituted
+% it with the floating point division provided by the |xfp|
+% package.
%
% Daniele Degiorgi spotted a fault in the kernel definition of
-% |\linethickness| that heavily influenced also |curve2e|; see below in
-% the code documentation part.
+% |\linethickness| that heavily influenced also |curve2e|; see
+% below in the code documentation part.
%
-% Thanks also to Jin-Hwan Cho and Juho Lee who suggested a small but
-% crucial modification in order to have \texttt{curve2e} work smoothly
-% also with XeTeX (XeLaTeX). Actually if |pict2e|, version 0.2x or later,
-% dated 2009/08/05 or later, is being used, such modification is not
-% necessary any more, but it's true that it became imperative when older
-% versions were used.
+% Jin-Hwan Cho and Juho Lee suggested a small but crucial
+% modification in order to have \texttt{curve2e} work smoothly
+% also with XeTeX (XeLaTeX). Actually if |pict2e|,
+% version 0.2x or later, dated 2009/08/05 or later, is being
+% used, such modification is not necessary any more, but it's
+% true that it became imperative when older versions were used.
%
-% Some others users spotted other “features” that did not produce the
-% desired results; they have been acknowledged by footnotes in
-% correspondence with the corrections that were made thanks their
-% feedback.
+% Some others users spotted other “features” that did not
+% produce the desired results; they have been acknowledged by
+% footnotes in correspondence with the corrections that were
+% made thanks their feedback.
%
% \StopEventually{%
% \begin{thebibliography}{9}
% \bibitem{pict2e} Gäßlein H., Niepraschk R., and Tkadlec J.
-% \emph{The \texttt{pict2e} package}, 2019, PDF documentation of
+% \emph{The \texttt{pict2e} package}, 2020, PDF documentation of
% \texttt{pict2e}; this package is part of any modern complete
-% distribution of the \TeX\ system; it may be read by means of the line
-% command \texttt{texdoc pict2e}. In case of a basic or partial system
-% installation, the package may be installed by means of the specific
-% facilities of the distribution.
+% distribution of the \TeX\ system; it may be read by means of
+% the line command \texttt{texdoc pict2e}. In case of a basic
+% or partial system installation, the package may be installed
+% by means of the specific facilities of the distribution.
% \end{thebibliography}
% }
%
@@ -510,24 +580,34 @@
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% \subsection{Some preliminary extensions to the \texttt{pict2e} package}
+% \subsection{Some preliminary extensions to the \texttt{pict2e}
+% package}
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% The necessary preliminary code has already been introduced. Here we
-% require the \texttt{color} and \texttt{graphicx} packages plus
-% the \texttt{pict2e} one; for the latter we make sure that a
-% sufficiently recent version is used. If you want to use package
-% \texttt{xcolor}, load it \emph{after} \texttt{curve2e}.
+% The necessary preliminary code has already been introduced.
+% Here we require the \texttt{color} and \texttt{graphicx}
+% packages plus the \texttt{pict2e} one; for the latter we make
+% sure that a sufficiently recent version is used. If you want
+% to use package \texttt{xcolor}, load it \emph{after}
+% \texttt{curve2e}.
%
-% Here we load also the |xparse| and |xfp| packages because we use their
-% functionalities; but we do load them only if they are not already
-% loaded with or without options; nevertheless we warn the user who wants
-% to load them explicitly: do this action before loading
-% \texttt{curve2e}.
-% The |xfp| package is absolutely required; if this package is not found
-% in the \TeX\ system installation, the loading of this new |curve2e| is
-% aborted, and the previous version 1.61 is loaded in its
-% place; the overall functionalities should non change much, but the
-% functionalities of |xfp| are not available.
+% Here we load also the |xparse| and |xfp|
+% packages because we use their functionalities;
+% but we do load them only if they are not
+% already loaded with or without options;
+% nevertheless we warn the user who wants
+% to load them explicitly: do this action before
+% loading \texttt{curve2e}. The |xfp| package is
+% absolutely required; if this package is not
+% found in the \TeX\ system installation,
+% loading of this new |curve2e| is aborted, and
+% the previous version 1.61 is loaded in its
+% place; the overall functionalities should not
+% change much, but the functionalities of |xfp|
+% are not available. Most of the functionalities of |xfp| and
+% |xparse| packages are already included into the \LaTeX
+% kernel; but there are some unusial features that have not
+% been included and might be useful also for |curve3e|; so we
+% load them and they will define only those unusual features.
%\iffalse
%<*package>
%\fi
@@ -553,41 +633,63 @@
\endinput
}
% \end{macrocode}
-% Since we already loaded package |xfp| or at least we explicitly load it
-% in our preamble, we add, if not already defined by the package, three
-% new commands that allow to make floating point tests, and two
-% “while” cycles\footnote{Thanks to Brian Dunn who spotted a bug in
-% the previous 2.0.x version definitions.}
+% Since we already loaded package |xfp| or at
+% least we explicitly load it in our preamble, we
+% add, if not already defined by the package,
+% a few new commands that allow to make floating
+% point tests, and two “while”
+% cycles\footnote{Thanks to Brian Dunn who
+% spotted a bug in the previous 2.0.x version
+% definitions.}. There are also two integer operations:
+% |\Mod| to compute the expression $m \mathrm{mod} n$, and
+% |\Ifodd| to test if an integer is odd: it mimics the native
+% command |\ifodd|, but it uses a robust construction, instead
+% of the original construction |\ifodd ...\else...\fi|.
+% There is also the string comparison test; the first two
+% arguments are the explicit or implicit strings to compare;
+% the last two arguments are the “true” and “false” codes.
% \begin{macrocode}
%
\ExplSyntaxOn
\AtBeginDocument{%
\ProvideExpandableDocumentCommand\fptest{m m m}{%
- \fp_compare:nTF{#1}{#2}{#3}\ignorespaces}
+ \fp_compare:nTF{#1}{#2}{#3}}
+\ProvideExpandableDocumentCommand\fptestT{m m}{%
+ \fp_compare:nTF{#1}{#2}{\relax}}
+\ProvideExpandableDocumentCommand\fptestF{m m}{%
+ \fp_compare:nTF{#1}{\relax}{#2}}
+%
\ProvideExpandableDocumentCommand\fpdowhile{m m}{%
- \fp_do_while:nn{#1}{#2}\ignorespaces}
+ \fp_do_while:nn{#1}{#2}}
\ProvideExpandableDocumentCommand\fpwhiledo{m m}{%
- \fp_while_do:nn{#1}{#2}\ignorespaces}
+ \fp_while_do:nn{#1}{#2}}
+\ProvideExpandableDocumentCommand\Modulo{m m}{%
+ \inteval{\int_mod:nn{#1}{#2}}}
+\ProvideExpandableDocumentCommand\Ifodd{m m m}{%
+ \int_if_odd:nTF{#1}{#2}{#3}}
+\ProvideExpandableDocumentCommand\Ifequal{m m m m}%
+ {\str_if_eq:eeTF{#1}{#2}{#3}{#4}}
}
\ExplSyntaxOff
% \end{macrocode}
-% The while cycles differ in the order of what they do; see the
-% |interface3.pdf| documentation file for details.
+% The while-do cycles differ in the order of what they do; see
+% the |interface3.pdf| documentation file for details.
%
-% The next macros are just for debugging. With the \texttt{trace} package
-% it would probably be better to define other macros, but this is not for
-% the users, but for the developers.
+% The next macros are just for debugging. With the
+% \texttt{trace} package it would probably be better to define
+% other macros, but this is not for the users, but for the
+% developers.
% \begin{macrocode}
\def\TRON{\tracingcommands\tw@ \tracingmacros\tw@}%
\def\TROF{\tracingcommands\z@ \tracingmacros\z@}%
% \end{macrocode}
%
-% Next we define some new dimension registers that will be used by the
-% subsequent macros; should they be already defined, there will not be
-% any redefinition; nevertheless the macros should be sufficiently
-% protected so as to avoid overwriting register values loaded by other
-% macro packages.
+% Next we define some new dimension registers that will be used
+% by the subsequent macros; should they be already defined,
+% there will not be any redefinition; nevertheless the macros
+% should be sufficiently protected so as to avoid overwriting
+% register values loaded by other macro packages.
% \begin{macrocode}
\newif\ifCV at polare \let\ifCV at polare\iffalse
\ifx\undefined\@tdA \newdimen\@tdA \fi
@@ -602,23 +704,23 @@
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Line thickness macros}
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% It is better to define a macro for setting a different value for the
-% line and curve thicknesses; the `|\defaultlinewidth| should contain
-% the equivalent of |\@wholewidth|, that is the thickness of thick lines;
-% thin lines are half as thick; so when the default line thickness is
-% specified to, say, 1pt, thick lines will be 1pt thick and thin lines
-% will be 0.5pt thick. The default whole width of thick lines is 0,8pt,
-% but this is specified in the kernel of \LaTeX\ and\slash or in
-% \texttt{pict2e}. On the opposite it is necessary to redefine
-% |\linethickness| because the \LaTeX\ kernel global definition does not
-% hide the space after the closed brace when you enter something such as
-% |\linethickness{1mm}| followed by a space or a new
-% line.\footnote{Thanks to Daniele
-% Degiorgi \texttt{degiorgi at inf.ethz.ch}).
-% This feature should have been eliminated
-% from the \LaTeXe\ <2020.02.02> patch level 4
-% update. This glitch has bee eliminated
-% according to the LaTeX Newsletter Nr.~32.}
+% It is better to define a macro for setting a different value
+% for the line and curve thicknesses; the `|\defaultlinewidth|
+% should contain the equivalent of |\@wholewidth|, that is the
+% thickness of thick lines; thin lines are half as thick; so
+% when the default line thickness is specified to, say, 1pt,
+% thick lines will be 1pt thick and thin lines will be 0.5pt
+% thick. The default whole width of thick lines is 0,8pt,
+% but this is specified in the kernel of \LaTeX\ and\slash or
+% in \texttt{pict2e}. On the opposite it is necessary to
+% redefine |\linethickness| because the \LaTeX\ kernel global
+% definition does not hide the space after the closed brace
+% when you enter something such as |\linethickness{1mm}|
+% followed by a space or a new line.\footnote{Thanks to Daniele
+% Degiorgi \texttt{degiorgi at inf.ethz.ch}).
+% This feature should have been eliminated from the \LaTeXe\
+% <2020.02.02> patch level 4 update. This glitch has been
+% eliminated according to the LaTeX Newsletter Nr.~32.}
% \begin{macrocode}
\gdef\linethickness#1{%
\@wholewidth#1\@halfwidth.5\@wholewidth\ignorespaces}%
@@ -627,22 +729,18 @@
\def\thinlines{\linethickness{.5\defaultlinewidth}}\thinlines
\ignorespaces}%
% \end{macrocode}
-% The |\ignorespaces| at the end of these macros is for avoiding spurious
-% spaces to get into the picture that is being drawn, because
-% these spaces introduce picture deformities often difficult to spot and
-% to eliminate.
%
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Improved line and vector macros}
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% The macro |\LIne| allows to draw a line with arbitrary inclination
-% as if it was a polygonal with just two vertices; actually it joins the
-% canvas coordinate origin with the specified relative coordinate;
-% therefore this object must be set in place by means of a |\put|
-% command.
-% Since its starting point is always at a relative 0,0 coordinate point
-% inside the box created with |\put|, the two arguments define the
-% horizontal and the vertical component respectively.
+% The macro |\LIne| allows to draw a line with arbitrary
+% inclination as if it was a polygonal with just two vertices;
+% actually it joins the canvas coordinate origin with the
+% specified relative coordinate; therefore this object must be
+% set in place by means of a |\put| command.
+% Since its starting point is always at a relative 0,0
+% coordinate point inside the box created with |\put|, the two
+% arguments define the horizontal and the vertical component respectively.
% \begin{macrocode}
\def\LIne(#1){{\GetCoord(#1)\@tX\@tY
\moveto(0,0)
@@ -650,39 +748,42 @@
}%
% \end{macrocode}
%
-% A similar macro |\segment| operates between two explicit points with
-% absolute coordinates, instead of relative to the position specified
-% by a |\put| command; it resorts to the |\polyline| macro that shall be
-% defined in a while. The |\@killglue| command might be unnecessary, but
-% it does not harm; it eliminates any explicit or implicit spacing that
+% A similar macro |\segment| operates between two explicit
+% points with absolute coordinates, instead of relative to the
+% position specified by a |\put| command; it resorts to the
+% |\polyline| macro that shall be defined in a while. The
+% |\@killglue| command might be unnecessary, but it does not
+% harm; it eliminates any explicit or implicit spacing that
% might precede this command.
% \begin{macrocode}
\def\segment(#1)(#2){\@killglue\polyline(#1)(#2)}%
% \end{macrocode}
-% By passing its ending points coordinates to the |\polyline| macro, both
-% macro arguments are a pair of coordinates, not their components; in
-% other words, if $P_1=(x_1, y_2)$ and $P_2=(x_2, y_2)$, then the first
-% argument is the couple $x_1, y_1$ and likewise the second argument is
-% $x_2, y_2$.
-% Notice that since |\polyline| accepts also the vertex coordinates in
-% polar form, also|\segment| accepts the polar form. Please remember that
-% the decimal separator is the decimal \emph{point}, while the
-% \emph{comma} acts as cartesian coordinate separator. This recommendation
-% is particularly important for non-English speaking users, since in all
-% other languages the decimal separator is or must by a comma.
+% By passing its ending points coordinates to the |\polyline|
+% macro, both macro arguments are a pair of coordinates, not
+% their components; in other words, if $P_1=(x_1, y_2)$ and
+% $P_2=(x_2, y_2)$, then the first argument is the couple $x_1, y_1$ and likewise the second argument is $x_2, y_2$.
+% Notice that since |\polyline| accepts also the vertex
+% coordinates in polar form, also |\segment| accepts the polar
+% form. Please remember that the decimal separator is the
+% decimal \emph{point}, while the \emph{comma} acts as cartesian
+% coordinate separator. This recommendation is particularly
+% important for non-anglophone users, since in all other
+% languages the decimal separator is or must by a comma.
%
-% The |\line| macro is redefined by making use of a division routine
-% performed in floating point arithmetics; for this reason the \LaTeX\
-% kernel and the overall \TeX\ system installation must be as recent as
-% the release date of the \texttt{xfp} package, i.e. 2018-10-17.
-% The floating point division macro receives in input two fractional
-% numbers and yields on output their fractional ratio.
-% Notice that this command |\line| should follow the same syntax as the
-% original pre~1994 \LaTeX\ version; but the new definition accepts the
-% direction coefficients in polar mode; that is, instead of specifying a
-% slope of $30^\circ$ with its actual sine and cosine values (or values
-% proportional to such functions), for example, |(0.5,0.866025)|, you may
-% specify it as |(30:1)|, i.e. as a unit vector with the required slope
+% The |\line| macro is redefined by making use of a division
+% routine performed in floating point arithmetics; for this
+% reason the \LaTeX\ kernel and the overall \TeX\ system
+% installation must be as recent as the release date of the
+% \texttt{xfp} package, i.e. 2018-10-17. The floating point
+% division macro receives in input two fractional numbers and
+% yields on output their fractional ratio. Notice that this
+% command |\line| should follow the same syntax as the
+% original pre~1994 \LaTeX\ version; but the new definition
+% accepts the direction coefficients also in polar mode; that
+% is, instead of specifying a slope of $30^\circ$ with its
+% actual sine and cosine values (or values proportional to such
+% functions), for example, |(0.5,0.866025)|, you may specify it
+% as |(30:1)|, i.e. as a unit vector with the required slope
% of $30^\circ$.
%
% The beginning of the macro definition is the same as that of \texttt{pict2e}:
@@ -691,26 +792,28 @@
\@linelen #2\unitlength
\ifdim\@linelen<\z@\@badlinearg\else
% \end{macrocode}
-% but as soon as it is verified that the line length is not negative,
-% things change remarkably; in facts the machinery for complex numbers is
-% invoked. This makes the code much simpler, not necessarily more
-% efficient; nevertheless |\DirOfVect| takes the only macro argument
-% (that actually contains a comma separated pair of fractional numbers)
-% and copies it to |\Dir at line| (an arbitrarily named control sequence)
-% after re-normalizing to unit magnitude; this is passed to |GetCoord|
-% that separates the two components into the control sequences |\d at mX|
-% and |\d at mY|; these in turn are the values that are actually operated
-% upon by the subsequent commands.
+% but as soon as it is verified that the line length is not
+% negative, things change remarkably; in facts the machinery for
+% complex numbers is invoked. This makes the code much simpler,
+% not necessarily more efficient; nevertheless |\DirOfVect|
+% takes the only macro argument (that actually contains a comma
+% separated pair of fractional numbers) and copies it to
+% |\Dir at line| (an arbitrarily named control sequence) after
+% re-normalizing to unit magnitude; this is passed to |GetCoord|
+% that separates the two components into the control sequences
+% |\d at mX| and |\d at mY|; these in turn are the values that are
+% actually operated upon by the subsequent commands.
% \begin{macrocode}
\expandafter\DirOfVect#1to\Dir at line
\GetCoord(\Dir at line)\d at mX\d at mY
% \end{macrocode}
-% The normalised vector direction is actually formed with the directing
-% cosines of the line direction; since the line length is actually the
-% horizontal component for non vertical lines, it is necessary to compute
-% the actual line length for non vertical lines by dividing the given
-% length by the magnitude of the horizontal cosine |\d at mX|, and the line
-% length is accordingly scaled:
+% The normalised vector direction is actually formed with the
+% directing cosines of the line direction; since the line length
+% is actually the horizontal component for non vertical lines,
+% it is necessary to compute the actual line length for non
+% vertical lines by dividing the given length by the magnitude
+% of the horizontal cosine |\d at mX|, and the line length is
+% accordingly scaled:
% \begin{macrocode}
\ifdim\d at mX\p@=\z@\else
\edef\sc at lelen{\fpeval{1 / abs(\d at mX)}}\relax
@@ -717,16 +820,18 @@
\@linelen=\sc at lelen\@linelen
\fi
% \end{macrocode}
-% Of course, if the line is vertical this division must not take place.
-% Finally the \texttt{moveto}, \texttt{lineto} and \texttt{stroke}
-% language keywords are invoked by means of the internal \texttt{pict2e}
-% commands in order to draw the line. Notice that even vertical lines are
-% drawn with the PDF language commands instead of resorting to the DVI
-% low level language that was used in both \texttt{pict2e} and the
-% original (pre 1994) \texttt{picture} commands; it had a meaning in the
-% old times, but it certainly does not have any nowadays, since lines are
-% drawn by the driver that produces the output in a human visible
-% document form, not by \TeX\ the program.
+% Of course, if the line is vertical this division must not take
+% place. Finally the \texttt{moveto}, \texttt{lineto} and
+% \texttt{stroke} language keywords are invoked by means of the
+% internal \texttt{pict2e} commands in order to draw the line.
+% Notice that even vertical lines are drawn with the PDF
+% language commands instead of resorting to the DVI low level
+% language that was used in both \texttt{pict2e} and the
+% original (pre 1994) \texttt{picture} commands; it had a
+% meaning in the old times, but it certainly does not have any
+% nowadays, since lines are drawn by the driver that produces
+% the output in a human visible document form, not by \TeX\ the
+% program.
% \begin{macrocode}
\moveto(0,0)\pIIe at lineto{\d at mX\@linelen}{\d at mY\@linelen}%
\strokepath
@@ -733,18 +838,19 @@
\fi
\endgroup\ignorespaces}%
% \end{macrocode}
-% The new definition of the command |\line|, besides the ease with which
-% is readable, does not do different things from the definition of
-% |pict2e| 2009, even if it did perform in a better way compared to the
-% 2004 version that was limited to integer direction coefficients up to
-% 999 in magnitude. Moreover this |curve2e| version accepts polar
-% coordinates as slope pairs, making it much simpler to draw lines with
+% The new definition of the command |\line|, besides the ease
+% with which is readable, does not do different things from the
+% definition of |pict2e| 2009, even if it did perform in a
+% better way compared to the 2004 version that was limited to
+% integer direction coefficients up to 999 in magnitude.
+% Moreover this |curve2e| version accepts polar coordinates as
+% slope pairs, making it much simpler to draw lines with
% specific slopes.
%
% It is necessary to redefine the low level macros \cs{moveto},
-% \cs{lineto}, and \cs{curveto}, because their original definitions
-% accept only cartesian coordinates. We proceed the same as for the
-% \cs{put} command.
+% \cs{lineto}, and \cs{curveto}, because their original
+% definitions accept only cartesian coordinates. We proceed the
+% same as for the \cs{put} command.
% \begin{macrocode}
\let\originalmoveto\moveto
\let\originallineto\lineto
@@ -762,58 +868,64 @@
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Dashed and dotted lines}
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Dashed and dotted lines are very useful in technical drawings; here we
-% introduce two macros that help drawing them in the proper way; besides
-% the obvious difference between the use of dashes or dots, they may
-% refer in a different way to the end points that must be specified to
-% the various macros.
+% Dashed and dotted lines are very useful in technical drawings;
+% here we introduce two macros that help drawing them in the
+% proper way; besides the obvious difference between the use of
+% dashes or dots, they may refer in a different way to the end
+% points that must be specified to the various macros.
%
-% The coordinates of the first point $P_1$, where le line starts, are
-% always referred to the origin of the coordinate axes; the end point
-% $P_2$ coordinates are referred to the origin of the axes if in
-% cartesian form, while with the polar form they are referred to $P_1$;
-% both coordinate types have their usefulness: see the documentation
-% |curve2e-manual.pdf| file.
+% The coordinates of the first point $P_1$, where le line
+% starts, are always referred to the origin of the coordinate
+% axes; the end point $P_2$ coordinates are referred to the
+% origin of the axes if in cartesian form, while with the polar
+% form they are referred to $P_1$; both coordinate types have
+% their usefulness: see the documentation |curve2e-manual.pdf|
+% file.
%
-% The above mentioned macros create dashed lines between two given
-% points, with a dash length that must be specified, or dotted lines,
-% with a dot gap that must be specified; actually the specified dash
-% length or dot gap is a desired one; the actual length or gap is
-% computed by integer division between the distance of the given points
-% and the desired dash length or dot gap; when dashes are involved, this
-% integer is tested in order to see if it is an odd number; if it's not,
-% it is increased by unity. Then the actual dash length or dot gap is
-% obtained by dividing the above distance by this number.
+% The above mentioned macros create dashed lines between two
+% given points, with a dash length that must be specified, or
+% dotted lines, with a dot gap that must be specified; actually
+% the specified dash length or dot gap is a desired one; the
+% actual length or gap is computed by integer division between
+% the distance of the given points and the desired dash length
+% or dot gap; when dashes are involved, this integer is tested
+% in order to see if it is an odd number; if it's not,
+% it is increased by unity. Then the actual dash length or dot
+% gap is obtained by dividing the above distance by this number.
%
-% Another vector $P_2-P_1$ is created by dividing it by this number;
-% then, when dashes are involved, it is multiplied by two in order to
-% have the increment from one dash to the next; finally the number of
-% patterns is obtained by integer division of this number by 2 and
-% increasing it by~1. Since the whole dashed or dotted line is put in
-% position by an internal |\put| command, is is not necessary to enclose
-% the definitions within groups, because they remain internal to the
-% |\put| argument box.
+% Another vector $P_2-P_1$ is created by dividing it by this
+% number; then, when dashes are involved, it is multiplied by
+% two in order to have the increment from one dash to the next;
+% finally the number of patterns is obtained by integer division
+% of this number by 2 and increasing it by~1. Since the whole
+% dashed or dotted line is put in position by an internal |\put|
+% command, is is not necessary to enclose the definitions within
+% groups, because they remain internal to the |\put| argument
+% box.
%
-% Figure~6 of the |curve2e-manual.pdf| user manual shows
-% the effect of the slight changing of the dash length in order to
-% maintain \emph{approximately} the same dash-space pattern along the line,
-% irrespective of the line length. The syntax is the following:
-% \begin{flushleft}
+% Figure~6 of the |curve2e-manual.pdf| user manual shows the
+% effect of the slight changing of the dash length in order to
+% maintain \emph{approximately} the same dash-space pattern
+% along the line, irrespective of the line length. The syntax is
+% the following:
+% \begin{Sintassi}
% \cs{Dashline}\parg{first point}\parg{second point}\marg{dash length}
-% \end{flushleft}
-% where \meta{first point} contains the coordinates of the starting point
-% and \meta{second point} the absolute (cartesian) or relative (polar)
-% coordinates of the ending point; of course the \meta{dash length},
-% which equals the dash gap, is mandatory. An optional asterisk is used to
-% be back compatible with previous implementations but its use is now
-% superfluous; with the previous implementation of the code, in facts,
-% if coordinates were specified in polar form, without the optional
-% asterisk the dashed line was misplaced, while if the asterisk was
-% specified, the whole object was put in the proper position. With this
-% new implementation, both the cartesian and polar coordinates always
-% play the role they are supposed to play independently from the
-% asterisk. The |\IsPolar| macro is introduced to analyse the coordinate
-% type used for the second argument, and uses such second argument
+% \end{Sintassi}
+% where \meta{first point} contains the coordinates of the
+% starting point and \meta{second point} the absolute
+% (cartesian) or relative (polar) coordinates of the ending
+% point; of course the \meta{dash length}, which equals the dash
+% gap, is mandatory. An optional asterisk is used to be back
+% compatible with previous implementations but its use is now
+% superfluous; with the previous implementation of the code, in
+% facts, if coordinates were specified in polar form, without
+% the optional asterisk the dashed line was misplaced, while if
+% the asterisk was specified, the whole object was put in the
+% proper position. With this new implementation, both the
+% cartesian and polar coordinates always play the role they are
+% supposed to play independently from the asterisk. The
+% |\IsPolar| macro is introduced to analyse the coordinate type
+% used for the second argument, and uses such second argument
% accordingly.
% \begin{macrocode}
\def\IsPolar#1:#2?{\def\@TempOne{#2}\unless\ifx\@TempOne\empty
@@ -855,27 +967,29 @@
\fi
% \end{macrocode}
%
-% A simpler |\Dotline| macro draws a dotted line between two given
-% points; the dots are rather small, therefore the inter dot distance is
-% computed in such a way as to have the first and the last dot at the
-% exact position of the dotted-line end-points; again the specified dot
-% distance is nominal in the sense that it is recalculated in such a way
-% that the first and last dots coincide with the line end points.
-% Again if the second point coordinates are in polar form they are
-% considered as relative to the first point.Since the dots must emerge
-% from the background of the drawing they should not be too small: they
-% must be seen; therefore their diameter cannot be tied to the unit
-% length of the particular drawing, but must have at visible size; by
-% default it is set to $0.5\,\mathrm{mm}$ (about 20 mills, in US units)
-% but through an optional argument to the macro, it may be set to any
-% desired size; remember that 1\,pt is about one third of a millimeter;
-% sometimes it might be too small; 1\,mm is a very black dot, therefore
-% users must pay attention when they specify the dot diameter,
-% so as not to exaggerate in either direction.
-% The syntax is as follows:
-%\begin{flushleft}
+% A simpler |\Dotline| macro draws a dotted line between two
+% given points; the dots are rather small, therefore the inter
+% dot distance is computed in such a way as to have the first
+% and the last dot at the exact position of the dotted-line
+% end-points; again the specified dot distance is nominal in
+% the sense that it is recalculated in such a way that the
+% first and last dots coincide with the line end points.
+% Again if the second point coordinates are in polar form they
+% are considered as relative to the first point. Since the dots
+% must emerge from the background of the drawing they should
+% not be too small: they must be seen; therefore their diameter
+% cannot be tied to the unit length of the particular drawing,
+% but must have at visible size; by default it is set to
+% $0.5\,\mathrm{mm}$ (about 20 mills, in US units) but through
+% an optional argument to the macro, it may be set to any
+% desired size; remember that 1\,pt is about one third of a
+% millimetre; sometimes it might be too small; 1\,mm is a very
+% black dot, therefore users must pay attention when they
+% specify the dot diameter, so as not to exaggerate in either
+% direction. The syntax is as follows:
+%\begin{Sintassi}
%\cs{Dotline}\parg{start point}\parg{end point}\marg{dot distance}\oarg{diameter}
-%\end{flushleft}
+%\end{Sintassi}
% \begin{macrocode}
\ifx\Dotline\undefined
\providecommand\Dotline{}
@@ -892,51 +1006,57 @@
\fi
% \end{macrocode}
%
-% Notice that vectors as complex numbers in their cartesian and polar
-% forms always represent a point position referred to a local origin
-% of the axes; this is why in figures~6 and~7 of the user manual
-% the dashed and dotted lines that start
-% from the lower right corner of the graph grid, and that use polar
-% coordinates, are put in their correct position thanks to the
-% different behaviour obtained with the |\IsPolar| macro.
+% Notice that vectors as complex numbers in their cartesian
+% and polar forms always represent a point position referred to
+% a local origin of the axes; this is why in figures~6 and~7
+% of the user manual the dashed and dotted lines that start
+% from the lower right corner of the graph grid, and that use
+% polar coordinates, are put in their correct position thanks
+% to the different behaviour obtained with the |\IsPolar|
+% macro.
%
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Coordinate handling}
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% The new macro |\GetCoord| splits a vector (or complex number)
-% specification into its components; in particular it distinguishes the
-% polar from the cartesian form of the coordinates. The latter have the
-% usual syntax \meta{x\texttt{,}y}, while the former have the syntax
-% \meta{angle\texttt{:}radius}. The |\put| and |\multiput| commands are
-% redefined to accept the same syntax; the whole work is done by
-% |\SplitNod@| and its subsidiaries.
+% The new macro |\GetCoord| splits a vector (or complex
+% number) specification into its components; in particular it
+% distinguishes the polar from the cartesian form of the
+% coordinates. The latter have the usual syntax
+% \meta{x\texttt{,}y}, while the former have the syntax
+% \meta{angle\texttt{:}radius}. The |\put| and |\multiput|
+% commands are redefined to accept the same syntax; the whole
+% work is done by |\SplitNod@| and its subsidiaries.
%
-% Notice that package |eso-pic| uses |picture| macros in its definitions,
-% but its original macro |\LenToUnit| is incompatible with this
-% |\GetCoord| macro; its function is to translate real lengths into
-% coefficients to be used as multipliers of the current |\unitlength|; in
-% case that the |eso-pic| had been loaded, at the |\begin{document}|
-% execution, the |eso-pic| macro is redefined using the e-\TeX\ commands
-% so as to make it compatible with these local macros.\footnote{Thanks to
-% Franz-Joseph Berthold who was so kind to spot the bug.}
+% Notice that package |eso-pic| uses |picture| macros in its
+% definitions, but its original macro |\LenToUnit| is
+% incompatible with this |\GetCoord| macro; its function is
+% to translate real lengths into coefficients to be used as
+% multipliers of the current |\unitlength|; in case that the
+% |eso-pic| had been loaded, at the |\begin{document}|
+% execution, the |eso-pic| macro is redefined using the
+% e-\TeX\ commands so as to make it compatible with these
+% local macros.\footnote{Thanks to Franz-Joseph Berthold who
+% was so kind to spot the bug.}
% \begin{macrocode}
\AtBeginDocument{\@ifpackageloaded{eso-pic}{%
\renewcommand\LenToUnit[1]{\strip at pt\dimexpr#1*\p@/\unitlength}}{}}%
% \end{macrocode}
-% The above redefinition is delayed at |\AtBeginDocument| in order to
-% have the possibility to check if the |eso-pic| package had actually
-% been loaded. Nevertheless the code is defined here just because the
-% original |eso-pic| macro was interfering with the algorithms of
-% coordinate handling.
+% The above redefinition is delayed at |\AtBeginDocument| in
+% order to have the possibility to check if the |eso-pic|
+% package had actually been loaded. Nevertheless the code is
+% defined here just because the original |eso-pic| macro was
+% interfering with the algorithms of coordinate handling.
%
-% But let us come to the real subject of this section. We define a
-% |\GettCoord| macro that passes control to the service macro with the
-% expanded arguments; expanding arguments allows to use macros to named
-% points, instead of explicit coordinates; with this version of |curve2e|
-% this facility is not fully exploited, but a creative user can use this
-% feature. Notice the usual trick to use a dummy macro that is
-% defined within a group with expanded arguments, but where the group is
-% closed by the macro itself, so that no traces remain behind after its
+% But let us come to the real subject of this section. We
+% define a |\GettCoord| macro that passes control to the
+% service macro with the expanded arguments; expanding
+% arguments allows to use macros to named points, instead of
+% explicit coordinates; with this version of |curve2e| this
+% facility is not fully exploited, but a creative user can
+% use this feature. Notice the usual trick to use a dummy
+% macro that is defined within a group with expanded
+% arguments, but where the group is closed by the macro
+% itself, so that no traces remain behind after its
% expansion.
% \begin{macrocode}
\def\GetCoord(#1)#2#3{\let\ifCV at polare\iffalse
@@ -955,60 +1075,67 @@
\def\SplitCartesian(#1,#2)#3#4{\edef#3{#1}\edef#4{#2}}
% \end{macrocode}
-% The macro that detects the form of the coordinates is |\IsPolar|;
-% it examines the parameter syntax in order to see if it contains a
-% colon; it has already been used with the definition of dashed and
-% dotted lines.
+% The macro that detects the form of the coordinates is
+% |\IsPolar|; it examines the parameter syntax in order to
+% see if it contains a colon; it has already been used with
+% the definition of dashed and dotted lines.
%
-% In order to accept polar coordinates with |\put| and |\multiput|
-% we resort to using |\GetCoord|; therefore the redefinition of
-% |\put| is very simple because it suffices to save the original
-% meaning of that macro and redefine the new one in terms of the
-% old one.
+% In order to accept polar coordinates with |\put| and
+% |\multiput| we resort to using |\GetCoord|; therefore the
+% redefinition of |\put| is very simple because it suffices
+% to save the original meaning of that macro and redefine the
+% new one in terms of the old one.
% \begin{macrocode}
\let\originalput\put
\def\put(#1){\bgroup\GetCoord(#1)\@tX\@tY
\edef\x{\noexpand\egroup\noexpand\originalput(\@tX,\@tY)}\x}
% \end{macrocode}
-% For |\multiput| it is more complicated, because the increments from one
-% position to the next cannot be done efficiently because the increments
-% in the original definition are executed within boxes, therefore any
-% macro instruction inside these boxes is lost. It is a good occasion to
-% modify the |\multiput| definition by means of the advanced macro
-% definitions provided by package |xparse|; we can add also some error
-% messages for avoiding doing anything when some mandatory parameters are
-% missing ore are empty, or do not contain anything different from an
-% ordered pair or a polar form. We add also an optional argument to
-% handle the increments outside the boxes.
+% For |\multiput| it is more complicated, because the
+% increments from one position to the next cannot be done
+% efficiently because the increments in the original
+% definition are executed within boxes, therefore any macro
+% instruction inside these boxes is lost. It is a good
+% occasion to modify the |\multiput| definition by means of
+% the advanced macro definitions provided by package
+% |xparse|; we can add also some error messages for avoiding
+% doing anything when some mandatory parameters are either
+% missing or empty, or do not contain anything different
+% from an ordered pair or a polar form. We add also an
+% optional argument to handle the increments outside the
+% boxes.
% The new macro has the following syntax:\\[2ex]
% \mbox{\small\cs{multiput}\oarg{shift}\parg{initial}\texttt{(\meta{increment})}\marg{number}\marg{object}\oarg{handler}}\\[2ex]
-% where the optional \meta{shift} is used to displace to whole
-% set of \meta{object}s from their original position;
+% where the optional \meta{shift} is used to displace to
+% whole set of \meta{object}s from their original position;
% \meta{initial} contains the cartesian or polar coordinates
-% of the initial point; \meta{increment} contains the cartesian or
-% polar increment for the coordinates to be used from the second
-% position to the last; \meta{number} il the total number of
-% \meta{object}s to be drawn; \meta{object} is the object to be put in
-% position at each cycle repetition; the optional \meta{handler} may be
-% used to control the current values of the horizontal and vertical
+% of the initial point; \meta{increment} contains the
+% cartesian or polar increment for the coordinates to be used
+% from the second position to the last; \meta{number} il the
+% total number of \meta{object}s to be drawn; \meta{object}
+% is the object to be put in position at each cycle
+% repetition; the optional \meta{handler} may be used to
+% control the current values of the horizontal and vertical
% increments.
-% The new definition contains two |\put| commands where the second is
-% nested within a while-loop which, in turn, is within the argument of
-% the first |\put| command. Basically it is the same idea that the
-% original macros, but now the increments are computed within the while
-% loop, but outside the argument of the inner |\put| command. If the
-% optional \meta{handler} is specified the increments are computed
-% from the macros specified by the user. Another new feature: the fourth
-% argument, that contains the number of objects to be put in place,
-% may be an integer expression such as for example |3*\N+1|.
+% The new definition contains two |\put| commands where the
+% second is nested within a while-loop which, in turn, is
+% within the argument of the first |\put| command. Basically
+% it is the same idea that the original macros, but now the
+% increments are computed within the while loop, but outside
+% the argument of the inner |\put| command. If the optional
+% \meta{handler} is specified the increments are computed
+% from the macros specified by the user. Another new feature:
+% the fourth argument, that contains the number of objects to
+% be put in place, may be an integer expression such as for
+% example |3*\N+1|.
%
-% The two increments components inside the optional argument may be set
-% by means of mathematical expressions operated upon by the |\fpeval|
-% function given by the |\xfp| package already loaded by |curve2e|. Of
-% course it is the user responsibility to pay attention to the scales of
-% the two axes and to write meaningful expressions; the figure and code
-% shown in the user manual of this package display some examples:
-% see the documentation |curve2e-manual.pdf| file.
+% The two increments components inside the optional argument
+% may be set by means of mathematical expressions operated
+% upon by the |\fpeval| function given by the |\xfp| package
+% already loaded by |curve2e|. Of course it is the user
+% responsibility to pay attention to the scales of the two
+% axes and to write meaningful expressions; the figure and
+% code shown in the user manual of this package displays some
+% examples: see the documentation |curve2e-manual.pdf| file.
% \begin{macrocode}
\RenewDocumentCommand{\multiput}{O{0,0} d() d() m m o }{%
\IfNoValueTF{#2}{\PackageError{curve2e}%
@@ -1033,14 +1160,16 @@
}\ignorespaces
}
% \end{macrocode}
-% And here it is the new |\xmultiput| command; remember: the internal
-% cycling \TeX\ counter |\@multicnt| is now accessible with the name
-% |multicnt| as if it was a \LaTeX\ counter, in particular the user can
-% access its contents with a command such as |\value{multicnt}|. Such
-% counter is \emph{stepped up} at each cycle, instead of being
-% \emph{stepped down} as in the original |\multiput| command. The code is
-% not so different from the one used for the new version of |\multiput|,
-% but it appears more efficient and its code more easily readable.
+% And here it is the new |\xmultiput| command; remember: the
+% internal cycling \TeX\ counter |\@multicnt| is now accessible
+% with the name |multicnt| as if it was a \LaTeX\ counter, in
+% particular the user can access its contents with a command
+% such as |\value{multicnt}|. Such counter is \emph{stepped up}
+% at each cycle, instead of being \emph{stepped down} as in the
+% original |\multiput| command. The code is not so different
+% from the one used for the new version of |\multiput|,
+% but it appears more efficient and its code more easily
+% readable.
% \begin{macrocode}
\NewDocumentCommand{\xmultiput}{O{0,0} d() d() m m o }{%
\IfNoValueTF{#2}{\PackageError{curve2e}{%
@@ -1065,47 +1194,54 @@
}}\ignorespaces
}
% \end{macrocode}
-% Notice that the internal macros |\R| and |\D|, (respectively the
-% current point coordinates, in form of a complex number, where to put
-% the \meta{object}, and the current displacement to find the next point)
-% are accessible to the user both in the \meta{object} argument field and
-% the \meta{handler} argument field. The code used in
-% figure~18 if the user manual shows how to create the hour marks of a
-% clock together with the rotated hour roman numerals.
+% Notice that the internal macros |\R| and |\D|, (respectively
+% the current point coordinates, in form of a complex number,
+% where to put the \meta{object}, and the current displacement
+% to find the next point) are accessible to the user both in
+% the \meta{object} argument field and the \meta{handler}
+% argument field. The code used in figure~18 of the user manual
+% shows how to create the hour marks of a clock together with
+% the rotated hour roman numerals.
%
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Vectors}
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% The redefinitions and the new definitions for vectors are a little more
-% complicated than with segments, because each vector is drawn as a
-% filled contour; the original \texttt{pict2e} 2004 macro checked if the
-% slopes are corresponding to the limitations specified by Lamport
-% (integer three digit signed numbers) and sets up a transformation in
-% order to make it possible to draw each vector as an horizontal
-% left-to-right arrow and then to rotate it by its angle about its tail
-% point; with |pict2e| 2009, possibly this redefinition of |\vector| is
-% not necessary, but we do it as well and for the same reasons we had for
-% redefining |\line|; actually there are two macros for tracing the
-% contours that are eventually filled by the principal macro; each
-% contour macro draws the vector with a \LaTeX\ or a PostScript styled
-% arrow tip whose parameters are specified by default or may be taken
-% from the parameters taken from the |PSTricks| package if this one is
-% loaded before |pict2e|; in any case we did not change the contour
-% drawing macros because if they are modified the same modification is
-% passed on to the arrows drawn with the |curve2e| package redefinitions.
+% The redefinitions and the new definitions for vectors are a
+% little more complicated than with segments, because each
+% vector is drawn as a filled contour; the original
+% \texttt{pict2e} 2004 macro checked if the slopes are
+% corresponding to the limitations specified by Lamport
+% (integer three digit signed numbers) and sets up a
+% transformation in order to make it possible to draw each
+% vector as an horizontal left-to-right arrow and then to
+% rotate it by its angle about its tail point; with |pict2e|
+% 2009, possibly this redefinition of |\vector| is not
+% necessary, but we do it as well and for the same reasons we
+% had for redefining |\line|; actually there are two macros for
+% tracing the contours that are eventually filled by the
+% principal macro; each contour macro draws the vector with a
+% \LaTeX\ or a PostScript styled arrow tip whose parameters are
+% specified by default or may be taken from the parameters
+% taken from the |PSTricks| package if this one is loaded
+% before |pict2e|; in any case we did not change the contour
+% drawing macros because if they are modified the same
+% modification is passed on to the arrows drawn with the
+% |curve2e| package redefinitions.
%
-% Because of these features the new macros are different from those used
-% for straight lines.
+% Because of these features the new macros are different from
+% those used for straight lines.
%
-% We start with the redefinition of |\vector| and we use the machinery
-% for vectors (as complex numbers) we used for |\line|. The actual point
-% is to let |\vector| accept the slope parameters also in polar form.
-% Therefore it suffices to save the original definition of |\vector|
-% as defined in |pict2e| and and use it as a fallback after redefining
-% |\vector| in a “vector” format.\footnote{The previous version 2.2.9
-% of this package contained a glitch that was visible only with line
-% widths larger than 1.5\.pt. I thank very much Ashish Kumar Das who
-% spotted this glitch and kindly informed me.}
+% We start with the redefinition of |\vector| and we use the
+% machinery for vectors (as complex numbers) we used for
+% |\line|. The actual point is to let |\vector| accept the
+% slope parameters also in polar form.
+% Therefore it suffices to save the original definition of
+% |\vector| as defined in |pict2e| and and use it as a fallback
+% after redefining |\vector| in a “vector” format.\footnote{The
+% previous version 2.2.9 of this package contained a glitch
+% that was visible only with line widths larger than 1.5\.pt. I
+% thank very much Ashish Kumar Das who spotted this glitch and
+% kindly informed me.}
% \begin{macrocode}
\let\original at vector\vector
\def\vector(#1)#2{%
@@ -1115,14 +1251,16 @@
\endgroup}%
% \end{macrocode}
%
-% We define the macro that does not require the specification of the
-% length or the $l_x$ length component; the way the new |\vector| macro
-% works does not actually require this specification, because \TeX\ can
-% compute the vector length, provided the two direction components are
-% exactly the horizontal and vertical vector components. If the
-% horizontal component is zero, the actual length must be specified as
-% the vertical component. The object defined with |\Vector|, as well as
-% |\vector|, must be put in place by means of a |\put| command.
+% We define the macro that does not require the specification
+% of the length or the $l_x$ length component; the way the new
+% |\vector| macro works does not actually require this
+% specification, because \TeX\ can compute the vector length,
+% provided the two direction components are exactly the
+% horizontal and vertical vector components. If the horizontal
+% component is zero, the actual length must be specified as
+% the vertical component. The object defined with |\Vector|,
+% as well as |\vector|, must be put in place by means of a
+% |\put| command.
% \begin{macrocode}
\def\Vector(#1){{%
\GetCoord(#1)\@tX\@tY
@@ -1133,11 +1271,11 @@
\fi}}
% \end{macrocode}
%
-% On the opposite the next macro specifies a vector by means of the
-% coordinates of its end points; the first point is where the vector
-% starts, and the second point is the arrow tip side. We need the
-% difference of these two coordinates, because it represents the actual
-% vector.
+% On the opposite the next macro specifies a vector by means of
+% the coordinates of its end points; the first point is where
+% the vector starts, and the second point is the arrow tip
+% side. We need the difference of these two coordinates,
+% because it represents the actual vector.
% \begin{macrocode}
\def\VECTOR(#1)(#2){\begingroup
\SubVect#1from#2to\@tempa
@@ -1145,8 +1283,9 @@
\endgroup\ignorespaces}
% \end{macrocode}
%
-% The double tipped vector is built on the |\VECTOR| macro by simply
-% drawing two vectors from the middle point of the double tipped vector.
+% The double tipped vector is built on the |\VECTOR| macro by
+% simply drawing two vectors from the middle point of the
+% double tipped vector.
% \begin{macrocode}
\def\VVECTOR(#1)(#2){{\SubVect#1from#2to\@tempb
\ScaleVect\@tempb by0.5to\@tempb
@@ -1155,53 +1294,58 @@
% \end{macrocode}
%
% The |pict2e| documentation says that if the vector length is
-% zero the macro draws only the arrow tip; this may work with macro
-% |\vector|, certainly not with |\Vector| and |\VECTOR|. This might be
-% useful for adding an arrow tip to a circular arc. See the documentation
-% |curve2e-manual.pdf| file.
+% zero the macro draws only the arrow tip; this may work with
+% macro |\vector|, certainly not with |\Vector| and |\VECTOR|.
+% This might be useful for adding an arrow tip to a circular
+% arc. See the documentation |curve2e-manual.pdf| file.
%
%
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Polylines and polygons}
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% We now define the polygonal line macro; its syntax is very simple:
-% \begin{flushleft}\ttfamily
+% We now define the polygonal line macro; its syntax is very
+% simple:
+% \begin{Sintassi}\ttfamily
% \cs{polyline}\oarg{join}\parg{$P_0$}\parg{$P_1$}\parg{$P_2$}...^^A
%\parg{$P_n$}
-% \end{flushleft}
-% Remember: |\polyline| has been incorporated into |pict2e| 2009, but we
-% redefine it so as to allow an optional argument to specify the line
-% join type.
+% \end{Sintassi}
+% Remember: |\polyline| has been incorporated into |pict2e|
+% 2009, but we redefine it so as to allow an optional argument
+% to specify the line join type.
%
% In order to write a recursive macro we need aliases for the
-% parentheses; actually we need only the left parenthesis, but some
-% editors complain about unmatched delimiters, so we define an alias also
-% for the right parenthesis.
+% parentheses; actually we need only the left parenthesis, but
+% some editors complain about unmatched delimiters, so we
+% define an alias also for the right parenthesis.
% \begin{macrocode}
\let\lp at r( \let\rp at r)
% \end{macrocode}
-% The first call to |\polyline|, besides setting the line joins,
-% examines the first point coordinates and moves the drawing position to
-% this point; afterwards it looks for the second point coordinates; they
-% start with a left parenthesis; if this is found the coordinates should
-% be there, but if the left parenthesis is missing (possibly preceded by
-% spaces that are ignored by the |\@ifnextchar| macro) then a warning
-% message is output together with the line number where the missing
-% parenthesis causes the warning: beware, this line number might point to
-% several lines further on along the source file!
-% In any case it's necessary to insert a |\@killglue|command, because
-% |\polyline| refers to absolute coordinates, and not necessarily is put
-% in position through a |\put| command that provides to eliminate any
-% spurious spaces preceding this command.
+% The first call to |\polyline|, besides setting the line
+% joins,
+% examines the first point coordinates and moves the drawing
+% position to this point; afterwards it looks for the second
+% point coordinates; they start with a left parenthesis; if
+% this is found the coordinates should be there, but if the
+% left parenthesis is missing (possibly preceded by spaces that
+% are ignored by the |\@ifnextchar| macro) then a warning
+% message is output together with the line number where the
+% missing parenthesis causes the warning: beware, this line
+% number might point to several lines further on along the
+% source file!
+% In any case it's necessary to insert a |\@killglue| command,
+% because |\polyline| refers to absolute coordinates, and not
+% necessarily is put in position through a |\put| command that
+% provides to eliminate any spurious spaces preceding this
+% command.
%
-% \begin{figure}[!hb]
+% \begin{figure}[!hb]\vspace*{-1ex}
% \begin{minipage}{0.55\textwidth}
-%\begin{verbatim}
-% \unitlength=0.07\hsize
-% \begin{picture}(8,8)(-4,-4)\color{red}
-% \polygon*(45:4)(135:4)(-135:4)(-45:4)
-% \end{picture}
-%\end{verbatim}
+%\begin{Sintassi}\ttfamily\obeylines
+% \cs{unitlength}=0.07\cs{hsize}
+% \cs{begin}\Marg{picture}(8,8)(-4,-4)\cs{color}\{red\}
+% \cs{polygon*}(45:4)(135:4)(-135:4)(-45:4)
+% \cs{end}\Marg{picture}
+%\end{Sintassi}
% \end{minipage}
% \hfill
% \begin{minipage}{0.4\textwidth}\centering
@@ -1209,14 +1353,15 @@
% \begin{picture}(8,8)(-4,-4)\color{red}
% \polygon*(45:4)(135:4)(-135:4)(-45:4)
% \end{picture}
-% \end{minipage}
-% \caption{The code and the result of defining a polygon with its vertex
-% polar coordinates}\label{fig:filled-polygon}
+% \end{minipage}\vspace*{-1ex}
+% \caption{The code and the result of defining a polygon with
+% its vertex polar coordinates}%
+% \label{fig:filled-polygon}
% \end{figure}
%
-% In order to allow a specification for the joints of the various
-% segments of a polyline it is necessary to allow for an optional
-% parameter; the default is the bevel join.
+% In order to allow a specification for the joints of the
+% various segments of a polyline it is necessary to allow for
+% an optional parameter; the default is the bevel join.
% \begin{macrocode}
\renewcommand*\polyline[1][\beveljoin]{\p at lylin@[#1]}
@@ -1229,10 +1374,11 @@
\ignorespaces}}
% \end{macrocode}
-% But if there is a second or further point coordinate, the recursive
-% macro |\p at lyline| is called; it works on the next point and checks for
-% a further point; if such a point exists the macro calls itself,
-% otherwise it terminates the polygonal line by stroking it.
+% But if there is a further point coordinate, the recursive
+% macro |\p at lyline| is called; it works on the next point and
+% checks for a further point; if such a point exists the macro
+% calls itself, otherwise it terminates the polygonal line by
+% stroking it.
% \begin{macrocode}
\def\p at lyline(#1){\GetCoord(#1)\d at mX\d at mY
\pIIe at lineto{\d at mX\unitlength}{\d at mY\unitlength}%
@@ -1239,13 +1385,14 @@
\@ifnextchar\lp at r{\p at lyline}{\strokepath\ignorespaces}}
% \end{macrocode}
%
-% The same treatment must be done for the \cs{polygon} macros; we use the
-% defining commands of package |xparse|, in order to use an optional
-% asterisk; as it is usual with |picture| convex lines, the command with
-% asterisk does not trace the contour, but fills the contour with the
-% current color.The asterisk is tested at the beginning and, depending on
-% its presence, a temporary switch is set to \texttt{true}; this being
-% the case the contour is filled, otherwise it is simply stroked.
+% The same treatment must be done for the \cs{polygon} macros; we
+% use the defining commands of package |xparse|, in order to use
+% an optional asterisk; as it is usual with |picture| convex
+% lines, the command with asterisk does not trace the contour,
+% but fills the contour with the current color.The asterisk is
+% tested at the beginning and, depending on its presence, a
+% temporary switch is set to \texttt{true}; this being the case
+% the contour is filled, otherwise it is simply stroked.
% \begin{macrocode}
\providecommand\polygon{}
\RenewDocumentCommand\polygon{s O{\beveljoin} }{\@killglue\begingroup
@@ -1267,198 +1414,372 @@
\endgroup
\ignorespaces}}
% \end{macrocode}
-% Now, for example, a filled polygon can be drawn using polar coordinates
-% for its vertices; see figure~\ref{fig:filled-polygon} on
+% Now, for example, a filled polygon can be drawn using polar
+% coordinates for its vertices; see
+% figure~\ref{fig:filled-polygon} on
% page~\pageref{fig:filled-polygon}.
%
-% Remember; the polygon polar coordinates are relative to the origin of
-% the local axes; therefore in order to put a polygon in a different
-% position, it is necessary to do it through a |\put| command.
+% Remember; the polygon polar coordinates are relative to the
+% origin of the local axes; therefore in order to put a polygon
+% in a different position, it is necessary to do it through
+% |\put| command.
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% \subsection{The red service grid}
+% \subsection{The colored service grid}
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% The next command is handy for debugging while editing one's
-% drawing; it draws a red grid with square meshes that are ten drawing
-% units apart; there is no graduation along the grid, since it is
-% supposed to be a debugging aid and users should know what they are
-% doing; nevertheless it is advisable to displace the grid by means of a
-% |\put| command so that its grid lines coincide with graph
-% coordinates that are multiples of~10. Missing to do so the readings
-% become cumbersome. The |\RoundUp| macro provides to increase the
-% grid dimensions to integer multiples of~ten.
-% Actually the new definition of this command does not need a |put|
-% command (although it is not prohibited to use it) because its syntax
-% now is the following one
-%\begin{flushleft}
-%\cs{GraphGrid}\parg{ll corner offset}\parg{grid dimensions}
-%\end{flushleft}
-% where the first argument is optional: if it is missing, the lower
-% left corner is put at the origin of the canvas coordinates. Of course
-% also the lower left corner offset is recommended to be specified with
-% coordinates that are integer multiples of~10; this is particularly
-% important when the |picture| environment offset is specified with non
-% integer multiple of~10 values.
-% Actually, since both arguments are delimited with round parentheses,
-% a single argument is assumed to contain the grid dimensions, while
-% if both arguments are given, the first one is the lower left corner
-% offset, and the second one the grid dimensions.
+% The next command is handy for debugging while
+% editing one's drawing; it draws a red grid with
+% square meshes that are ten drawing units apart;
+% there is no graduation along the grid, since it
+% is supposed to be a debugging aid and users
+% should know what they are doing. The corner
+% displacement does not need to be with
+% coordinates multiples of !0; the new version of
+% |curve2e| draws the square inner grid lines so
+% as according to the dimensions of the grid
+% squares (10~|\unitlength| apart) the
+% interior line may coincide only with the
+% square median line, or there are four lines
+% apart, or, besides a thicker median line, there
+% are lines 1~|\unitlength| apart, just as in a
+% normal technical millimetre drawing paper. The
+% syntax id the following
+%\begin{Sintassi}
+%\cs{GraphGrid}\parg{picture dimensions}\parg{corner offset} \oarg{color}
+%\end{Sintassi}
+% where the first argument is mandatory, while
+% the second and the third ones are optional.
+% The default value for the \meta{color} argument
+% is ‘red’; if another color is preferred,
+% it must be chosen among the relatively light
+% ones, in order to avoid confusion with the real
+% drawing elements. The second argument plays the
+% same role as the second optional argument of
+% the |picture| environment; it is the offset of
+% the lower left picture corner with respect to
+% the origin of the coordinates.
%
-% In order to render the red grid a little more automatic, a subsidiary
-% service macro of the |picture| environment has been redefined in order
-% to store the coordinates of the lower left and upper right corners
-% of the canvas (the compulsory dimensions and the optional lower left
-% corner shift arguments to the |picture| opening statement) in two
-% new variables, so that when the user specifies the (non vanishing)
-% dimensions of the canvas, the necessary data are already available
-% and there is no need to repeat them to draw the grid. The new
-% argument-less macro is named |\AutoGrid|, while the complete
-% macro is |\GraphGrid| that requires its arguments as specified
-% above. The advantage of the availability of both commands,
-% consists in the fact that |\AutoGrid| covers the whole canvas,
-% while |\GraphGrid| may compose a grid that covers either the whole
-% canvas or just a part of it. In both cases, though, it is necessary
-% the all the canvas coordinates are specified as multiples of 10
-% (|\unitlength|s). This is simple when |\GraphGrid| is used, while
-% with |\AutoGrid| the specification is in the opening environment
-% statement; and such multiples of 10 might not be the best ones
-% for the final drawing and should be fine tuned after finishing
-% the drawing and the grid is not necessary anymore.
-% The actual |\AutoGrid| command definition accepts two parenthesis
-% delimited arguments, that are not being used in the macro expansion;
-% in this way it is easier to replace |\GraphGrid| with |\AutoGrid| if
-% it is desired to do so. The opposite action, of course is not so simple
-% if the |\AutoGrid| command is not followed by one or two arguments
-% as |\GraphGrid| requires. Approximately |\AutoGrid| may be viewed as
-% a |\GraphGrid| version were both arguments are optional.
+% If the second argument is missing, the lower
+% left corner is put at the origin of the canvas
+% coordinates. Of course also the lower left
+% corner offset is recommended to be specified
+% with coordinates that are integer values.
+% Actually, since both arguments are delimited
+% with round parentheses, a single argument is
+% assumed to contain both comma separated grid
+% dimensions.
+%
+% In order to render the coloured grid a little
+% more automatic, a subsidiary service macro of
+% the |picture| environment has been redefined in
+% order to store the coordinates of the canvas
+% dimensions and of the lower left corner offset
+% (the compulsory dimensions and the optional
+% lower left corner shift arguments to the
+% |picture| opening statement) in two new
+% variables, so that when the user specifies the
+% (non vanishing) dimensions of the canvas, the
+% necessary data are already available and there
+% is no need to repeat them to draw the grid.
+%
+% The new argument-less macro is named
+% |\AutoGrid|, while the complete macro is
+% |\GraphGrid| that requires its arguments as
+% specified above. The advantage of the
+% availability of both commands, consists in the
+% fact that |\AutoGrid| covers the whole canvas,
+% while |\GraphGrid| may compose a grid that
+% covers either the whole canvas or just a part of
+% it. In both cases, though, it is necessary the
+% all the canvas coordinates are specified as
+% integer values, better if multiples of 10
+% (|\unitlength|s), but not mandatory. This is
+% simple when |\GraphGrid| is used, while with
+% |\AutoGrid| the default specification are
+% already contained in the opening environment
+% statement.
+%
+% Nevertheless even |\AutoGride| accepts both
+% parameters as optional round parentheses
+% delimited arguments. |\AutoGrid| differs from
+% |\GraphGrid| only on the fact thay its
+% arguments are both optional, while for
+% |\GraphGrid| the first argument is mandatory;
+% therefore very often it is possibile to
+% substitute |\GraphGrid| with |\AutoGrid|, while
+% the opposite is forbidden unless at least the
+% first optional argument is specified.
+%
+% The |AutoGrid| syntax is almost identical to
+% the one of |\GraphGrid|:
+%\begin{Sintassi}
+%\cs{GrAutoGrid}\parg{picture dimensions}\parg{corner offset} \oarg{color}
+%\end{Sintassi}
% \begin{macrocode}
\def\@picture(#1,#2)(#3,#4){%
- \edef\pict at urcorner{#1,#2}% New statement
- \edef\pict at llcorner{#3,#4}% New statement
+ \edef\pict at dimen{#1,#2} % New 2.4.0
+ \edef\pict at offset{#3,#4}% New 2.4.0
\@picht#2\unitlength
\setbox\@picbox\hb at xt@#1\unitlength\bgroup
\hskip -#3\unitlength
\lower #4\unitlength\hbox\bgroup
\ignorespaces}
+
+% \end{macrocode}
+% In order to draw grids with differently spaced
+% grid lines, a single |\griglia| command
+% (“griglia” stands for ”grid”, but it is less
+% likely common to other packages control
+% sequences and is similar to the English word)
+% This command syntax is the following:
+% \begin{Sintassi}
+%\cs{griglia}\marg{line thickness}\marg{inter line space} \oarg{color}
+% \end{Sintassi}
+% The main grid squares are 10 units apart, and
+% are always drawn on the canvas; the internal
+% lines are at specified 5, or 2, or 1 units
+% apart; suitable tests are made by the main grid
+% macro to use this or that spacing. The control
+% sequences with upper case initials in the
+% following definition contain values computed by
+% the main macro; those with lowercase initials
+% are local values. The computations made with
+% the |\fpeval| function are a way to compute
+% integer multiples of 10, 5, 2, and 1, the
+% spacing values for the horizontal and vertical
+% grid lines. Notice that if users prefer to have
+% the grid contain just the main lines 10 units
+% apart, before activating the grid drawing by
+% means of |\AutoGrid| or |\GraphGrid|, they can
+% specify |\noinnerlines| and the inner lines are
+% skipped in that particular |picture|
+% environment; if they specify |\noinnerlines|
+% right after the |\begin{document}| statement,
+% this setting becomes global and no |picture|
+% environment is going to contain any inner lines.
+% \begin{macrocode}
+\newif\ifinnerlines \let\ifinnerlines\iftrue
+\def\noinnerlines{\let\ifinnerlines\iffalse}
+
+\newcommand\griglia[2]{%
+\linethickness{#1\p@}%
+\edef\ggllx{\Goffx}
+\fpdowhile{\ggllx!>\GridWd}{%
+\fptest{\ggllx=\fpeval{#2*(round(\ggllx/#2,0))}}%
+{\segment(\ggllx,\Goffy)(\ggllx,\GridHt)}{\relax}%
+\edef\ggllx{\fpeval{\ggllx+#2}}}%
%
-\def\Gr at phGrid(#1,#2){\bgroup\textcolor{red}{\linethickness{.1\p@}%
-\RoundUp#1modulo10to\@GridWd \RoundUp#2modulo10to\@GridHt
-\@tempcnta=\@GridWd \divide\@tempcnta10\relax \advance\@tempcnta\@ne
-\multiput(0,0)(10,0){\@tempcnta}{\line(0,1){\@GridHt}}%
-\@tempcnta=\@GridHt \divide\@tempcnta10\advance\@tempcnta\@ne
-\multiput(0,0)(0,10){\@tempcnta}{\line(1,0){\@GridWd}}\thinlines}%
+\edef\gglly{\Goffy}
+\fpdowhile{\gglly!>\GridHt}{%
+\fptest{\gglly=\fpeval{#2*(round(\gglly/#2,0))}}%
+{\segment(\Goffx,\gglly)(\GridWd,\gglly)}{\relax}
+\edef\gglly{\fpeval{\gglly+#2}}}}
+
+% \end{macrocode}
+% The grid main macro comes next. The first 6
+% lines of its code are used to get the
+% properties of the grid, as the grid colour, and
+% computes the fixed elements such as the single
+% coordinates of the canvas, the actual
+% coordinates of its box relative to the offset
+% canvas lower left corner. Such values are
+% independent of the grid line density. The
+% following macros use the |\griglia| macro to
+% draw each set of grid lines of the proper
+% thickness, when the actual dimensions are
+% taken into account.
+% \begin{macrocode}
+\NewDocumentCommand\Gr at phGrid{d() d()}{\bgroup
+\color{\GridColor}
+\edef\Gdim{#1}\edef\Goff{#2}
+\GetCoord(\Gdim)\Gllx\Glly
+\GetCoord(\Goff)\Goffx\Goffy
+\edef\GridWd{\fpeval{\Gllx+\Goffx}}%
+\edef\GridHt{\fpeval{\Glly+\Goffy}}%
+%
+\griglia{1.0}{10}
+%
+\ifinnerlines
+ \griglia{0.70}{5}%
+ \unless\ifdim \unitlength < 1mm
+ \griglia{0.70}{5}%
+ \griglia{0.35}{1}%
+ \fi
+\fi
+\egroup
+\ignorespaces}
+
+% \end{macrocode}
+% Eventually the user macros |\AutoGrid| and
+% |\GrapgGrid| macros are defined. Their
+% definitions are almost identical, the only
+% difference being the fact that their first
+% arguments era optional for the first macro and
+% mandatory for the second one. The mandatory
+% and optional arguments are assigned the initial
+% default values, as defined by the |picture|
+% opening statement arguments. In facts, due to
+% the agility of the |\AutoGrid| macro, one may
+% wonder if the other macro has to be defined;
+% Its utility is mainly for backwards
+% compatibility. Nevertheless the companion
+% document \textsf{curve2e-manual} displays a few
+% examples where |\GraphGrid| is used, just to
+% show its usage.
+% \begin{macrocode}
+\NewDocumentCommand\AutoGrid%
+{D(){\pict at dimen} D(){\pict at offset} O{cyan!50!white}}{\bgroup
+\def\GridColor{#3}%
+\put(0,0){\Gr at phGrid(#1)(#2)}%
\egroup\ignorespaces}
-\NewDocumentCommand\AutoGrid{d() d()}{\bgroup%
-\put(\pict at llcorner){\expandafter\Gr at phGrid\expandafter(\pict at urcorner)}%
+\NewDocumentCommand\GraphGrid%
+{R(){\pict at dimen} D(){\pict at offset} O{cyan!50!white}}
+{\bgroup
+\def\GridColor{#3}%
+\put(#2){\Gr at phGrid(#1)(#2)}%
\egroup\ignorespaces}
-
-\NewDocumentCommand\GraphGrid{r() d()}{%
-\IfValueTF{#2}{\put(#1){\Gr at phGrid(#2)}}%
- {\put(0,0){\Gr at phGrid(#1)}}}
-
% \end{macrocode}
-% Rounding up is useful because also the grid margins fall on coordinates
-% multiples of~10.
+% For backwards compatibility we keep the macro
+% used to round up the grid margins coordinates
+% to multiples of~10.
% \begin{macrocode}
\def\RoundUp#1modulo#2to#3{\edef#3{\fpeval{(ceil(#1/#2,0))*#2}}}%
%
% \end{macrocode}
-% The |\Integer| macro takes a possibly fractional number whose decimal
-% separator, if present, \textit{must} be the decimal point and uses the
-% point as an argument delimiter. If one has the doubt that the number
-% being passed to |\Integer| might be an integer, he/she should call the
-% macro with a further point; if the argument is truly integer this point
-% works as the delimiter of the integer part; if the argument being
-% passed is fractional this extra point gets discarded as well as the
-% fractional part of the number. This maro used to be used within the
-% definition of |\RoundUp|; with the |xfp| facilities the latter macro
-% does not need it any more, but it continues to be used in several other
+% The next |\Integer| macro takes a possibly
+% fractional numeric argument whose decimal
+% separator, if present, \textit{must} be the
+% decimal point and uses the point as an argument
+% delimiter. If users have the doubt that the
+% number being passed to |\Integer| might be an
+% integer, they should call the macro with a
+% further point; if the argument is truly integer
+% this point works as the delimiter of the
+% integer part; if the argument being passed is
+% fractional this extra point gets discarded as
+% well as the fractional part of the number. This
+% macro was used within the definition of
+% |\RoundUp|; with the |xfp| facilities the
+% latter macro does not need it any more, but
+% it continues to be used in several other
% macros.
% \begin{macrocode}
\def\Integer#1.#2??{#1}%
+
% \end{macrocode}
%
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \section{Labelling the graphical elements}
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% While drawing any thing with the \pack{curve2e} package, it might be
-% necessary to identify some graphical objects with some sort of “label”.^^A
-%\footnote{Do not confuse this identifier label with the \cs{label}
-% command.}
+%
+% While drawing anything with the \pack{curve2e}
+% package, it might be necessary to identify some
+% graphical objects with some sort of “label”.^^A
+%\footnote{Do not confuse this identifier label
+% with the \cs{label} command.}
%
-% Some commands such as \cs{legenda} (legend), \cs{Zbox}, and \cs{Pbox}
-% have been always used in the documentation of this package and its
-% siblings; but we used them in many other documents; therefore we
-% thought it was useful to have them available with the general user of
+% Some commands such as \cs{legenda}
+% (\emph{legend}), \cs{Zbox}, and \cs{Pbox} have
+% been always used in the documentation of this
+% package and its siblings; but we used them in
+% many other documents; therefore we thought it
+% was useful to have them available to any user of
% \pack{curve2e}.
%
%Their commands follow the following syntax.
-%\begin{flushleft}\ttfamily\obeylines
+%\begin{Sintassi}
%|\Pbox|\parg{coordinates}\oarg{position}\marg{formula}\oarg{dot diameter}\meta{\texttt{*}}\aarg{angle}
%|\Zbox|\parg{coordinates}\oarg{position}\marg{formula}\oarg{dot diameter}
%|\legenda|\parg{coordinates}\marg{formula}
-%\end{flushleft}
+%\end{Sintassi}
%
-% These commands have similar but different functionalities; the most
-% general one is |\Pbox|, while the others are simplified versions that
-% have a simpler syntax, and a subset of the |\Pbox| functionalities.
-% While we describe the arguments of |\Pbox| we emphasise the small
-% differences with the other two commands.
+% These commands have similar but different
+% functionalities; the most general one is
+% |\Pbox|, while the others are simplified
+% versions that have a simpler syntax, and a
+% subset of the |\Pbox| functionalities. While we
+% describe the arguments of |\Pbox| we emphasise
+% the small differences with the other two
+% commands.
%\begin{description}
-%\item[\meta{coordinates}] are the coordinates (explicit, or in vector
-% form) of the reference point of the “label”; for |\legenda| it is the
-% lower left corner of the framed legend contents. They are delimited
-% with the usual matched parentheses, and their default value is
-% \texttt{(0,0)}, therefore either users specify other coordinates,
-% or use the |\put| command to place the legend where they prefer.
+%\item[\meta{coordinates}]
+% are the coordinates (explicit, or in vector
+% form) of the reference point of the “label”;
+% for |\legenda| it is the lower left corner of
+% the framed legend contents. They are delimited
+% with the usual matched parentheses, and their
+% default value is \texttt{(0,0)}, therefore
+% either users specify other coordinates, or use
+% the |\put| command to place the legend where
+% they prefer.
%
-%\item[\meta{position}] is the optional position of the reference point
-% relative to the “label” contents: this means that if the “label”
-% should be NE relative to the visible (or invisible) dot it labels,
-% the \meta{position} codes should be \texttt{tr} (top and right); the
-% default \meta{position} is \texttt{cc} so that
-% the “label” is vertically and horizontally centred at the reference
-% point; actually these position parameters should always be specified if
-% the dot diameter is positive (therefore visible), otherwise the
-% “label” and the dot overwrite each other.
-%%
-%\item[\meta{formula}] may be almost anything; \meta{formula} means
-% that the argument is typeset in math mode; if some text is desired
-% the argument must be surrounded by a matched couple of dollar signs;
-% in any case it is possible to enter text mode by using a box (for example through a |\hbox| or a |\parbox|) so that actually this
-% mandatory argument may contain almost anything.
-%%
-%\item[\meta{dot diameter}] the dot diameter default value is positive;
-% for |\Zbox| this parameter equals |1\unitlength|, while for |\Pbox|
-% it equals \texttt{0.5ex}; the user should be careful in
-% modifying this value; but if the dot diameter is set to zero, the
-% dot is absent and the |\Zbox| command behaves almost as an unframed
-% legend. The small difference is that |\Zbox| accepts a \meta{position}
-% parameter while the |\legend| command does not.
-%%
-%\item[\meta{\texttt{*}}] is an optional star; if specified the
-% “label” is framed with a visible border, otherwise it is framed
-% with an invisible one but with a blank gap that tries to
-% adjust its thickness so that the “label” is always at the same distance
-% from the reference point; if this reference point corresponds to
-% a box corner it thickness is reduced by approximately a factor equal to
-% $\sqrt{0.5}$, in oder to take into account the diagonal of the
-% blank gap angle.
-%%
-%\item[\meta{angle}] is the rotation angle (in degrees) of the “label”
-% about its reference point; sometimes such “labels” have to be
-% rotated 90° anticlockwise; sometimes they need a positive or
-% negative rotation angle in order to match the general direction of
-% the “labelled” object, be it an oblique line, an axis, or whatever.
-% We found it very useful also to label the cartesian axes, but
-% also in other situations. For example, in order to label the $x$ axis
-% the |\Pbox| command might have the arrow tip coordinates for the
-% reference point and have \texttt{tr} for the \meta{position};
-% for the $y$ axis, the reference point is again the arrow tip,
-% and the position would be again \texttt{tr} if the “label”
-% sits on the left of the axis.
+%\item[\meta{position}]
+% is the optional position of the reference point
+% relative to the “label” contents: this means
+% that if the “label” should be NE (North East)
+% relative to the visible (or invisible) dot it
+% labels, the \meta{position} codes should be
+% \texttt{tr} (top right); the default
+% \meta{position} is \texttt{cc} so that the
+% “label” is vertically and horizontally centred
+% at the reference point; actually these position
+% parameters should always be specified if
+% the dot diameter is positive (therefore
+% visible), otherwise the “label” and the dot
+% overwrite each other.
+%
+%\item[\meta{formula}]
+% may be almost anything; \meta{formula} means
+% that the argument is typeset in math mode; if
+% some text is desired the argument must be
+% surrounded by a matched couple of dollar signs;
+% in any case it is possible to enter text mode by
+% using a box (for example through a |\hbox| or a
+% |\parbox|) so that actually this mandatory
+% argument may contain almost anything.
+%
+%\item[\meta{dot diameter}] the dot diameter
+% default value is positive; for |\Zbox| this
+% parameter equals |1\unitlength|, while for
+% |\Pbox| it equals \texttt{0.5ex}; the user
+% should be careful in modifying this value; but
+% if the dot diameter is set to zero, the dot is
+% absent and the |\Zbox| command behaves almost as
+% an unframed legend. The small difference is that
+% |\Zbox| accepts a \meta{position} parameter
+% while the |\legend| command does not.
+%
+%\item[\meta{\texttt{*}}] is an optional star; if
+% specified the “label” is framed with a visible
+% border, otherwise it is framed with an invisible
+% one but with a blank gap that tries to adjust
+% its thickness so that the “label” is always at
+% the same distance from the reference point; if
+% this reference point corresponds to a box corner
+% it thickness is reduced by approximately a
+% factor equal to $\sqrt{0.5}$, in oder to take
+% into account the diagonal of the blank gap
+% angle.
+%
+%\item[\meta{angle}] is the rotation angle (in
+% degrees) of the “label” about its reference
+% point; sometimes such “labels” have to be
+% rotated 90° anticlockwise; sometimes they need a
+% positive or negative rotation angle in order to
+% match the general direction of the “labelled”
+% object, be it an oblique line, an axis, or
+% whatever. We found it very useful also to
+% label the cartesian axes, but also in other
+% situations. For example, in order to label the
+% $x$ axis the |\Pbox| command might have the
+% arrow tip coordinates for the reference point
+% and have \texttt{tr} for the \meta{position};
+% for the $y$ axis, the reference point is again
+% the arrow tip, and the position would be again
+% \texttt{tr} if the “label” sits on the left of
+% the axis.
%\end{description}
%
% \begin{macrocode}
@@ -1468,9 +1789,9 @@
\put(#1){\rotatebox{#6}{\makebox(0,0){%
\settowidth\PbDim{#2}%
\edef\Rapp{\fpeval{\PbDim/{1ex}}}%
-\fptest{\Rapp > 1.5}{\fboxsep=0.5ex}{\fboxsep=0.75ex}%
+\fptest{\Rapp>1.5}{\fboxsep=0.5ex}{\fboxsep=0.75ex}%
\IfBooleanTF{#5}{\fboxrule=0.4pt}{\fboxrule=0pt}%
-\fptest{#4 = 0sp}%
+\fptest{#4=0sp}%
{\makebox(0,0)[#2]{\fbox{$\relax#3\relax$}}}%
{\edef\Diam{\fpeval{(#4)/\unitlength}}%
\makebox(0,0){\circle*{\Diam}}%
@@ -1485,119 +1806,180 @@
\providecommand\legenda{}
\newbox\legendbox
-\RenewDocumentCommand\legenda{ D(){0,0} m}{\put(#1){%
+\RenewDocumentCommand\legenda{D(){0,0} m}{\put(#1){%
\setbox\legendbox\hbox{$\relax#2\relax$}%
- \edef\@tempA{\fpeval{(\wd\legendbox + 3\p@)/\unitlength}}%
+ \edef\@tempA{\fpeval{(\wd\legendbox+3\p@)/\unitlength}}%
\edef\@tempB{\fpeval{(\ht\legendbox+\dp\legendbox+3\p@)/\unitlength}}%
\framebox(\@tempA,\@tempB){\box\legendbox}}\ignorespaces}
% \end{macrocode}
-% With the above labelling facilities and with use of the \pack{xfp}
-% functionalities it is not difficult to create diagrams with linear
-% or logarithmic axes. In effects the \pack{graphpaper} class uses
-% these labelling macros and several other ones.
+% With the above labelling facilities and with use
+% of the \pack{xfp} functionalities it is not
+% difficult to create diagrams with linear or
+% logarithmic axes. In effects the
+% \pack{graphpaper} class uses these labelling
+% macros and several other ones.
+%
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \section{Math operations on fractional operands}
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% This is not the place to complain about the fact that all programs of
-% the \TeX\ system use only integer arithmetics; now, with the 2018
-% distribution of the modern \TeX\ system, package |xfp| is available:
-% this package resorts in the background to language \LaTeX\,3; with this
-% language now it is possible to compute fractional number operations; the
-% numbers are coded in decimal, not in binary, and it is possible also to
-% use numbers written as in computer science, that is as a fractional,
-% possibly signed, number followed by an expression that contains the
-% exponent of~10 necessary to (ideally) move the fractional separator
-% in one or the other direction according to the sign of the exponent
-% of~ 10; in other words the L3 library for floating point calculations
-% accepts such expressions as \texttt{123.456}, \texttt{0.12345e3}, and
-% \texttt{12345e-3}, and any other equivalent expression. If the first
-% number is integer, it assumes that the decimal separator is to the
-% right of the rightmost digit of the numerical string.
+% This is not the place to complain about the fact
+% that all programs of the \TeX\ system use only
+% integer arithmetics; now, with the 2018
+% distribution of the modern \TeX\ system,
+% package |xfp| is available: this package resorts
+% in the background to language \LaTeX\,3; with
+% this language now it is possible to compute
+% fractional number operations; the numbers are
+% coded in decimal notation, not in binary one,
+% and it is possible also to use numbers written
+% as in computer science, that is as a fractional,
+% possibly signed, number followed by an
+% expression that contains the exponent of~10
+% necessary to (ideally) move the fractional
+% separator in one or the other direction
+% according to the sign of the exponent of~ 10; in
+% other words the L3 library for floating point
+% calculations accepts such expressions as
+% \texttt{123.456}, \texttt{0.12345e3}, and
+% \texttt{12345e-3}, and any other equivalent
+% expression. If the first number is integer, it
+% assumes that the decimal separator is to the
+% right of the rightmost digit of the numerical
+% string.
%
-% Floating point calculations may be done through the |\fpeval| L3
-% function with a very simple syntax:
-% \begin{flushleft}
+% Floating point calculations may be done through
+% the |\fpeval| L3 function with a very simple
+% syntax:
+% \begin{Sintassi}
% \cs{fpeval}\marg{mathematical expression}
-% \end{flushleft}
-% where \meta{mathematical expression} can contain the usual algebraic
-% operation sings, |`+' - * / ** ^| and the function names of the most
-% common algebraic, trigonometric, and transcendental functions; for
-% direct and inverse trigonometric functions it accepts arguments in
-% radians and in sexagesimal degrees; it accepts the group of
-% rounding/truncating operators; it can perform several kinds of
-% comparisons; as to now (Nov. 2019) the todo list includes the direct
-% and inverse hyperbolic functions. The mantissa length of the floating
-% point operands amounts to~16 decimal digits. Further details may be
-% read in the documentations of the |xfp| and |interface3| packages, just
-% by typing into a command line window the command \texttt{texdoc
-% \meta{document}}, where \meta{document} is just the name of the above
-% named files without extension.
+% \end{Sintassi}
+% where \meta{mathematical expression} can contain
+% the usual algebraic operation sings,
+% |`+' - * / ** ^| and the function names of the
+% most common algebraic, trigonometric, and
+% transcendental functions; for direct and inverse
+% trigonometric functions it accepts arguments in
+% radians and in sexagesimal degrees; it accepts
+% the group of rounding/truncating operators; it
+% can perform several kinds of comparisons; as to
+% now (Nov. 2019) the todo list includes the
+% direct and inverse hyperbolic functions. The
+% mantissa length of the floating point operands
+% amounts to~16 decimal digits. Further details
+% may be read in the documentations of the |xfp|
+% and |interface3| packages, just by typing into a
+% command line window the command \texttt{texdoc
+% \meta{document}}, where \meta{document} is just
+% the name of the above named files without the
+% need of stating the extension.
%
-% Furthermore we added a couple of interface macros with the
-% internal L3 floating point functions; |\fptest| and |\fpdowhile|.
-% They have the following syntax:
-%\begin{flushleft}\ttfamily\obeylines
+% Furthermore we added a few interface macros with
+% the internal L3 floating point functions;
+% |\fptest| and |\fpdowhile|. They have the
+% following syntax.
+%\begin{Sintassi}\ttfamily\obeylines
% \string\fptest\marg{logical expression}\marg{true code}\marg{false code}
+% \string\fptestT\marg{logical expression}\marg{true code}
+% \string\fptestF\marg{logicalexpression}\marg{false code}
% \string\fpdowhile\marg{logical expression}\marg{code}
-%\end{flushleft}
-% The \meta{logical expression} compares the values of any kind by means
-% of the usual \texttt{>}, \texttt{=}, and \texttt{<} operators that may
-% be negated with the “not’ operator \texttt{!}; furthermore the logical
-% results of these comparisons may be acted upon with the “and” operator
-% \texttt{\&\&} and the “or” operator \texttt{\string|\string|}.
-% The \meta{true code}, and \meta{code} are executed if or while the
-% \meta{logical expression} is true, while the \meta{false code} is
-% executed if the \meta{logical expression} is false
+%\end{Sintassi}
+% The \meta{logical expression} compares
+% numerical values of any kind by means of the
+% usual \texttt{>}, \texttt{=}, and \texttt{<}
+% operators that may be negated with the “not”
+% operator \texttt{!}; furthermore the logical
+% results of these comparisons may be acted upon
+% with the “and” operator \texttt{\&\&} and the
+% “or” operator \texttt{\string|\string|}.
+% The \meta{true code}, and \meta{code} are
+% executed if or while the \meta{logical
+% expression} is true, while the \meta{false code}
+% is executed if the \meta{logical expression}
+% is false
%
-% Before the availability of the |xfp| package, it was necessary to fake
-% fractional number computations by means of the native e-\TeX\ commands
-% |\dimexpr|, i.e. to multiply each fractional number by the unit |\p@|
-% (1\,pt) so as to get a length; operate on such lengths, and then
-% stripping off the `pt' component from the result; very error prone and
-% with less precision as the one that the modern decimal floating point
-% calculations can do. Of course it is not so important to use fractional
-% numbers with more that 5 or 6 fractional digits, because the other
-% \TeX\ and \LaTeX\ macros cannot handle them, but it is very convenient
-% to have simpler and more readable code. We therefore switched to the
-% new floating point functionality, even if this maintains the |curve2e|
-% functionality, but renders this package unusable with older \LaTeX\
-% kernel installations. It has already been explained that the input of
-% this up-to-date version of |curve2e| is aborted if the |xfp| package is
-% not available, but the previous version 1.61 version is loaded in its
-% place; very little functionality is lost, but, evidently, this new
-% version performs in a better way.
+% This package defines Some other advanced
+% commands, although they are not used for
+% drawing; they might be useful for some users.
+% They are |\Modulo|, |\Ifodd|, |\IfEqual|; namely
+% the function to compute the expression
+% $x= a \mod b$, in other words the remainder of
+% the integer quotient of $a/b$; the equivalent of
+% the native command |\ifodd| with the difference
+% that it can test directly an integer expression;
+% similarly |\IfEqual| extends the functionality
+% of the native command |\ifx|, but can compare
+% any kind of tokens; they are all robust commands
+% while the original tests are fragile.
%
+% Before the availability of the |xfp| package, it
+% was necessary to fake fractional number
+% computations by means of the native e-\TeX\
+% commands |\dimexpr|, i.e. to multiply each
+% fractional number by the unit |\p@| (1\,pt) so
+% as to get a length; operate on such lengths, and
+% then stripping off the `pt' component from the
+% result; very error prone and with less
+% precision as the one that the modern decimal
+% floating point calculations can do. Of course it
+% is not so important to use fractional numbers
+% with more than 5 or 6 fractional digits,
+% because the other \TeX\ and \LaTeX\ macros
+% cannot handle them, but it is very convenient to
+% have simpler and more readable code. We
+% therefore switched to the new floating point
+% functionality, even if this maintains the
+% |curve2e| functionality, but renders this
+% package unusable with older \LaTeX\ kernel
+% installations. It has already been explained
+% that the input of this up-to-date version of
+% |curve2e| is aborted if the |xfp| package is not
+% available, but the previous 1.61 version is
+% loaded in its place; very little functionality
+% is lost, but, hopefully, this new version
+% performs in a better way.
%
+%
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{The division macro}
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% The most important macro is the division of two fractional numbers; we
-% seek a macro that gets dividend and divisor as fractional numbers and
-% saves their ratio in a macro; this is done in a simple way with the
-% following code.
+% The most important macro is the division of two
+% fractional numbers; we seek a macro that gets
+% dividend and divisor as fractional numbers and
+% saves their ratio in a macro; this is done in a
+% simple way with the following code.
% \begin{macrocode}
\def\DividE#1by#2to#3{\edef#3{\fpeval{#1 / #2}}}
% \end{macrocode}
-% In order to avoid problems with divisions by zero, or with numbers that
-% yield results too large to be used as multipliers of lengths, it would
-% be preferable that the above code be preceded or followed by some tests
-% and possible messages. Actually we decided to avoid such tests and
-% messages, because the internal L3 functions already provide some. This
-% was done in the previous versions of this package, when the |\fpeval|
-% L3 function was not available.
+% In order to avoid problems with divisions by
+% zero, or with numbers that yield results too
+% large to be used as multipliers of unit lengths,
+% it would be preferable that the above code be
+% preceded or followed by some tests and possible
+% messages.
+% Actually we decided to avoid such tests and
+% messages, because the internal L3 functions
+% already provide some. This was done in the
+% previous versions of this package, when the
+% |\fpeval| L3 function was not available.
%
-% Notice that operands |#1| and |#2| may be integer numbers or
-% fractional, or mixed numbers. They may be also dimensions, but while
-% dimensions in printer points (72.27pt=1in) are handled as assumed, when
-% different units are used, the length must be enclosed in parentheses:
+% Notice that operands |#1| and |#2| may be
+% integer numbers or fractional, or mixed numbers.
+% They may be also dimensions: in this case our
+% function |\fpeval| treats the unit symbols as
+% special numerical constants that transform the
+% dimensions into typographical points; for
+% example |mm| is the (dimensionless) ratio of
+% two lengths
+%$1\mathrm{pt}/1\mathrm{mm}=(72{,}27\mathrm{pt/in})/(25{,}4\mathrm{mm/in})=2{,}84527559055118$;
+% therefore both expressions
%\begin{verbatim}
-%\DividE(1mm)by(3mm) to\result
+%\DividE(1mm)by(3mm)to\result
+%\Divide 1mm by 3mm to\result
%\end{verbatim}
-% yields correctly |\result=0.33333333|. Without parentheses the result
-% is unpredictable.
+% yield correctly |\result=0.33333333|.
%
% For backwards compatibility we need an alias.
% \begin{macrocode}
@@ -1604,51 +1986,49 @@
\let\DivideFN\DividE
% \end{macrocode}
%
-% We do the same in order to multiply two integer o fractional numbers
-% held in the first two arguments and the third argument is a definable
-% token that will hold the result of multiplication in the form of a
-% fractional number, possibly with a non null fractional part; a null
-% fractional part is stripped away
+% We do the same in order to multiply two integer
+% or fractional numbers held in the first two
+% arguments, and the third argument is a definable
+% token that will hold the result of
+% multiplication in the form of a fractional
+% number, possibly with a non null fractional
+% part; a null fractional part is stripped off.
% \begin{macrocode}
\def\MultiplY#1by#2to#3{\edef#3{\fpeval{#1 * #2}}}\relax
\let\MultiplyFN\MultiplY
% \end{macrocode}
-% but with multiplication it is better to avoid computations with
-% lengths.
+% but with multiplication it is better to avoid
+% computations with lengths.
%
-% The next macro uses the |\fpeval| macro to get
-% the numerical value of a measure in points. One has to call |\Numero|
-% with a control sequence and a dimension, with the following syntax;
-% the dimension value in points is assigned to the control sequence.
-%\begin{flushleft}
-%\cs{Numero}\meta{control sequence}\meta{dimension}
-%\end{flushleft}
+% The next macro uses the |\fpeval| macro to get
+% the numerical value of a measure in points. One
+% has to call |\Numero| with a control sequence
+% and a dimension, with the following syntax; the
+% dimension value in points is assigned to the
+% control sequence.
+%\begin{Sintassi}
+%\cs{Numero}\meta{control sequence result}\meta{dimension}
+%\end{Sintassi}
% \begin{macrocode}
-\unless\ifdefined\Numero
- \def\Numero#1#2{\edef#1{\fpeval{round(#2,6)}}\ignorespaces}%
-\fi
+\providecommand\Numero[2]{\edef#1{\fpeval{round(#2,6)}}}
% \end{macrocode}
-% The numerical value is rounded to 6 fractional digits that are more
-% than sufficient for the graphical actions performed by |curve2e|.
+% The numerical value is rounded to 6 fractional
+% digits that are more than sufficient for the
+% graphical actions performed by |curve2e|.
%
-% The |\ifdefined| primitive command is provided by the e-\TeX\
-% extension of the typesetting engine; the test does not create any hash
-% table entry; it is a different way than the
-% \verb|\ifx\csname...\endcsname| test,
-% because the latter first possibly creates a macro meaning \verb|\relax|
-% then executes the test; therefore an undefined macro name is always
-% defined to mean |\relax|.
-%
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Trigonometric functions}
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% We now start with trigonometric functions. In previous versions of
-% this package we defined the macros |\SinOf|, |\CosOf| and |\TanOf|
-% (|\CotOf| did not appear so essential) by means of the parametric
-% formulas that require the knowledge of the tangent of the half angle.
-% We wanted, and still want, to specify the angles in sexagesimal
-% degrees, not in radians, so that accurate reductions to the main
-% quadrants are possible. The bisection formulas are
+% We now start with trigonometric functions. In
+% previous versions of this package we defined the
+% macros |\SinOf|, |\CosOf|, and |\TanOf|
+% (|\CotOf| did not appear so essential)
+% by means of the parametric formulas that require
+% the knowledge of the tangent of the half angle.
+% We wanted, and still want, to specify the angles
+% in sexagesimal degrees, not in radians, so that
+% accurate reductions to the main quadrants are
+% possible. The bisection formulas are
% \begin{eqnarray*}
% \sin\theta &=& \frac{2}{\cot x + \tan x}\\
% \cos\theta &=& \frac{\cot x - \tan x}{\cot x + \tan x}\\
@@ -1658,28 +2038,36 @@
% \end{eqnarray*}
% is the half angle in degrees converted to radians.
%
-% But now, in this new version, the availability of the floating point
-% computations with the specific L3 library makes all the above
-% superfluous; actually the above approach gave good results but it was
-% cumbersome and limited by the fixed radix computations of the \TeX\
+% But now, in this new version, the availability
+% of the floating point computations with the
+% specific L3 library makes all the above
+% superfluous; actually the above approach gave
+% good results but it was cumbersome and limited
+% by the fixed radix computations of the \TeX\
% system programs.
%
-% Matter of facts, we compared the results (with 6 fractional digits) the
-% computations executed with the \texttt{sind} function name, in order to
-% use the angles in degrees, and a table of trigonometric functions with
-% the same number of fractional digits, and we did not find any
-% difference, not even one unit on the sixth decimal digit. Probably the
-% |\fpeval| computations, without rounding before the sixteenth
-% significant digit, are much more accurate, but it is useless to have a
-% better accuracy when the other \TeX\ and \LaTeX\ macros would not be
-% able to exploit them.
+% Matter of facts, we compared the results (with 6
+% fractional digits) of the computations executed
+% with the \texttt{sind} function name, in order
+% to use the angles in degrees, and a table of
+% trigonometric functions with the same number of
+% fractional digits, and we did not find any
+% difference, not even one unit on the sixth
+% decimal digit. Probably the |\fpeval|
+% computations, without rounding before the
+% sixteenth significant digit, are much more
+% accurate, but it is useless to have a higher
+% accuracy when the other \TeX\ and \LaTeX\
+% macros would not be able to exploit them.
%
-% Having available such powerful instrument, even the tangent appears to
-% be of little use for the kind of computations that are supposed to be
+% Having available such powerful instrument, even
+% the tangent appears to be of little use for the
+% kind of computations that are supposed to be
% required in this package.
%
-% The codes for the computation of |\SinOf| and |\CosOf| of the angle in
-% degrees is now therefore the following
+% The codes for the computation of |\SinOf| and
+% |\CosOf| of the angle in degrees is now
+% therefore the following
% \begin{macrocode}
\def\SinOf#1to#2{\edef#2{\fpeval{round(sind#1,6)}}}\relax
\def\CosOf#1to#2{\edef#2{\fpeval{round(cosd#1,6)}}}\relax
@@ -1686,250 +2074,317 @@
% \end{macrocode}
%
%
-% Sometimes the argument of a complex number is necessary; therefore with
-% macro \verb|\ArgOfVect| we calculate the four quadrant arctangent (in
-% degrees) of the given vector taking into account the sings of the
-% vector components. We use the |xfp| |atand| with two arguments, so
-% that it automatically takes into account all the signs for determining
-% the argument of vector $x,y$ by giving the values $x$ and $y$ in the
+% Sometimes the argument of a complex number is
+% necessary; therefore with macro |\ArgOfVect| we
+% calculate the four quadrant arctangent (in
+% degrees) of the given vector taking into account
+% the sings of the vector components. We use the
+% |xfp| |atand| with two arguments, so that it
+% automatically takes into account all the signs
+% for determining the argument of vector $x,y$ by
+% giving the values $x$ and $y$ in the
% proper order to the function |atan|:
%\[
%\mbox{if\quad } x + \mathrm{i}y = M\mathrm{e}^{\mathrm{i}\varphi}\mbox{\quad then\quad }
%\varphi = \mathtt{\string\fpeval\{atand(\mbox{$y$},\mbox{$x$})\}}
%\]
-% The |\ArgOfVect| macro receives on input a vector and determines its
-% four quadrant argument; it only checks if both vector components are
-% zero, because in this case nothing is done, and the argument is
-% assigned the value zero.
+% The |\ArgOfVect| macro receives on input a
+% vector and determines its four quadrant
+% argument; it only checks if both vector
+% components are zero, because in this case
+% nothing is done, and the argument is assigned
+% the value zero.
% \begin{macrocode}
\def\ArgOfVect#1to#2{\GetCoord(#1){\t at X}{\t at Y}%
-\fptest{\t at X=\z@ && \t at Y=\z@}{\edef#2{0}%
-\PackageWarning{curve2e}{Null vector}{Check your data\MessageBreak
-Computations go on, but the results may be meaningless}}{%
-\edef#2{\fpeval{round(atand(\t at Y,\t at X),6)}}}\ignorespaces}
+\fptest{\t at X=\z@&&\t at Y=\z@}{\edef#2{0}%
+\PackageWarning{curve2e}{Null vector}{%
+Check your data\MessageBreak
+Computations go on, but the results may be meaningless}%
+}{\edef#2{\fpeval{round(atand(\t at Y,\t at X),6)}}}%
+\ignorespaces}
% \end{macrocode}
-% Since the argument of a null vector is meaningless, we
-% set it to zero in case that input data refer to such a null vector.
-% Computations go on anyway, but the results may be meaningless; such
-% strange results are an indications that some controls on the code
+% Since the argument of a null vector is
+% meaningless, we set it to zero in case that
+% input data refer to such a null vector.
+% Computations go on anyway, but the results may
+% be meaningless; such strange results are an
+% indications that some controls on the code
% should be done by the user.
%
-% It is worth examining the following table, where the angles of nine
-% vectors $45^\circ$ degrees apart from one another are computed from
+% It is worth examining the following table, where
+% the angles of nine vectors $45^\circ$ degrees
+% apart from one another are computed by using
% this macro.
% \begin{center}
% \begin{tabular}{l*9r}
-% Vector &0,0 &1,0 &1,1 & 0,1 & -1,1& -1,0&-1,-1&0,-1&1,-1\\
+% Vector &0,\,0 &1,\,0 &1,\,1 & 0,\,1 & -1,\,1& -1,\,0&-1,\,-1&0, -1&1,\,-1\\
% Angle & 0 & 0 & 45 & 90 & 135 & 180 &-135 & -90& -45
% \end{tabular}
% \end{center}
-% Real computations with the |\ArgOfVect| macro produce those very
-% numbers without the need of rounding; |\fpeval| produces all trimming
-% of lagging zeros and rounding by itself.
+% Real computations with the |\ArgOfVect| macro
+% produce those very numbers without the need of
+% rounding; |\fpeval| produces by itself all the
+% necessary trimming of lagging zeros and the
+% result rounding.
%
%
%
-%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Arcs and curves preliminary information}
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% We would like to define now a macro for drawing circular arcs of any
-% radius and any angular aperture; the macro should require the arc
-% center, the arc starting point and the angular aperture. The arc has
-% its reference point in its center, therefore it does not need to be put
-% in place by the command |\put|; nevertheless if |\put| is used, it may
-% displace the arc into another position.
+% We would like to define now a macro for drawing
+% circular arcs of any radius and any angular
+% aperture; the macro should require the arc
+% center, the arc starting point and the angular
+% aperture. The arc has its reference point in its
+% center, therefore it does not need to be put in
+% place by the command |\put|; nevertheless if
+% |\put| is used, it may displace the arc into
+% another position.
%
% The command should have the following syntax:
-% \begin{flushleft}\ttfamily
+% \begin{Sintassi}
% \cs{Arc}(\meta{center})(\meta{starting point})\marg{angle}
-% \end{flushleft}
+% \end{Sintassi}
% which is totally equivalent to:
-% \begin{flushleft}\ttfamily
+% \begin{Sintassi}
% \cs{put}(\meta{center})\marg{\upshape\cs{Arc}(0,0)(\meta{starting
% point})\marg{angle}}
-% \end{flushleft}
-% If the \meta{angle}, i.e. the arc angular aperture, is positive the arc
-% runs counterclockwise from the starting point; clockwise if it is
-% negative.
-% Notice that since the \meta{starting point} is relative to the
-% \meta{center} point, its polar coordinates are very convenient, since
-% they become \parg{\meta{start angle}:\meta{radius}}, where the
-% \meta{start angle} is relative to the arc center. Therefore you can
-% think about a syntax such as this one:
-%\begin{flushleft}
-%\cs{Arc}\parg{\meta{center}}\parg{\normalfont{\itshape start angle}\texttt{:}{\itshape radius}}\marg{angle}
-%\end{flushleft}
+% \end{Sintassi}
+% If the \meta{angle}, i.e. the arc angular
+% aperture, is positive the arc runs
+% counterclockwise from the starting
+% point; clockwise if it is negative.
+% Notice that since the \meta{starting point} is
+% relative to the \meta{center} point, its polar
+% coordinates are very convenient, since they
+% become \parg{\meta{start angle}:\meta{radius}},
+% where the \meta{start angle} is relative to the
+% arc center. Therefore you can think about a
+% syntax such as this one:
+%\begin{Sintassi}
+%\cs{Arc}\parg{center}\parg{start angle\texttt{\upshape :}{radius}}\marg{angle}
+%\end{Sintassi}
%
-% The difference between the |pict2e| |\arc| definition consists in a
-% very different syntax:
-%\begin{flushleft}
+% The difference between the |pict2e| |\arc|
+% definition consists in a very different syntax:
+%\begin{Sintassi}
%\cs{arc}\Oarg{\meta{start angle}\texttt{,}\meta{end angle}}\marg{radius}
-%\end{flushleft}
-% and the center is assumed to be at the coordinate established with a
-% required |\put| command; moreover the difference in specifying angles
-% is that \meta{end angle} equals the sum of \meta{start angle} and
-% \meta{angle}. With the definition of this |curve2e| package
-% use of a |\put| command is not prohibited, but it may be used for fine
-% tuning the arc position by means of a simple displacement; moreover the
-% \meta{starting point} may be specified with polar coordinates (that are
-% relative to the arc center).
+%\end{Sintassi}
+% and the center is assumed to be at the
+% coordinate established with a required |\put|
+% command; moreover the difference in
+% specifying angles is that \meta{end angle}
+% equals the sum of \meta{start angle} and
+% \meta{angle}. With the definition of this
+% |curve2e| package use of a |\put| command is not
+% prohibited, but it may be used for fine tuning
+% the arc position by means of a simple
+% displacement; moreover the \meta{starting point}
+% may be specified with polar coordinates (that
+% are relative to the arc center).
%
-% It's necessary to determine the end point and the control points of the
-% Bézier spline(s) that make up the circular arc.
+% It's necessary to determine the end point and
+% the control points of the Bézier spline(s) that
+% make up the circular arc.
%
-% The end point is obtained from the rotation of the starting point
-% around the center; but the \texttt{pict2e} command |\pIIe at rotate| is
-% such that the pivoting point appears to be non relocatable.
-% It is therefore necessary to resort to low level \TeX\ commands and the
-% defined trigonometric functions and a set of macros that operate on
-% complex numbers used as vector roto-amplification operators.
+% The end point is obtained from the rotation of
+% the starting point around the center; but the
+% \texttt{pict2e} command |\pIIe at rotate| is such
+% that the pivoting point appears to be non
+% relocatable. It is therefore necessary to resort
+% to low level \TeX\ commands and the defined
+% trigonometric functions and a set of macros that
+% operate on complex numbers used as vector
+% roto-amplification operators.
%
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Complex number macros}
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% In this package \emph{complex number} is a vague phrase; it may be used
-% in the mathematical sense of an ordered pair of real numbers; it can be
-% viewed as a vector joining the origin of the coordinate axes to the
-% coordinates indicated by the ordered pair; it can be interpreted as a
-% roto-amplification operator that scales its operand and rotates it
-% about a pivot point; besides the usual conventional representation used
-% by the mathematicians where the ordered pair is enclosed in round
-% parentheses (which is in perfect agreement with the standard code used
-% by the |picture| environment) there is the other conventional
-% representation used by the engineers that stresses the
-% roto-amplification nature of a complex number:
+% In this package \emph{complex number} is a vague
+% phrase; it may be used in the mathematical sense
+% of an ordered pair of real numbers; it can be
+% viewed as a vector joining the origin of the
+% coordinate axes to the coordinates indicated by
+% the ordered pair; it can be interpreted as a
+% roto-amplification operator that scales its
+% operand and rotates it about a pivot point;
+% besides the usual conventional representation
+% used by the mathematicians where the ordered
+% pair is enclosed in round parentheses (which is
+% in perfect agreement with the standard code used
+% by the |picture| environment) there is the
+% other conventional representation used by the
+% engineers that stresses the roto-amplification
+% nature of a complex number:
%\[
%(x, y) = x + \mathrm{j}y =M \mathrm{e}^{\mathrm{j}\theta}
%\]
-% Even the imaginary unit is indicated with $\mathrm{i}$ by
-% mathematicians and with $\mathrm{j}$ by engineers. In spite of
-% these differences, such objects, the \emph{complex numbers}, are used
-% without any problem by both mathematicians and engineers.
+% Even the imaginary unit is indicated with
+% $\mathrm{i}$ by mathematicians and with
+% $\mathrm{j}$ by engineers. In spite of
+% these differences, such objects, the
+% \emph{complex numbers}, are used without any
+% problem by both mathematicians and engineers.
%
-% The important point is that these objects can be summed, subtracted,
-% multiplied, divided, raised to any power (integer, fractional, positive
-% or negative), be the argument of transcendental functions according to
-% rules that are agreed upon by everybody. We do not need all these
-% properties, but we need some and we must create the suitable macros for
-% doing some of these operations.
+% The important point is that these objects can be
+% summed,% subtracted, multiplied, divided, raised
+% to any power (integer, fractional, positive or
+% negative), be the argument of transcendental
+% functions according to rules that are agreed
+% upon by everybody. We do not need all these
+% properties, but we need some and we must create
+% the suitable macros for doing some of these
+% operations.
%
-% In facts we need macros for summing, subtracting, multiplying, dividing
-% complex numbers, for determining their directions (unit vectors or
-% versors); a unit vector is the complex number divided by its magnitude
-% so that the result is the cartesian or polar form of the Euler's
-% formula
+% In facts we need macros for summing,
+% subtracting, multiplying, dividing complex
+% numbers, for determining their directions
+% (unit vectors or versors); a unit vector is the
+% complex number divided by its magnitude so that
+% the result is the cartesian or polar form of the
+% Euler's formula
% \[
% \mathrm{e}^{\mathrm{j}\phi} = \cos\phi+\mathrm{j}\sin\phi
% \]
%
-% The magnitude of a vector is determined by taking the positive square
-% root of the sum of the squared real and imaginary parts (often called \emph{Pitagorean sum}); see further on.
+% The magnitude of a vector is determined by
+% taking the positive square root of the sum of
+% the squared real and imaginary parts (often
+% called \emph{Pitagorean sum}); see further on.
%
-% It's better to represent each complex number with one control sequence;
-% this implies frequent assembling and disassembling the pair of real
-% numbers that make up a complex number. These real components are
-% assembled into the defining control sequence as a couple of
-% coordinates, i.e.\ two comma separated integer or fractional signed
-% decimal numbers.
+% It's better to represent each complex number
+% with one control sequence; this implies frequent
+% assembling and disassembling the pair of real
+% numbers that make up a complex number. These
+% real components are assembled into the defining
+% control sequence as a couple of coordinates,
+% i.e.\ two comma separated integer or fractional
+% signed decimal numbers.
%
-% For assembling two real numbers into a complex number we use the
-% following elementary macro:
+% For assembling two real numbers into a complex
+% number we use the following elementary macro:
% \begin{macrocode}
-\def\MakeVectorFrom#1#2to#3{\edef#3{#1,#2}\ignorespaces}%
+\def\MakeVectorFrom#1#2to#3{\edef#3{#1,#2}}%
% \end{macrocode}
-% Another elementary macro copies a complex number into another one:
+% Another elementary macro copies a complex number
+% into another one:
% \begin{macrocode}
\def\CopyVect#1to#2{\edef#2{#1}\ignorespaces}%
% \end{macrocode}
-% The magnitude is determined with the macro |\ModOfVect| with delimited
-% arguments; as usual it is assumed that the results are retrieved by
+% The magnitude is determined with the macro
+% |\ModOfVect| with delimited arguments; as usual
+% it is assumed that the results are retrieved by
% means of control sequences, not used directly.
%
-% In the preceding version of package |curve2e| the magnitude $M$ was
-% determined by taking the moduli of the real and imaginary parts, by
-% changing their signs if necessary; the larger component was
-% then taken as the reference one, so that, if $a$ is larger than $b$,
-% the square root of the sum of their squares is computed as such:
+% In the preceding versions of package |curve2e|
+% the magnitude $M$ was determined by taking the
+% moduli of the real and imaginary parts, by
+% changing their signs if necessary; the larger
+% component was then taken as the reference one,
+% so that, if $a$ is larger than $b$, the square
+% root of the sum of their squares is computed as
+% such:
% \[
% M = \sqrt{a^2+b^2} = \vert a\vert\sqrt{1+(b/a)^2}
% \]
-% In this way the radicand never exceeds 2 and it was quite easy to get
-% its square root by means of the Newton iterative process; due to the
-% quadratic convergence, five iterations were more than sufficient. When
-% one of the components was zero, the Newton iterative process was
-% skipped.
+% In this way the radicand never exceeds 2 and it
+% was quite easy to get its square root by means
+% of the Newton iterative process; due to the
+% quadratic convergence, five iterations were more
+% than sufficient. When one of the components was
+% zero, the Newton iterative process was skipped.
%
-% With the availability of the |xfp| package and its floating point
-% algorithms it is much easier to compute the magnitude of a complex
-% number; since these algorithms allow to use very large numbers, it is
-% not necessary to normalise the complex number components to the largest
-% one; therefore the code is much simpler than the one used for
-% implementing the Newton method in the previous versions of this
-% package.
+% With the availability of the |xfp| package
+% functionalities and its floating point
+% algorithms it is much easier to compute the
+% magnitude of a complex number; since these
+% algorithms allow to use very large numbers, it
+% is not necessary to normalise the complex
+% number components to the largest one; therefore
+% the code is much simpler than the one used for
+% implementing the Newton method used in the
+% previous
+% versions of this package.
% \begin{macrocode}
\def\ModOfVect#1to#2{\GetCoord(#1)\t at X\t at Y
-\edef#2{\fpeval{round(sqrt(\t at X*\t at X + \t at Y*\t at Y),6)}}%
-\ignorespaces}%
+\edef#2{\fpeval{round(sqrt(\t at X*\t at X + \t at Y*\t at Y),6)}}\ignorespaces}%
% \end{macrocode}
%
-% Since the macro for determining the magnitude of a vector is available,
-% we can now normalise the vector to its magnitude, therefore getting the
-% Cartesian form of the direction vector. If by any chance the direction
-% of the null vector is requested, the output is again the null vector,
-% without normalisation.
+% Since the macro for determining the magnitude of
+% a vector is available, we can now normalise the
+% vector to its magnitude, therefore getting the
+% Cartesian form of the direction vector.
+% If by any chance the direction of the null
+% vector is requested, the output is again the
+% null vector, without
+% normalisation.
% \begin{macrocode}
\def\DirOfVect#1to#2{\GetCoord(#1)\t at X\t at Y
\ModOfVect#1to\@tempa
-\fptest{\@tempa=\z@}{}{%
+\fptestF{\@tempa=\z@}{%
\edef\t at X{\fpeval{round(\t at X/\@tempa,6)}}%
\edef\t at Y{\fpeval{round(\t at Y/\@tempa,6)}}%
}\MakeVectorFrom\t at X\t at Y to#2\ignorespaces}%
% \end{macrocode}
%
-% A cumulative macro uses the above ones to determine with one call both
-% the magnitude and the direction of a complex number. The first argument
-% is the input complex number, the second its magnitude, and the third is
-% again a complex number normalised to unit magnitude (unless the input
-% was the null complex number); remember always that output quantities
-% must be specified with control sequences to be used at a later time.
+% A cumulative macro uses the above ones to
+% determine with one call both the magnitude and
+% the direction of a complex number.
+% The first argument is the input complex number,
+% the second its magnitude, and the third is again
+% a complex number normalised to unit magnitude
+% (unless the input was the null complex number);
+% remember always that output quantities must be
+% specified with control sequences to be used at a
+% later time.
% \begin{macrocode}
\def\ModAndDirOfVect#1to#2and#3{%
\ModOfVect#1to#2%
\DirOfVect#1to#3\ignorespaces}%
% \end{macrocode}
-% The next macro computes the magnitude and the direction of the
-% difference of two complex numbers; the first input argument is the
-% minuend, the second is the subtrahend; the output quantities are the
-% third argument containing the magnitude of the difference and the
-% fourth is the direction of the difference. Please notice the difference
-% between |\ModAndDirOfVect| and |\DistanceAndDirOfVect|; the former
-% computes the modulus and the direction of a complex number, that is a
-% vector with its tail in the origin of the axes; the latter measures
-% the length of the difference of two complex numbers; in a way
-% |\ModAndDirOfVect| \meta{vector}| to |\meta{macro}| and |\meta{versor}
-% produces the same result as
-% |\DistanceAndDirOfVect| \meta{vector}| minus {0,0} to |\meta{macro}| and |\meta{versor}.
-% Actually |\DistanceAndDirOfVect| yields the distance of two complex
-% numbers and the direction of their difference.
-% The service macro |\SubVect| executes the difference of two complex
-% numbers and is described further on; its code implements just this
-% statement.
+% The next macro computes the magnitude and the
+% direction of the difference of two complex
+% numbers; the first input argument is the
+% minuend, the second is the subtrahend; the
+% output quantities are the third argument
+% containing the magnitude of the difference and
+% the fourth is the direction of the difference.
+% Please notice the difference between
+% |\ModAndDirOfVect| and |\DistanceAndDirOfVect|;
+% the former computes the modulus and the
+% direction of a complex number, that is a vector
+% with its tail in the origin of the axes; the
+% latter measures the length of the difference of
+% two complex numbers; in a way |\ModAndDirOfVect|
+% \meta{vector} |to| \meta{macro} |and|
+% \meta{versor} produces the same result as
+% |\DistanceAndDirOfVect| \meta{vector}
+% |minus {0,0} to| \meta{macro} |and|
+% \meta{versor}.
+% Actually |\DistanceAndDirOfVect| yields the
+% distance of two complex numbers and the
+% direction of their difference.
+% The service macro |\SubVect| executes the
+% difference of two complex numbers and is
+% described further on; its code implements just
+% this statement.
% \begin{macrocode}
\def\DistanceAndDirOfVect#1minus#2to#3and#4{%
\SubVect#2from#1to\@tempa
\ModAndDirOfVect\@tempa to#3and#4\ignorespaces}%
% \end{macrocode}
-% We now have two macros intended to fetch just the real or,
-% respectively, the imaginary part of the input complex number.
+% We now have two macros intended to fetch just
+% the real or, respectively, the imaginary part of
+% the input complex number.
% \begin{macrocode}
-\def\XpartOfVect#1to#2{%
-\GetCoord(#1)#2\@tempa\ignorespaces}%
+\def\XpartOfVect#1to#2{\GetCoord(#1)#2\@tempa\ignorespaces}%
%
-\def\YpartOfVect#1to#2{%
-\GetCoord(#1)\@tempa#2\ignorespaces}%
+\def\YpartOfVect#1to#2{\GetCoord(#1)\@tempa#2\ignorespaces}%
% \end{macrocode}
-% With the next macro we create a direction vector (second argument) from
-% a given angle (first argument, in degrees).
+% With the next macro we create a direction vector
+% (second argument) from a given angle (first
+% argument, in degrees).
% \begin{macrocode}
\def\DirFromAngle#1to#2{%
\edef\t at X{\fpeval{round(cosd#1,6)}}%
@@ -1937,8 +2392,9 @@
\MakeVectorFrom\t at X\t at Y to#2\ignorespaces}%
% \end{macrocode}
%
-% Sometimes it is necessary to scale (multiply) a vector by an arbitrary
-% real factor; this implies scaling both the real and imaginary part of the
+% Sometimes it is necessary to scale (multiply) a
+% vector by an arbitrary real factor; this implies
+% scaling both the real and imaginary part of the
% input given vector.
% \begin{macrocode}
\def\ScaleVect#1by#2to#3{\GetCoord(#1)\t at X\t at Y
@@ -1946,19 +2402,20 @@
\edef\t at Y{\fpeval{#2 * \t at Y}}%
\MakeVectorFrom\t at X\t at Y to#3\ignorespaces}%
% \end{macrocode}
-% Again, sometimes it is necessary to reverse the direction of rotation;
-% this implies changing the sign of the imaginary part of a given complex
-% number; this operation produces the complex conjugate of the given
-% number.
+% Again, sometimes it is necessary to reverse the
+% direction of rotation; this implies changing the
+% sign of the imaginary part of a given complex
+% number; this operation produces the complex
+% conjugate of the given number.
% \begin{macrocode}
\def\ConjVect#1to#2{\GetCoord(#1)\t at X\t at Y
-\edef\t at Y{-\t at Y}%
-\MakeVectorFrom\t at X\t at Y to#2\ignorespaces}%
+\edef\t at Y{-\t at Y}\MakeVectorFrom\t at X\t at Y to#2\ignorespaces}%
% \end{macrocode}
%
-% With all the low level elementary operations we can now proceed to the
-% definitions of the binary operations on complex numbers. We start with
-% the addition:
+% With all the low level elementary operations we
+% can now proceed to the definitions of the binary
+% operations on complex numbers. We start with the
+% addition:
% \begin{macrocode}
\def\AddVect#1and#2to#3{\GetCoord(#1)\tu at X\tu at Y
\GetCoord(#2)\td at X\td at Y
@@ -1975,250 +2432,314 @@
\MakeVectorFrom\t at X\t at Y to#3\ignorespaces}%
% \end{macrocode}
%
-% For the multiplication we need to split the operation according to the
-% fact that we want to multiply by the second operand or by the complex
-% conjugate of the second operand; it would be nice if we could use the
-% usual postfixed asterisk notation for the complex conjugate, but in the
-% previous versions of this package we could not find a simple means for
-% doing so. Therefore the previous version contained a definition of the
-% |\MultVect| macro that followed a simple syntax with an optional
-% asterisk \emph{prefixed} to the second operand. Its syntax, therefore,
-% allowed the following two forms:
-%\begin{flushleft}\ttfamily
+% For the multiplication we need to split the
+% operation according to the fact that we want to
+% multiply by the second operand or by the complex
+% conjugate of the second operand; it would be
+% nice if we could use the usual postfixed
+% asterisk notation for the complex conjugate, but
+% in the previous versions of this package we
+% could not find a simple means for doing so.
+% Therefore the previous version contained a
+% definition of the |\MultVect| macro that
+% followed a simple syntax with an optional
+% asterisk \emph{prefixed} to the second operand.
+% Its syntax, therefore, allowed the following
+% two forms:
+%\begin{Sintassi}\ttfamily
%\cs{MultVect}\meta{first factor} by \meta{second factor} to \meta{output macro}\\
%\cs{MultVect}\meta{first factor} by $\star$ \meta{second factor} to \meta{output macro}\\
-%\end{flushleft}
+%\end{Sintassi}
%
-% With the availability of the |xparse| package and its special argument
-% descriptors for the arguments, we were able to define a different
-% macro, |\Multvect|, with both optional positions for the asterisk:
-% \emph{after} and \emph{before}; its syntax allows the following four
-% forms:
-%\begin{flushleft}
-%\cs{Multvect}\marg{first factor}\marg{second factor}\meta{output macro}\\
-%\cs{Multvect}\marg{first factor}$\star$\marg{second factor}\meta{output macro}\\
-%\cs{Multvect}\marg{first factor}\marg{second factor}$\star$\meta{output macro}\\
-%\cs{Multvect}\marg{first factor}$\star$\marg{second factor}\meta{output macro}\\
+% With the availability of the |xparse| package
+% and its special argument descriptors for the
+% arguments, we were able to define a different
+% macro, |\Multvect|, with both optional positions
+% for the asterisk: \emph{after} and
+% \emph{before}; its syntax allows the
+% following four forms:
+%\begin{Sintassi}
+%\cs{Multvect}\marg{first factor}\marg{second factor}\meta{output macro}
+%\cs{Multvect}\marg{first factor}$\star$\marg{second factor}\meta{output macro}
+%\cs{Multvect}\marg{first factor}\marg{second factor}$\star$\meta{output macro}
%\cs{Multvect}\marg{first factor}$\star$\marg{second factor}$\star$\meta{output macro}
-%\end{flushleft}
+%\end{Sintassi}
%
-% Nevertheless we maintain a sort of interface between the old syntax
-% and the new one, so that the two old forms can be mapped to two
-% suitable forms of the new syntax. Old documents are still compilable;
-% users who got used to the old syntax can maintain their habits.
+% Nevertheless we maintain a sort of interface
+% between the old syntax and the new one, so that
+% the two old forms can be mapped to two suitable
+% forms of the new syntax. Old documents are still
+% compilable; users who got used to the old syntax
+% can maintain their habits.
%
-% First we define the new macro: it receives the three arguments, the
-% first two as balanced texts; the last one must always be a macro,
-% therefore a single (complex) token that does not require braces, even
-% if it is not forbidden to use them. Asterisks are optional.
-% The input arguments are transformed into couples of argument and
-% modulus; this makes multiplication much simpler as the output modulus
-% is just the product of the input moduli, while the output argument is
-% just the sum of input arguments; eventually it is necessary to
-% transform this polar version of the result into an ordered couple of
-% cartesian values to be assigned to the output macro.
-% In order to maintain the single macros pretty simple we need a couple
-% of service macros and a named counter. We use |\ModOfVect| previously
-% defined, and a new macro |\ModAndAngleOfVect| with the following
-% syntax:
-%\begin{flushleft}\ttfamily
-%\cs{ModAndAngleOfVect}\meta{input vector} to \meta{output modulus} and \meta{output angle in degrees}
-%\end{flushleft}
-% The output quantities are always macros, so they do not need balanced
-% bracing; angles in degrees are always preferred because, in case of
-% necessity, they are easy to reduce to the range $-180^\circ < \alpha \leq +180^\circ$.
+% First we define the new macro: it receives the
+% three arguments, the first two as balanced
+% texts; the last one must always be a macro,
+% therefore a single (complex) token that does not
+% require braces, even if it is not forbidden
+% to use them. Asterisks are optional. The input
+% arguments are transformed into couples of
+% argument and modulus; this makes multiplication
+% much simpler as the output modulus is just the
+% product of the input moduli, while the output
+% argument is just the sum of input arguments;
+% eventually it is necessary to transform this
+% polar version of the result into an ordered
+% couple of cartesian values to be assigned to the
+% output macro. In order to maintain the single
+% macros pretty simple we need a couple of service
+% macros and a named counter. We use |\ModOfVect|
+% previously defined, and a new macro
+% |\ModAndAngleOfVect| with the following syntax:
+%\begin{Sintassi}\ttfamily \cs{ModAndAngleOfVect}\meta{input vector} to \meta{output modulus} and \meta{output angle in degrees}
+%\end{Sintassi}
+% The output quantities are always macros, so they
+% do not need balanced bracing; angles in degrees
+% are always preferred because, in case of
+% necessity, they are easy to reduce to the range
+% $-180^\circ < \alpha \leq +180^\circ$.
% \begin{macrocode}
\def\ModAndAngleOfVect#1to#2and#3{\ModOfVect#1to#2\relax
\ArgOfVect#1to#3\ignorespaces}
% \end{macrocode}
-% We name a counter in the upper range accessible with all the modern
-% three typesetting engines, |pdfLaTeX|, |LuaLaTeX| and |XeLaTeX|.
+% We name a new service counter
% \begin{macrocode}
\newcount\MV at C
% \end{macrocode}
-% This \TeX\ counter definition uses the property of modern typesetting
-% engines that use the \eTeX\ extensions, that can define a very large
-% number of counters.
%
-% Now comes the real macro\footnote{A warm thank-you to Enrico Gregorio,
-% who kindly attracted my attention on the necessity of braces when using
-% this kind of macro; being used to the syntax with delimited arguments
-% I had taken the bad habit of avoiding braces. Braces are very
-% important, but the syntax of the original \TeX\ language, that did not
-% have available the L3 one, spoiled me with the abuse of delimited
-% arguments.}:
+% Now comes the real macro\footnote{A warm
+% thank-you to Enrico Gregorio, who kindly
+% attracted my attention on the necessity of
+% braces when using this kind of macro; being
+% used to the syntax with delimited arguments I
+% had taken the bad habit of avoiding braces.
+% Braces are very important, but the syntax of the
+% original \TeX\ language, that did not
+% have available the L3 one, spoiled me with the
+% abuse of delimited arguments.}:
% \begin{macrocode}
-\NewDocumentCommand\Multvect{m s m s m}{%
-\MV at C=0
-\ModAndAngleOfVect#1to\MV at uM and\MV at uA
+\NewDocumentCommand\Multvect{m s m s m}%
+{\ModAndAngleOfVect#1to\MV at uM and\MV at uA
\ModAndAngleOfVect#3to\MV at dM and\MV at dA
-\IfBooleanT{#2}{\MV at C=1}\relax
-\IfBooleanT{#4}{\MV at C=1}\relax
-\unless\ifnum\MV at C=0\edef\MV at dA{-\MV at dA}\fi
-\edef\MV at rM{\fpeval{round((\MV at uM * \MV at dM),6)}}%
-\edef\MV at rA{\fpeval{round((\MV at uA + \MV at dA),6)}}%
-\GetCoord(\MV at rA:\MV at rM)\t at X\t at Y
-\MakeVectorFrom\t at X\t at Y to#5}
+\fptestT{%
+\IfBooleanTF{#2}{1}{0}+\IfBooleanTF{#4}{1}{0}!=0}%
+{\edef\MV at dA{-\MV at dA}}%
+\edef\MV at rM{\fpeval{round((\MV at uM*\MV at dM),6)}}%
+\edef\MV at rA{\fpeval{round((\MV at uA+\MV at dA),6)}}%
+\edef#5{\fpeval{\MV at rM*cosd\MV at rA},\fpeval{\MV at rM*sind\MV at rA}}}
+
% \end{macrocode}
%
-% The macro to remain backward compatible, reduce to two simple macros
-% that take the input delimited arguments and passes them in braced form
-% to the above general macro:
+% In order to remain backward compatible, the
+% macro reduces to two simple macros that take
+% the input delimited arguments and passes them
+% in braced form to the above
+% general macro:
% \begin{macrocode}
-\def\MultVect#1by{\@ifstar{\let\MV at c\@ne\@MultVect#1by}%
- {\let\MV at c\empty\@MultVect#1by}}
+\def\MultVect#1by{\@ifstar{\let\MV at c1\@MultVect#1 by}{\let\MV at c0\@MultVect#1by}}
\def\@MultVect#1by#2to#3{%
- \unless\ifx\MV at c\empty\Multvect{#1}{#2}*{#3}\else
- \Multvect{#1}{#2}{#3}\fi}
+ \fptest{\MV at c!=0}{\Multvect{#1}{#2}*{#3}}%
+ {\Multvect{#1}{#2}{#3}}%
+}%
% \end{macrocode}
-% Testing of both the new and the old macros shows that they behave as
-% expected, although, using real numbers for trigonometric functions,
-% some small rounding unit on the sixth decimal digit still remains;
-% nothing to worry about with a package used for drawing.
+% Testing of both the new and the old macros shows
+% that they behave as expected, although, using
+% real numbers for trigonometric functions, some
+% small rounding unit on the sixth decimal digit
+% still remains; nothing to worry about with a
+% package used for drawing.
%
%
-% The division of two complex numbers implies scaling down the dividend
-% by the magnitude of the divisor and by rotating the dividend scaled
+% The division of two complex numbers implies
+% scaling down the dividend by the magnitude of
+% the divisor and by rotating the dividend scaled
% vector by the conjugate versor of the divisor:
%\[
% \frac{\vec{N}}{\vec{D}}= \frac{\vec{N}}{M\vec{u}}=
% \frac{\vec{N}}{M}\vec{u}^{\mkern2mu\star}
%\]
-%therefore:
+% therefore:
% \begin{macrocode}
\def\DivVect#1by#2to#3{\Divvect{#1}{#2}{#3}}
-\NewDocumentCommand\Divvect{ m m m }{%
-\ModAndDirOfVect#2to\@Mod and\@Dir
-\edef\@Mod{\fpeval{1 / \@Mod}}%
-\ConjVect\@Dir to\@Dir
-\ScaleVect#1by\@Mod to\@tempa
-\Multvect{\@tempa}{\@Dir}#3\ignorespaces}%
+\NewDocumentCommand \Divvect{m m m}%
+{\ModOfVect#2to\DV at dD
+\fptest{\DV at dD=0}{\PackageWarning{curve2e}{^^J%
+******************************************^^J%
+Division by zero!^^J%
+Result set to maxdimen in scaled points^^J%
+******************************************^^J}%
+\edef#3{\fpeval{\maxdimen*2**16},0}}%
+{\edef\DV at sF{\fpeval{1/\DV at dD**2}}%
+\Multvect{#2}{\DV at sF,0}{\DV at dD}%
+\Multvect{#1}{\DV at dD}*{#3}}}%
% \end{macrocode}
-% Macros |\DivVect| and |\Divvect| are almost equivalent; the second is
-% possibly slightly more robust. They match the corresponding macros for
+% Macros |\DivVect| and |\Divvect| are almost
+% equivalent; the second is possibly slightly more
+% robust. They match the corresponding macros for
% multiplying two vectors.
+% Attention! The new macro |\Divvect| performs a
+% test on a zero valued divisor; in case it issues
+% a warning, and sets the result as the maxdimen
+% value expressed in scaled points and it does not
+% stop the job; the following results are going to
+% be very wrong, but the strongly emphasised
+% warning message in the console and\slash or in
+% the log file warns users to review their data.
%
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Arcs and curved vectors}
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% We are now in the position of really doing graphic work.
+% We are now in the position of really doing
+% graphic work.
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsubsection{Arcs}
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% We provide two ways of producing arcs so as to use different although
-% similar macros macros; they follow the following syntax:
-%\begin{flushleft}
-% \cs{Arc}\parg{center coordinates}\parg{starting cartesian point}\marg{angle}
+% We provide two ways to produce arcs so as to use
+% different although similar macros; they follow
+% the following syntax:
+%\begin{Sintassi}
+% \cs{Arc}\parg{center coordinates}\parg{starting point cartesian coordinates}\marg{angle}
%
-% \cs{Arc}\parg{centercoordinates}\parg{starting polar point}\marg{ange}
-%\end{flushleft}
-%The difference between these macros and that of the standard
-% \pack{pict2e} package assumes that these new ones are easier to use;
-% the standard one; The latter does no require the center coordinates
-% and must be put in place with a |\put| command; its reference point
-% becomes the arc center; is it necessary to specify the coordinates
-% of both the starting and the ending point angles and the radius;
-% this implies that the user specifies compatible data; not too
-% difficult, but it is delicate for choosing the correct angles and
-% the correct distance from the implicit center.
+% \cs{Arc}\parg{centercoordinates}\parg{starting point polar coordinates}\marg{ange}
+%\end{Sintassi}
%
-% These new alternative macros leave the calculation of the radius
-% the software and the Pythagorean distance between the center and
-% the staring point and require the specification of the rotation
-% angle; but even in this way, used in the previous version of this
-% package, the cartesian coordinates of the staring point are very
-% easy when they imply an angle of an inter number of right angles
-% starting from the $x$ axis, but thy bicome non that easy when the
-% center and the starting point don't share either their abscissas
-% or their ordinates. The new alternate syntax uses the polar
-% coordinates; their reference point is the arc center and it appears
-% to be easier to specify the position of the starting point, because
-% its angle and it distance are both specified by the user. With the
-% drawings madre with the extended |picture| environment it seem to
-% be easier to have available both the absolute cartesian specification
-% and the centred polar specification.
+% The difference between these macros and that of
+% the standard \pack{pict2e} package assumes that
+% these new ones are easier to use. The latter
+% does no require the center coordinates and must
+% be put in place with a |\put| command; its
+% reference point becomes the arc center; is it
+% necessary to specify the coordinates of both the
+% starting and the ending point angles and the
+% radius; this implies that the user specifies
+% compatible data; not too difficult, but it is
+% delicate for choosing the correct angles and the
+% correct distance from the implicit center.
%
-% Therefore wetracing a circular arc of arbitrary center, arbitrary
-% starting point and arbitrary aperture; the first macro checks the
-% aperture; if this is not zero it actually proceeds with the necessary
-% computations, otherwise it does nothing.
+% These new alternative macros leave the
+% calculation of the radius to the software and
+% the Pythagorean distance between the center and
+% the starting point, and require the
+% specification of the rotation angle; but even
+% in this way, used in the previous version of
+% this package, the cartesian coordinates of the
+% staring point are very easy when they imply
+% an angle of an integer number of right angles
+% starting from the $x$ axis, but they become not
+% that easy when the center and the starting point
+% don't share either their abscissas or their
+% ordinates. The new alternate syntax uses the
+% polar coordinates; their reference point is the
+% arc center and it appears to be easier to
+% specify the position of the starting point,
+% because its angle and it distance are both
+% specified by the user. With the drawings made
+% with the extended |picture| environment it seems
+% to be easier to have available both the absolute
+% cartesian specification and the centred polar
+% specification.
+%
+% Therefore tracing a circular arc of arbitrary
+% center, arbitrary starting point and arbitrary
+% aperture; the first macro checks the aperture;
+% if this is not zero it actually proceeds with
+% the necessary computations, otherwise it does
+% nothing.
% \begin{macrocode}
\def\Arc(#1)(#2)#3{\begingroup
-\@tdA=#3\p@
-\unless\ifdim\@tdA=\z@
- \@Arc(#1)(#2)%
-\fi
-\endgroup\ignorespaces}%
+\edef\tempG{#3}%
+\fptestF{#3=0}{\@Arc(#1)(#2)}}%
% \end{macrocode}
-% The aperture is already memorised in |\@tdA|; the |\@Arc| macro
-% receives the center coordinates in the first argument and the
-% coordinates of the starting point in the second argument. Fo easier calculation we assume that the angles are positve when rotating counterclockwise; if the user specificato is negative, we change sign, but remember the original sign so that in the end the arc will floe in the right direction
+% The aperture is already memorised in |\@tdA|;
+% the |\@Arc| macro receives the center
+% coordinates in the first argument and the
+% coordinates of the starting point in the second
+% argument. For easier calculation we assume that
+% the angles are positive when rotating
+% counterclockwise; if the user specification is
+% negative, we change sign, but remember the
+% original sign so that in the end the arc will
+% floe=w in the right direction
% \begin{macrocode}
+
\def\@Arc(#1)(#2){%
-\ifdim\@tdA>\z@
- \let\Segno+%
-\else
- \@tdA=-\@tdA \let\Segno-%
-\fi
+\fptest{\tempG>\z@}%
+ {\let\Segno+}%
+ {\let\Segno-%
+ \edef\tempG{\fpeval{abs(\tempG)}}%
+ }%
% \end{macrocode}
-% The rotation angle sign is memorised in |\Segno| and |\@tdA| now
-% contains the absolute value of the arc aperture.
+% The rotation angle sign is memorised in |\Segno|
+% and |\@tdA| now contains the absolute value of
+% the arc aperture.
%
-% If the rotation angle is larger than $360^\circ$ a message is issued
-% that informs the user that the angle will be reduced modulo
-% $360^\circ$; this operation is performed by successive subtractions
-% rather than with modular arithmetics on the assumption that in general
+% If the rotation angle is larger than $360^\circ$
+% a message is issued that informs the user that
+% the angle will be reduced modulo $360^\circ$;
+% this operation is performed by successive
+% subtractions rather than with modular
+% arithmetics on the assumption that in general
% one subtraction suffices.
% \begin{macrocode}
-\Numero\@gradi\@tdA
-\ifdim\@tdA>360\p@
- \PackageWarning{curve2e}{The arc aperture is \@gradi\space degrees
- and gets reduced\MessageBreak%
- to the range 0--360 taking the sign into consideration}%
- \@whiledim\@tdA>360\p@\do{\advance\@tdA-360\p@}%
-\fi
+\fptestT{\tempG>360}{%
+ \PackageWarning{curve2e}%
+ {The arc aperture is \tempG\space degrees
+ and gets reduced^^J%
+ to the interval 0--360 taking the sign into
+ consideration}%
+ \edef\tempG{\Modulo{\tempG}{360}}%
+ }%
% \end{macrocode}
-% Now the radius is determined and the drawing point is moved to the
-% starting point.
+% Now the radius is determined and the drawing
+% point is moved to the starting point.
% \begin{macrocode}
\GetCoord(#2)\@pPunX\@pPunY
\ifCV at polare
\ModOfVect#2to\@Raggio
\CopyVect#1to\@Cent
- \AddVect#2and#1to\@pPun% punto da cui parte l'arco
+ \AddVect#2and#1to\@pPun% starting point
\GetCoord(\@pPun)\@pPunX\@pPunY
\else
- \SubVect#2from#1to\@V \ModOfVect\@V to\@Raggio
+ \SubVect#2from#1to\@V
+ \ModOfVect\@V to\@Raggio
\CopyVect#2to\@pPun
- \CopyVect#1to\@Cent \GetCoord(\@pPun)\@pPunX\@pPunY
+ \CopyVect#1to\@Cent
+ \GetCoord(\@pPun)\@pPunX\@pPunY
\fi
% \end{macrocode}
-% From now on it's better to define a new macro that will be used also in
-% the subsequent macros that draw arcs; here we already have the starting
-% point coordinates and the angle to draw the arc, therefore we just call
-% the new macro, stroke the line and exit.
+% From now on it's better to define a new macro
+% that will be used also in the subsequent macros
+% that draw arcs; here we already have the
+% starting point coordinates and the angle to
+% draw the arc, therefore we just call the new
+% macro, stroke the line and exit.
% \begin{macrocode}
-\@@Arc\strokepath\ignorespaces}%
+\@@Arc\strokepath\endgroup\ignorespaces}%
% \end{macrocode}
-% And the new macro |\@@Arc| starts with moving the drawing point to the
-% first point and does everything needed for drawing the requested arc,
-% except stroking it; we leave the |\strokepath| command to the
-% completion of the calling macro and nobody forbids to use the |\@@Arc|
-% macro for other purposes.
+% And the new macro |\@@Arc| starts with moving
+% the drawing point to the first point and does
+% everything needed for drawing the requested arc,
+% except stroking it; we leave the |\strokepath|
+% command to the completion of the calling macro
+% and nobody forbids to use the |\@@Arc| macro for
+% other purposes.
% \begin{macrocode}
-\def\@@Arc{\pIIe at moveto{\@pPunX\unitlength}{\@pPunY\unitlength}%
+\def\@@Arc{%
+\pIIe at moveto{\@pPunX\unitlength}%
+ {\@pPunY\unitlength}%
% \end{macrocode}
-% If the aperture is larger than $180^\circ$ it traces a semicircle in
-% the right direction and correspondingly reduces the overall aperture.
+% If the aperture is larger than $180^\circ$ it
+% traces a% semicircle in the right direction and
+% correspondingly reduces
+% the overall aperture.
% \begin{macrocode}
-\ifdim\@tdA>180\p@
- \advance\@tdA-180\p@
- \Numero\@gradi\@tdA
+\fptestT{\tempG>180}{%
+ \edef\tempG{\fpeval{\tempG-180}}%
\SubVect\@pPun from\@Cent to\@V
\AddVect\@V and\@Cent to\@sPun
- \Multvect{\@V}{0,-1.3333333}\@V
+ \Multvect{\@V}{0,-1.3333333}{\@V}%
\if\Segno-\ScaleVect\@V by-1to\@V\fi
\AddVect\@pPun and\@V to\@pcPun
\AddVect\@sPun and\@V to\@scPun
@@ -2225,25 +2746,32 @@
\GetCoord(\@pcPun)\@pcPunX\@pcPunY
\GetCoord(\@scPun)\@scPunX\@scPunY
\GetCoord(\@sPun)\@sPunX\@sPunY
- \pIIe at curveto{\@pcPunX\unitlength}{\@pcPunY\unitlength}%
- {\@scPunX\unitlength}{\@scPunY\unitlength}%
- {\@sPunX\unitlength}{\@sPunY\unitlength}%
- \CopyVect\@sPun to\@pPun
-\fi
+ \pIIe at curveto{\@pcPunX\unitlength}%
+ {\@pcPunY\unitlength}%
+ {\@scPunX\unitlength}%
+ {\@scPunY\unitlength}%
+ {\@sPunX\unitlength}%
+ {\@sPunY\unitlength}%
+ \CopyVect\@sPun to\@pPun}%
% \end{macrocode}
-% If the remaining aperture is not zero it continues tracing the rest of
-% the arc. Here we need the extrema of the arc and the coordinates of the
-% control points of the Bézier cubic spline that traces the arc. The
-% control points lay on the perpendicular to the vectors that join the
-% arc center to the starting and end points respectively.
+% If the remaining aperture is not zero it
+% continues tracing the rest of the arc. Here we
+% need the extrema of the arc and the coordinates
+% of the control points of the Bézier cubic spline
+% that traces the arc. The control points lay on
+% the perpendicular to the vectors that join the
+% arc center to the% starting and end points
+% respectively.
%
-% With reference to figure~11 of the user manual |curve2e-manual.pdf|
-% file, the points $P_1$ and $P_2$
-% are the arc end-points; $C_1$ and $C_2$ are the Bézier-spline
-% control-points; $P$ is the arc mid-point, that should be distant from
-% the center of the arc the same as $P_1$ and $P_2$.
-% Choosing a convenient orientation of the arc relative to the coordinate
-% axes, the coordinates of these five points are:
+% With reference to figure~12 of the
+% |curve2e-manual.pdf| file, the points $P_1$ and
+% $P_2$ are the arc end-points; $C_1$ and $C_2$
+% are the Bézier-spline control-points; $P$ is the
+% arc mid-point, that should be distant from the
+% center of the arc the same as $P_1$ and $P_2$.
+% Choosing a convenient orientation of the arc
+% relative to the coordinate axes, the coordinates
+% of these five points are:
%\begin{align*}
%P_1 &= (-R\sin\theta, 0)\\
%P_2 &= (R\sin\theta, 0)\\
@@ -2251,32 +2779,37 @@
%C_2 &= (R\sin\theta-K\cos\theta, K\sin\theta)\\
%P &= (0, R(1-\cos\theta))
%\end{align*}
-% The Bézier cubic spline interpolating the end and mid points is given by
-% the parametric equation:
+% The Bézier cubic spline interpolating the end
+% and mid points is given by the parametric
+% equation:
%\begin{equation*}
-%P= P_1(1-t)^3 + C_1 3(1-t)^2t + C_2 3(1-t)t^2 + P_2t^3
+%P= P_1(1-t)^3 + 3C_1 (1-t)^2t + 3C_2 (1-t)t^2 + P_2t^3
%\end{equation*}
-% where the mid point is obtained for $t=0.5$; the four coefficients then
-% become $1/8, 3/8, 3/8, 1/8$ and the only unknown remains $K$. Solving
-% for $K$ we obtain the formula
-% \begin{equation}\label{equ:corda}
+% where the mid point is obtained for $t=0.5$;
+% the four coefficients then become
+% $1/8, 3/8, 3/8, 1/8$ and the only unknown
+% remains $K$. Solving for $K$ we obtain the
+% formula
+%\begin{equation}\label{equ:corda}
% K= \frac{4}{3}\,\frac{1-\cos\theta}{\sin\theta}R
-%= \frac{4}{3}\,\frac{1-\cos\theta}{\sin^2\theta}s
-% \end{equation}
-% where $\theta$ is half the arc aperture, $R$ is its radius, and $s$ is
-% half the arc chord.
+% =\frac{4}{3}\,\frac{1-\cos\theta}{\sin^2\theta}s
+%\end{equation}
+% where $\theta$ is half the arc aperture, $R$ is
+% its radius, and $s$ is half the arc chord.
% \begin{macrocode}
-\ifdim\@tdA>\z@
- \DirFromAngle\@gradi to\@Dir \if\Segno-\ConjVect\@Dir to\@Dir \fi
+\fptestT{\tempG>0}{%
+ \DirFromAngle\tempG to\@Dir
+ \if\Segno-\ConjVect\@Dir to\@Dir \fi
\SubVect\@Cent from\@pPun to\@V
\Multvect{\@V}{\@Dir}\@V
\AddVect\@Cent and\@V to\@sPun
- \@tdA=.5\@tdA \Numero\@gradi\@tdA
- \DirFromAngle\@gradi to\@Phimezzi
+ \edef\tempG{\fpeval{\tempG/2}}%
+ \DirFromAngle\tempG to\@Phimezzi
\GetCoord(\@Phimezzi)\@cosphimezzi\@sinphimezzi
\@tdB=1.3333333\p@ \@tdB=\@Raggio\@tdB
- \@tdC=\p@ \advance\@tdC -\@cosphimezzi\p@ \Numero\@tempa\@tdC
- \@tdB=\@tempa\@tdB
+ \@tdC=\p@ \advance\@tdC -\@cosphimezzi\p@
+ \Numero\@tempa\@tdC
+ \@tdB=\@tempa\@tdB
\DividE\@tdB by\@sinphimezzi\p@ to\@cZ
\ScaleVect\@Phimezzi by\@cZ to\@Phimezzi
\ConjVect\@Phimezzi to\@mPhimezzi
@@ -2295,101 +2828,150 @@
\GetCoord(\@pcPun)\@pcPunX\@pcPunY
\GetCoord(\@scPun)\@scPunX\@scPunY
\GetCoord(\@sPun)\@sPunX\@sPunY
- \pIIe at curveto{\@pcPunX\unitlength}{\@pcPunY\unitlength}%
- {\@scPunX\unitlength}{\@scPunY\unitlength}%
- {\@sPunX\unitlength}{\@sPunY\unitlength}%
-\fi}
+ \pIIe at curveto{\@pcPunX\unitlength}%
+ {\@pcPunY\unitlength}%
+ {\@scPunX\unitlength}%
+ {\@scPunY\unitlength}%
+ {\@sPunX\unitlength}%
+ {\@sPunY\unitlength}%
+}}%
% \end{macrocode}
+% It is important to remember that the cubic spline
+% used to draw the arc is not the equation of an
+% arc circumference, but a very good approximation;
+% the approximation error is zero at the arc end
+% points and at the midpoint by construction. The
+% approximation error is maximum more or less at
+% the mid point between $\textsf{P}_1$ and
+% $\textsf{P}$, and between $\textsf{P}$ and
+% $\textsf{P}_2$.
+% See figure~\ref{fig:arc error}, where the red
+% line should be much more close to the desired
+% arc, and the black arc is the one obtained with
+% the \cs{Arc} macro.
+%\begin{figure}\centering
+%\unitlength=0.00925\textwidth
+%\begin{picture}(100,50)(-50,0)
+%{\linethickness{1pt}\Arc(0,0)(50,0){180}}\relax
+%{\color{red}\Arc(0,0)(50,0){90}\relax
+% \Arc(0,0)(0,50){90}}\relax
+%\Zbox(50,0)[l]{P_2}[1]
+%\Zbox(0,50)[b]{P}[1]
+%\Zbox(-50,0)[r]{P_1}[1]
+%\Zbox(0,0)[br]{O}[1]
+%\VVECTOR(0,0)(45:50)\Zbox(45:25)[tl]{R}[0]
+%\end{picture}
+%\caption{Approximation of a Bézier arc (black) to a circumference arc (red)}%
+%\label{fig:arc error}
+%\end{figure}
%
+% As it can be seen in figure~\ref{fig:arc error}
+% the error is hardly noticed and in most
+% circumstances the error is negligible, since it
+% amounts to about 2\% of the radius with an arc
+% opening of 180°; it becomes absolutely invisible
+% if the arc aperture gets smaller and smaller; in
+% a 90° arc the error exists but it is invisible.
+% In rare circumstances it might be necessary to
+% split the total arc in two or three sub-arcs.
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsubsection{Arc vectors}
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% We exploit much of the above definitions of the |\Arc| macro for
-% drawing circular arcs with an arrow at one or both ends; the first
-% macro |\VectorArc| draws an arrow at the ending point of the arc; the
-% second macro |\VectorARC| (alias |\VVectorArc|) draws arrows at both
-% ends; the arrows tips have the same shape as those for vectors;
-% actually they are drawn by putting a vector of zero length at the
-% proper arc end(s), therefore they are styled as traditional \LaTeX\ or
-% PostScript arrows according to the specific option to the
-% \texttt{pict2e} package.
+% We exploit much of the above definitions of the
+% |\Arc| macro for drawing circular arcs with an
+% arrow tip at one or both ends; the first macro
+% |\VectorArc| draws an arrow at the ending point
+% of the arc; the second macro |\VectorARC| (with
+% alias |\VVectorArc|) draws arrows at both ends;
+% the arrows tips have the same shape as those for
+% vectors; actually they are drawn by putting a
+% vector of zero length at the proper arc end(s),
+% therefore they are styled as traditional \LaTeX\
+% or PostScript arrows according to the specific
+% option to the \texttt{pict2e} package.
%
-% It goes by itself the the ending point may be specified as absolute
-% cartesian coordinates or centred polar ones, the same as it was
-% described above for the arcs without vector tips.
+% It goes by itself that the ending point may be
+% specified as absolute cartesian coordinates or
+% centred polar ones, the same as it was described
+% above for the arcs without vector tips.
%
-% But the arc drawing done here shortens it so as not to overlap on the
-% arrow tip(s); the only arrow tip (or both tips) are also lightly tilted
-% in order to avoid the impression of a corner where the arc enters the
-% arrow tip.
+% But the arc drawing done here shortens it so as
+% not to overlap on the arrow tip(s); the only
+% arrow tip (or both tips) are also lightly tilted
+% in order to avoid the impression of a corner
+% where the arc enters the arrow tip.
%
-% All these operations require a lot of ``playing'' with vector
-% directions, but even if the operations are numerous, they do not do
-% anything else but: (a) determining the end point and its direction;
-% (b) determining the arrow length as an angular quantity, i.e. the arc
-% amplitude that must be subtracted from the total arc to be drawn;
-% (c) the direction of the arrow should correspond to the tangent
-% to the arc at the point where the arrow tip is attached; (d) tilting
-% the arrow tip by half its angular amplitude; (e) determining the
-% resulting position and direction of the arrow tip so as to draw a zero
-% length vector; (f\/) possibly repeating the same procedure for the
-% other end of the arc; (g) shortening the total arc angular amplitude by
-% the amount of the arrow tip(s) already set, and finally (h) drawing
-% the circular arc that joins the starting point to the final arrow or
-% one arrow to the other one.
+% All these operations require a lot of “playing”
+% with vector directions, but even if the
+% operations are numerous, they do not do anything
+% else but: (a) determining the end point and
+% its direction; (b) determining the arrow length
+% as an angular quantity, i.e. the arc amplitude
+% that must be subtracted from the total arc to be
+% drawn; (c) the direction of the arrow should
+% correspond to the tangent to the arc at the point
+% where the arrow tip is attached; (d) tilting the
+% arrow tip by half its angular amplitude; (e)
+% determining the resulting position and direction
+% of the arrow tip so as to draw a zero length
+% vector; (f\/) possibly repeating the same
+% procedure for the other end of the arc; (g)
+% shortening the total arc angular amplitude by the
+% amount of the arrow tip(s) already set, and
+% finally (h) drawing the circular arc that joins
+% the starting point to the final arrow or one
+% arrow to the other one.
%
-% The calling macros are very similar to the |\Arc| macro initial one:
+% The calling macros are very similar to the |\Arc|
+% macro initial one:
% \begin{macrocode}
\def\VectorArc(#1)(#2)#3{\begingroup
-\@tdA=#3\p@ \ifdim\@tdA=\z@\else
- \@VArc(#1)(#2)%
-\fi
-\endgroup\ignorespaces}%
-%
-\def\VectorARC(#1)(#2)#3{\begingroup
-\@tdA=#3\p@
-\ifdim\@tdA=\z@\else
- \@VARC(#1)(#2)%
-\fi
-\endgroup\ignorespaces}%
-%
-\let\VVectorArc\VectorARC
-%
+\def\tempG{#3}%
+\fptestF{#3=0}{\@VArc(#1)(#2)}}%
% \end{macrocode}
%
-% The single arrow tipped arc is defined with the following long macro
-% where all the described operations are performed more or less in the
-% described succession; probably the macro requires a little cleaning,
-% but since it works fine we did not try to optimise it for time or
-% number of tokens. The final part of the macro is almost identical to
-% that of the plain arc; the beginning also is quite similar. The central
-% part is dedicated to the positioning of the arrow tip and to the
-% necessary calculations for determining the tip tilt and the reduction
-% of the total arc length; pay attention that the arrow length, stored in
-% |\@tdE| is a real length, while the radius stored in |\@Raggio| is just
-% a multiple of the |\unitlength|, so that the division (that yields a
-% good angular approximation to the arrow length as seen from the center
-% of the arc) must be done with real lengths. The already defined
-% |\@@Arc| macro actually draws the curved vector stem without stroking
-% it.
+% The single arrow tipped arc is defined with the
+% following long macro where all the described
+% operations are performed more or less in the
+% described succession; probably the macro requires
+% a little cleaning, but since it works fine we did
+% not try to optimise it for time or number of
+% tokens. The final part of the macro is almost
+% identical to that of the plain arc; the
+% beginning also is quite similar. The central part
+% is dedicated to the positioning of the arrow tip
+% and to the necessary calculations for determining
+% the tip tilt and the reduction of the total arc
+% length; pay attention that the arrow length,
+% stored in |\@tdE| is a real length, while the
+% radius stored in |\@Raggio| is just a multiple of
+% the |\unitlength|, so that the division (that
+% yields a good angular approximation to the
+% arrow length as seen from the center of the
+% arc) must be done with real lengths. The already
+% defined |\@@Arc| macro actually draws the curved
+% vector stem without stroking it.
% \begin{macrocode}
\def\@VArc(#1)(#2){%
-\ifdim\@tdA>\z@
- \let\Segno+%
-\else
- \@tdA=-\@tdA \let\Segno-%
-\fi \Numero\@gradi\@tdA
-\ifdim\@tdA>360\p@
- \PackageWarning{curve2e}{The arc aperture is \@gradi\space degrees
- and gets reduced\MessageBreak%
- to the range 0--360 taking the sign into consideration}%
- \@whiledim\@tdA>360\p@\do{\advance\@tdA-360\p@}%
-\fi
+\fptest{\tempG>\z@}%
+ {\let\Segno+}%
+ {\let\Segno-%
+ \edef\tempG{\fpeval{abs(\tempG)}}}%
+\let\@gradi\tempG
+\fptestT{\tempG>360}
+ {\PackageWarning{curve2e}%
+ {The arc aperture is \tempG\space degrees
+ and gets reduced^^J%
+ to the range 0--360 taking the sign into
+ consideration}%
+ \edef\tempG{\Modulo{\tempG}{360}}%
+ }%
+\let\@gradi\tempG
\GetCoord(#2)\@pPunX\@pPunY
\ifCV at polare
\ModOfVect#2to\@Raggio \CopyVect#2to\@V
\CopyVect#1to\@Cent
- \AddVect#2and#1to\@pPun% punto da cui parte l'arco
+ \AddVect#2and#1to\@pPun% punto iniziale
\GetCoord(\@pPun)\@pPunX\@pPunY
\else
\SubVect#1from#2to\@V \ModOfVect\@V to\@Raggio
@@ -2418,32 +3000,43 @@
\advance\@tdA -\@tdE \Numero\@gradi\@tdA
\CopyVect#1to\@Cent \GetCoord(\@pPun)\@pPunX\@pPunY
\@@Arc
-\strokepath\ignorespaces}%
+\strokepath\endgroup\ignorespaces}%
%
% \end{macrocode}
%
-% The macro for the arc terminated with arrow tips at both ends is again
-% very similar, but it is necessary to repeat the arrow tip
-% positioning also at the starting point. The |\@@Arc| macro draws the
-% curved stem.
+% The macro for the arc terminated with arrow tips
+% at both ends is again very similar, but it is
+% necessary to repeat the arrow tip positioning
+% also at the starting point. The |\@@Arc| macro
+% draws the curved stem.
% \begin{macrocode}
+%
+\def\VectorARC(#1)(#2)#3{\begingroup
+\def\tempG{#3}%
+ \fptestF{#3=0}{\@VARC(#1)(#2)}}%
+%
+\let\VVectorArc\VectorARC% alias
+%
+
\def\@VARC(#1)(#2){%
-\ifdim\@tdA>\z@
- \let\Segno+%
-\else
- \@tdA=-\@tdA \let\Segno-%
-\fi \Numero\@gradi\@tdA
-\ifdim\@tdA>360\p@
- \PackageWarning{curve2e}{The arc aperture is \@gradi\space degrees
+\fptest{\tempG>\z@}%
+ {\let\Segno+}%
+ {\let\Segno-%
+ \edef\tempG{\fpeval{abs(\tempG)}}}%
+\let\@gradi\tempG
+\fptestT{\tempG>360}{%
+ \PackageWarning{curve2e}%
+ {The arc aperture is \@gradi\space degrees
and gets reduced\MessageBreak%
- to the range 0--360 taking the sign into consideration}%
- \@whiledim\@tdA>360\p@\do{\advance\@tdA-360\p@}%
-\fi
+ to the range 0--360 taking the sign into
+ consideration}%
+ \edef\tempG{\Modulo{\tempG}{360}\p@}}
+ \@tdA=\tempG\p@ \let\@gradi\tempG
\GetCoord(#2)\@pPunX\@pPunY
\ifCV at polare
\ModOfVect#2to\@Raggio \CopyVect#2to\@V
\CopyVect#1to\@Cent
- \AddVect#2and#1to\@pPun% punto da cui parte l'arco
+ \AddVect#2and#1to\@pPun% punto iniziale
\GetCoord(\@pPun)\@pPunX\@pPunY
\else
\SubVect#1from#2to\@V \ModOfVect\@V to\@Raggio
@@ -2450,13 +3043,13 @@
\CopyVect#2to\@pPun
\CopyVect#1to\@Cent \GetCoord(\@pPun)\@pPunX\@pPunY
\fi
+%
\@tdE=\pIIe at FAW\@wholewidth \@tdE=\pIIe at FAL\@tdE
\DividE\@tdE by \@Raggio\unitlength to\DeltaGradi
-\@tdD=\DeltaGradi\p@
-\@tdD=57.29578\@tdD \Numero\DeltaGradi\@tdD
+\edef\DeltaGradi{\fpeval{57.29578*\DeltaGradi}}
\@tdD=\if\Segno--\fi\@gradi\p@ \Numero\@tempa\@tdD
\DirFromAngle\@tempa to\@Dir
-\Multvect{\@V}{\@Dir}\@sPun% corrects the end point
+\Multvect{\@V}{\@Dir}\@sPun% correct the end point
\edef\@tempA{\if\Segno--\fi1}%
\Multvect{\@sPun}{0,\@tempA}\@vPun
\DirOfVect\@vPun to\@Dir
@@ -2477,7 +3070,7 @@
\@tdE\if\Segno--\fi\DeltaGradi\p@
\Numero\@tempB{0.5\@tdE}%
\DirFromAngle\@tempB to\@Dird
-\Multvect{\@vPun}{\@Dird}\@vPun% corrects the starting point
+\Multvect{\@vPun}{\@Dird}\@vPun% correct the starting point
\DirOfVect\@vPun to\@Dir\GetCoord(\@Dir)\@xnum\@ynum
\put(\@pPunX,\@pPunY){\vector(\@xnum,\@ynum){0}}% starting point arrow tip
\edef\@tempa{\if\Segno--\fi\DeltaGradi}%
@@ -2487,32 +3080,41 @@
\AddVect\@Cent and\@V to\@pPun
\GetCoord(\@pPun)\@pPunX\@pPunY
\@@Arc
-\strokepath\ignorespaces}%
+\strokepath\endgroup\ignorespaces}%
% \end{macrocode}
%
-% It must be understood that the curved vectors, the above circular arcs
-% terminated with an arrow tips at one or both ends, have a nice
-% appearance only if the arc radius is not too small, or, said in a
-% different way, if the arrow tip angular width does not exceed a
-% maximum of a dozen degrees (and this is probably already too much); the
-% tip does not get curved as the arc is, therefore there is not a smooth
-% transition from the curved stem and the straight arrow tip if this one
-% is large in comparison to the arc radius.
+% It must be understood that the curved vectors,
+% i.e.~the above circular arcs terminated with an
+% arrow tips at one or both ends, have a nice
+% appearance only if the arc radius is not too
+% small, or, said in a different way, if the arrow
+% tip angular width does not exceed a maximum of a
+% dozen degrees (and this is probably already too
+% much); the tip does not get curved as the arc is,
+% therefore there is not a smooth transition from
+% the curved stem and the straight arrow tip if
+% this one is large in comparison to the arc
+% radius.
%
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{General curves}
-%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% The most used method to draw curved lines with computer programs is to
-% connect several simple curved lines, general “arcs”, one to another
-% generally maintaining the same tangent at the junction. If the
-% direction changes we are dealing with a cusp.
+%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% The most used method to draw curved lines with
+% computer programs is to connect several simple
+% curved lines, general “arcs”, one to another
+% generally maintaining the same tangent at the
+% junction. If the direction changes we are dealing
+% with a cusp.
%
-% The simple general arcs that are directly implemented in every program
-% that displays typeset documents, are those drawn with the parametric
-% curves called \emph{Béźier splines}; given a sequence of points in the
-% $x,y$ plane, say $P_0, P_1, P_2, p_3, \dots$ (represented as coordinate
-% pairs, i.e. by complex numbers), the most common Bézier splines are the
+% The simple general arcs that are directly
+% implemented in every program that displays
+% typeset documents, are those drawn with the
+% parametric curves called \emph{Béźier splines};
+% given a sequence of points in the $x,y$ plane,
+% say $P_0, P_1, P_2, P_3, \dots$ (represented as
+% coordinate pairs, i.e. by complex numbers), the
+% most common Bézier splines are the
% following ones:
% \begin{align}
% \mathcal{B}_1 &= P_0(1-t) + P_1t \label{equ:B-1} \\
@@ -2521,61 +3123,81 @@
% \label{equ:B-3}
% \end{align}
%
-% All these splines depend on parameter $t$; they have the property that
-% for $t=0$ each line starts at the first point, while for $t=1$ they
-% reach the last point; in each case the generic point $P$ on each curve
-% takes off with a direction that points to the next point, while it
-% lands on the destination point with a direction coming from the
-% penultimate point; moreover, when $t$ varies from 0 to 1, the curve arc
-% is completely contained within the convex hull formed by the polygon
-% that has the spline points as vertices.
+% All these splines depend on parameter $t$; they
+% have the property that for $t=0$ each line starts
+% at the first point, while for $t=1$ they reach
+% the last point; in each case the generic point
+% $P$ on each curve takes off with a direction
+% that points to the next point, while it lands on
+% the destination point with a direction coming
+% from the penultimate point; moreover, when $t$
+% varies from 0 to 1, the curve arc is completely
+% contained within the convex hull formed by the
+% polygon that has the spline points as vertices.
%
-% Last but not least first order splines implement just straight lines
-% and they are out of question for what concerns maxima, minima,
-% inflection points and the like. Quadratic splines draw just
-% parabolas, therefore they draw arcs that have the concavity just on one
-% side of the path; therefore no inflection points. Cubic splines are
-% extremely versatile and can draw lines with maxima, minima and
-% inflection points. Virtually a multi-arc curve may be drawn by a set of
-% cubic splines as well as a set of quadratic splines (fonts are a good
-% example: Adobe Type~1 fonts have their contours described by cubic
-% splines, while TrueType fonts have their contours described with
-% quadratic splines; at naked eye it is impossible to notice the
-% difference).
+% Last but not least first order splines implement
+% just straight lines and they are out of question
+% for what concerns maxima, minima, inflection
+% points and the like. Quadratic splines draw
+% just parabolas, therefore they draw arcs that
+% have the concavity just on one side of the path;
+% therefore no inflection points. Cubic splines are
+% extremely versatile and can draw lines with
+% maxima, minima and inflection points.
+% Virtually a multi-arc curve may be drawn by a set
+% of cubic splines as well as a set of quadratic
+% splines (fonts are a good example: Adobe Type~1
+% fonts have their contours described by cubic
+% splines, while TrueType fonts have their contours
+% described with quadratic splines; at naked eye it
+% is impossible to notice the difference).
%
-% Each program that processes the file to be displayed is capable of
-% drawing first order Bézier splines (segments) and third order Bézier
-% splines, for no other reason, at least, because they have to draw
-% vector fonts whose contours are described by Bézier splines; sometimes
-% they have also the program commands to draw second order Bézier
-% splines, but not always these machine code routines are available to
-% the user for general use. For what concerns |pdftex|, |xetex| and
-% |luatex|, they have the user commands for straight lines and cubic
-% arcs. At least with |pdftex|, quadratic arcs must be simulated with a
-% clever use of third order Bézier splines.
+% Each program that processes the file to be
+% displayed is capable of drawing first order
+% Bézier splines (segments) and third order Bézier
+% splines, for no other reason, at least, because
+% they have to draw vector fonts whose contours are
+% described by Bézier splines; sometimes they have
+% also the program commands to draw second order
+% Bézier splines, but not always these machine code
+% routines are available to the user for general
+% use. For what concerns |pdftex|, |xetex| and
+% |luatex|, they have the user commands for
+% straight lines and cubic arcs. At least with
+% |pdftex|, quadratic arcs must be simulated with
+% a clever use of third order Bézier splines.
%
-% Notice that the \LaTeXe\ environment |picture| by itself is capable of
-% drawing both cubic and quadratic Bézier splines as single arcs; but it
-% resorts to ``poor man'' solutions. The |pict2e| package removes all the
-% old limitations and implements the interface macros for sending the
-% driver the necessary drawing information, including the transformation
-% from typographical points (72.27\,pt/inch) to PostScript big points
-% (72\,bp/inch). But for what concerns the quadratic spline it resorts to
-% the clever use of a cubic spline.
+% Notice that the \LaTeXe\ environment |picture|
+% by itself is capable of drawing both cubic and
+% quadratic Bézier splines as single arcs; but it
+% resorts to “poor man” solutions. The |pict2e|
+% package removes all the old limitations and
+% implements the interface macros for sending the
+% driver the necessary drawing information,
+% including the transformation from typographical
+% points (72.27\,pt/inch) to PostScript big points
+% (72\,bp/inch). But for what concerns the
+% quadratic spline it resorts to the clever use of
+% a cubic spline.
%
-% Therefore here we treat first the drawings that can be made with cubic
-% splines; then we describe the approach to quadratic splines.
+% Therefore here we treat first the drawings that
+% can be made with cubic splines; then we describe
+% the approach to quadratic splines.
%
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\subsection{Cubic splines}
-%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Now we define a macro for tracing a general, not necessarily circular,
-% arc. This macro resorts to a general triplet of macros with which it is
-% possible to draw almost anything. It traces a single Bézier spline from
-% a first point where the tangent direction is specified to a second
-% point where again it is specified the tangent direction. Actually this
-% is a special (possibly useless) case where the general |\curve| macro
-% of |pict2e| could do the same or a better job. In any case\dots
+%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Now we define a macro for tracing a general, not
+% necessarily circular, arc. This macro resorts to
+% a general triplet of macros with which it is
+% possible to draw almost anything. It traces a
+% single Bézier spline from a first point where the
+% tangent direction is specified to a second point
+% where again it is specified the tangent
+% direction. Actually this is a special (possibly
+% useless) case where the general |\curveto| macro
+% of |pict2e| could do the same or a better
+% job. In any case\dots
% \begin{macrocode}
\def\CurveBetween#1and#2WithDirs#3and#4{%
\StartCurveAt#1WithDir{#3}\relax
@@ -2583,51 +3205,71 @@
}%
% \end{macrocode}
%
-% Actually the above macro is a special case of concatenation of the
-% triplet formed by macros |\StartCurve|, |\CurveTo| and|\CurveFinish|;
-% the second macro can be repeated an arbitrary number of times.
-% In any case the directions specified with the direction arguments
-% the angle between the indicated tangent and the arc chord may give
-% raise to some little problems when they are very close to 90° in
-% absolute value. Some control is exercised on these values, but some
-% tests might fail if the angle derives from other calculations; this
-% is a good place to use polar forms for the direction vectors. The
-% same comments apply also to the more general macro |\Curve|,
+% Actually the above macro is a special case of
+% concatenation of the triplet formed by macros
+% |\StartCurve|, |\CurveTo| and |\CurveFinish|; the
+% second macro can be repeated an arbitrary number
+% of times. In any case the directions specified
+% with the direction arguments the angle between
+% the indicated tangent and the arc chord may give
+% raise to some little problems when they are very
+% close to 90° in absolute value. Some control is
+% exercised on these values, but some tests might
+% fail if the angle derives from other
+% calculations; this is a good place to use polar
+% forms for the direction vectors. The same
+% comments apply also to the more general macro
+% |\Curve|,
%
-% The first macro initialises the drawing and the third one strokes it;
-% the real work is done by the second macro. The first macro initialises
-% the drawing but also memorises the starting direction; the second macro
-% traces the current Bézier arc reaching the destination point with the
-% specified direction, but memorises this direction as the one with which
-% to start the next arc. The overall curve is then always smooth because
-% the various Bézier arcs join with continuous tangents. If a cusp is
-% desired it is necessary to change the memorised direction at the end of
-% the arc before the cusp and before the start of the next arc; this is
-% better than stroking the curve before the cusp and then starting
-% another curve, because the curve joining point at the cusp is not
-% stroked with the same command, therefore we get two superimposed curve
-% terminations. To avoid this imperfection, we need another small macro
-% |\ChangeDir| to perform this task.
+% The first macro initialises the drawing and the
+% third one strokes it; the real work is done by
+% the second macro. The first macro initialises the
+% drawing but also memorises the starting
+% direction; the second macro traces the current
+% Bézier arc reaching the destination point with
+% the specified direction, but memorises this
+% direction as the one with which to start the next
+% arc. The overall curve is then always smooth
+% because the various Bézier arcs join with
+% continuous tangents.
+% If a cusp is desired it is necessary to change
+% the memorised direction at the end of the arc
+% before the cusp and before the start of the next
+% arc; this is better than stroking the curve
+% before the cusp and then starting another curve,
+% because the curve joining point at the cusp is
+% not stroked with the same command, therefore we
+% get two superimposed curve terminations.
+% To avoid this imperfection, we need another small
+% macro |\ChangeDir| to perform this task.
%
-% It is necessary to recall that the direction vectors point to the
-% control points, but they do not define the control points themselves;
-% they are just directions, or, even better, they are simply vectors with
-% the desired direction; the macros themselves provide to the
-% normalisation and memorisation.
+% It is necessary to recall that the direction
+% vectors point to the control points, but they do
+% not define the control points themselves; they
+% are just directions, or, even better, they are
+% simply vectors with the desired direction; the
+% macros themselves provide to the normalisation
+% and memorisation.
%
-% The next desirable feature would be to design a macro that accepts
-% optional node directions and computes the missing ones according to a
-% suitable strategy. We can think of many such strategies, but none seems
-% to be generally applicable, in the sense that one strategy might give
-% good results, say, with sinusoids and another one, say, with cardioids,
-% but neither one is suitable for both cases.
+% The next desirable feature would be to design a
+% macro that accepts optional node directions and
+% computes the missing ones according to a suitable
+% strategy. We can think of many such strategies,
+% but none seems to be generally applicable, in the
+% sense that one strategy might give good results,
+% say, with sinusoids and another one, say, with
+% cardioids, but neither one is suitable for both
+% cases.
%
-% For the moment we refrain from automatic direction computation, but we
-% design the general macro as if directions were optional.
+% For the moment we refrain from automatic
+% direction computation, but we design the general
+% macro as if directions were optional.
%
-% Here we begin with the first initialising macro that receives with the
-% first argument the starting point and with the second argument the
-% direction of the tangent (not necessarily normalised to a unit vector)
+% Here we begin with the first initialising macro
+% that receives with the first argument the
+% starting point and with the second argument the
+% direction of the tangent (not necessarily
+% normalised to a unit vector)
% \begin{macrocode}
\def\StartCurveAt#1WithDir#2{%
\begingroup
@@ -2639,7 +3281,8 @@
\DirOfVect\@Dzero to\@Dzero
\ignorespaces}
% \end{macrocode}
-% And this re-initialises the direction to create a cusp:
+% And this re-initialises the direction to create
+% a cusp:
% \begin{macrocode}
\def\ChangeDir<#1>{%
\GetCoord(#1)\@tempa\@tempb
@@ -2648,59 +3291,78 @@
\ignorespaces}
% \end{macrocode}
%
-% The next macros are the finishing ones; the first strokes the whole
-% curve, while the second fills the (closed) curve with the default
-% color; both close the group that was opened with |\StartCurve|. The
-% third macro is explained in a while; we anticipate it is functional to
-% chose between the first two macros when a star is possibly used to
-% switch between stroking and filling.
+% The next macros are the finishing ones; the first
+% strokes the whole curve, while the second fills
+% the (closed) curve with the default color; both
+% close the group that was opened with
+% |\StartCurve|. The third macro is going to be
+% explained in a while; we anticipate it is
+% functional to chose between the first two macros
+% when a star is possibly used to switch between
+% stroking and filling.
% \begin{macrocode}
-\def\CurveFinish{\strokepath\endgroup\ignorespaces}%
+\def\CurveFinish{\strokepath\endgroup\ignorespaces}
\def\FillCurve{\fillpath\endgroup\ignorespaces}
\def\CurveEnd{\fillstroke\endgroup\ignorespaces}
% \end{macrocode}
%
-% In order to draw the internal arcs it would be desirable to have a
-% single macro that, given the destination point, computes the control
-% points that produce a cubic Bézier spline that joins the starting point
-% with the destination point in the best possible way. The problem is
-% strongly ill defined and has an infinity of solutions; here we give two
-% solutions: $(a)$ a supposedly smart one that resorts to osculating
-% circles and requires only the direction at the destination point; and
-% $(b)$ a less smart solution that requires the control points to be
-% specified in a certain format.
+% In order to draw the internal arcs it would be
+% desirable to have a single macro that, given the
+% destination point, computes the control points
+% that produce a cubic Bézier spline that joins the
+% starting point with the destination point in the
+% best possible way. The problem is strongly ill
+% defined and has an infinity of solutions; here we
+% give two solutions: $(a)$ a supposedly smart one
+% that resorts to osculating circles and requires
+% only the direction at the destination point; and
+% $(b)$ a less smart solution that requires the
+% control points to be specified in a certain
+% format.
%
-% We start with solution $(b)$, |\CbezierTo|, the code of which is
-% simpler than that of solution $(a)$; then we will produce the solution
-% $(a)$, |\CurveTo|, that will become the main building block for a
-% general path construction macro, |\Curve|.
+% We start with solution $(b)$, |\CbezierTo|, the
+% code of which is simpler than that of solution
+% $(a)$; then we will produce the solution $(a)$,
+% |\CurveTo|, that will become the main
+% building block for a general path construction
+% macro, |\Curve|.
%
-% The “naïve” macro |\CBezierTo| simply uses the previous point direction
-% saved in |\@Dzero| as a unit vector by the starting macro; specifies
-% a destination point, the distance of the first control point from the
-% starting point, the destination point direction that will save also for
-% the next arc-drawing macro as a unit vector, and the distance of the
-% second control point from the destination point along this last
-% direction. Both distances must be positive possibly fractional
-% numbers. The syntax therefore is the following:
-%\begin{flushleft}
-%\cs{CbezierTo}\meta{end
-% point}|WithDir|\meta{direction}|AndDists|\meta{$K_0$}|And|\meta{$K_1$}
-%\end{flushleft}
-% where \meta{end point} is a vector macro or a comma separated pair of
-% values; again \meta{direction} is another vector macro or a comma
-% separated pair of values, that not necessarily indicate a unit vector,
-% since the macro provides to normalise it to unity; \meta{$K_0$} and
-% \meta{$K_1$} are the distances of the control points from their
-% respective node points; they must be integers or fractional positive
-% numbers. If \meta{$K_1$} is a number, it must be enclosed in curly
-% braces, while if it is a macro name (containing the desired fractional
+% The “naïve” macro |\CBezierTo| simply uses the
+% previous point direction saved in |\@Dzero| as a
+% unit vector by the starting macro; specifies a
+% destination point, the distance of the first
+% control point from the starting point, the
+% destination point direction that will save also
+% for the next arc-drawing macro as a unit vector,
+% and the distance of the second control point from
+% the destination point along this last direction.
+% Both distances must be positive possibly
+% fractional numbers. The syntax therefore is the
+% following:
+%\begin{Sintassi}
+%\cs{CbezierTo}\meta{end point}|WithDir|\meta{direction}%
+%|AndDists|\meta{$K_0$}|And|\meta{$K_1$}
+%\end{Sintassi}
+% where \meta{end point} is a vector macro or a
+% comma separated pair of values; again
+% \meta{direction} is another vector macro or a
+% comma separated pair of values, that not
+% necessarily indicate a unit vector, since the
+% macro provides to normalise it to unity;
+% \meta{$K_0$} and \meta{$K_1$} are the distances
+% of the control points from their respective node
+% points; they must be integers or fractional
+% positive numbers. If \meta{$K_1$} is a number, it
+% must be enclosed in curly braces, while if it is
+% a macro name (containing the desired fractional
% or integer value) there is no need for braces.
%
-% This macro uses the input information in order to activate the internal
-% |pict2e| macro |\pIIe at curveto| with the proper arguments, and to save
-% the final direction into the same |\@Dzero| macro for successive use
-% of other arc-drawing macros.
+% This macro uses the input information in order to
+% activate the internal |pict2e| macro
+% |\pIIe at curveto| with the proper arguments, and to
+% save the final direction into the same |\@Dzero|
+% macro for successive use of other arc-drawing
+% macros.
% \begin{macrocode}
\def\CbezierTo#1WithDir#2AndDists#3And#4{%
\GetCoord(#1)\@tX\@tY \MakeVectorFrom\@tX\@tY to\@Puno
@@ -2712,107 +3374,138 @@
\GetCoord(\@Cuno)\@XCuno\@YCuno
\GetCoord(\@Puno)\@XPuno\@YPuno
\pIIe at curveto{\@XCzero\unitlength}{\@YCzero\unitlength}%
- {\@XCuno\unitlength}{\@YCuno\unitlength}%
- {\@XPuno\unitlength}{\@YPuno\unitlength}%
+ {\@XCuno\unitlength}%
+ {\@YCuno\unitlength}%
+ {\@XPuno\unitlength}%
+ {\@YPuno\unitlength}%
\CopyVect\@Puno to\@Pzero
\CopyVect\@Duno to\@Dzero
\ignorespaces}%
% \end{macrocode}
%
-% With this building block it is not difficult to set up a macro that
-% draws a Bézier arc between two given points, similarly to the other
-% macro |\CurveBetween| previously described and defined here:
-%
+% With this building block it is not difficult to
+% set up a macro that draws a Bézier arc between
+% two given points, similarly to the other macro
+% |\CurveBetween| previously described and
+% defined here:
% \begin{macrocode}
-\def\CbezierBetween#1And#2WithDirs#3And#4UsingDists#5And#6{%
-\StartCurveAt#1WithDir{#3}\relax
+\def\CbezierBetween#1And#2WithDirs#3And#4UsingDists#5And#6{\StartCurveAt#1WithDir{#3}\relax
\CbezierTo#2WithDir#4AndDists#5And{#6}\CurveFinish}
% \end{macrocode}
%
-% An example of use is shown in figure~13 of the user manual
-% |curve2e-manual.pdf| file; notice that the tangents at the end points
-% are the same for the black curve drawn with |\CurveBetween| and the
-% five red curves drawn with |\CbezierBetween|; the five red curves
-% differ only for the distance of their control point $C_0$ from the
-% starting point; the differences are remarkable and the topmost curve
-% even presents a slight inflection close to the end point. These effects
-% cannot be obtained with the “smarter” macro |\CurveBetween|. But
-% certainly this simpler macro is more difficult to use because the
-% distances of the control points are difficult to estimate and require a
-% number of cut-and-try experiments.
+% An example of use is shown in figure~13 of the
+% |curve2e-manual.pdf| file; notice that the
+% tangents at the end points are the same for the
+% black curve drawn with |\CurveBetween| and the
+% five red curves drawn with |\CbezierBetween|; the
+% five red curves differ only for the distance of
+% their control point $C_0$ from the starting
+% point; the differences are remarkable and the
+% topmost curve even presents a slight inflection
+% close to the end point.
+% These effects cannot be obtained with the
+% “smarter” macro |\CurveBetween|. But certainly
+% this simpler macro is more difficult to use
+% because the distances of the control points
+% are difficult to estimate and require a number
+% of cut-and-try experiments.
%
-% The ``smarter'' curve macro comes next; it is supposed to determine the
-% control points for joining the previous point (initial node) with the
-% specified direction to the next point (final node) with another
-% specified direction.
-
-% Since the control points are along the specified directions, it is
-% necessary to determine the distances from the adjacent curve nodes.
-% This must work correctly even if nodes and directions imply an
-% inflection point somewhere along the arc.
+% The “smarter” curve macro comes next; it is
+% supposed to determine the control points for
+% joining the previous point (initial node) with
+% the specified direction to the next point (final
+% node) with another specified direction.
%
-% The strategy we devised consists in determining each control point as
-% if it were the control point of a circular arc, precisely an arc of an
-% osculating circle, i.e. a circle tangent to the curve at that node. The
-% ambiguity of the stated problem may be solved by establishing that the
-% chord of the osculating circle has the same direction as the chord of
-% the arc being drawn, and that the curve chord is divided into two equal
-% parts each of which should be interpreted as half the chord of the
-% osculating circle.
+% Since the control points are along the specified
+% directions, it is necessary to determine the
+% distances from the adjacent curve nodes. This
+% must work correctly even if nodes and directions
+% imply an inflection point somewhere along the
+% arc.
%
-% This makes the algorithm a little rigid; sometimes the path drawn is
-% very pleasant, while in other circumstances the determined curvatures
-% are too large or too small. We therefore add some optional information
-% that lets us have some control over the curvatures; the idea is based
-% on the concept of \emph{tension}, similar but not identical to the one
-% used in the drawing programs \MF\ and \MP. We add to the direction
-% information, with which the control nodes of the osculating circle arcs
-% are determined, a scaling factor that should be intuitively related to
-% the tension of the arc (actually, since the tension of the ‘rope’ is
-% high when this parameter is low, probably a name such as ‘looseness’
-% would be better suited): the smaller this number, the closer the arc
-% resembles a straight line as a rope subjected to a high tension; value
-% zero is allowed, while a value of 4 is close to ``infinity'' and turns
-% a quarter circle into a line with an unusual loop; a value of 2 turns a
-% quarter circle almost into a polygonal line with rounded vertices
-%. Therefore these tension factors should be used only for fine tuning
-% the arcs, not when a path is drawn for the first time.
+% The strategy we devised consists in determining
+% each control point as if it were the control
+% point of a circular arc, precisely an arc of an
+% osculating circle, i.e. a circle tangent to the
+% curve at that node. The ambiguity of the stated
+% problem may be solved by establishing that the
+% chord of the osculating circle has the same
+% direction as the chord of the arc being drawn,
+% and that the curve chord is divided into two
+% equal parts each of which should be interpreted
+% as half the chord of the osculating circle.
%
-% We devised a syntax for specifying direction and tensions:
-%\begin{flushleft}
+% This makes the algorithm a little rigid;
+% sometimes the path drawn is very pleasant, while
+% in other circumstances the determined curvatures
+% are too large or too small. We therefore add some
+% optional information that lets us have some
+% control over the curvatures; the idea is based on
+% the concept of \emph{tension}, similar but not
+% identical to the one used in the drawing programs
+% \MF\ and \MP. We add to the direction
+% information, with which the control nodes of the
+% osculating circle arcs are determined, a scaling
+% factor that should be intuitively related to the
+% tension of the arc (actually, since the tension
+% of the ‘rope’ is high when this parameter is low,
+% probably a name such as ‘looseness’ would be
+% better suited): the smaller this number, the
+% closer the arc resembles to a straight line as a
+% rope subjected to a high tension; value zero is
+% allowed, while a value of 4 is close to
+% “infinity” and turns a quarter circle into a line
+% with an unusual loop; a value of 2 turns a
+% quarter circle almost into a polygonal line with
+% rounded vertices.
+% Therefore these tension factors should be used
+% only for fine tuning the arcs, not when a path is
+% drawn for the first time.
+%
+% We devised a syntax for specifying direction and
+% tensions:
+%\begin{Sintassi}
% \meta{direction\texttt{\upshape;}tension factors}
-%\end{flushleft}
-% where \emph{direction} contains a pair of fractional numbers that not
-% necessarily refer to the components of a unit vector direction, but
-% simply to a vector with the desired orientation (polar form is OK); the
-% information contained from the semicolon (included) to the rest of the
-% specification is optional; if it is present, the \emph{tension factors}
-% is simply a comma separated pair of fractional or integer numbers that
-% represent respectively the tension at the starting or the ending node
-% of a path arc.
+%\end{Sintassi}
+% where \emph{direction} contains the complex
+% number that not necessarily refers to the
+% components of a unit vector direction, but simply
+% to a vector with the desired orientation (polar
+% form is OK); the information contained from the
+% semicolon (included) to the rest of the
+% specification is optional; if it is present, the
+% \emph{tension factor} is simply a comma separated
+% pair of fractional or integer numbers that
+% represent respectively the tension at the
+% starting or the ending node of a path arc.
%
-% We therefore need a macro to extract the mandatory and optional parts:
+% We therefore need a macro to extract the
+% mandatory and optional parts:
% \begin{macrocode}
\def\@isTension#1;#2!!{\def\@tempA{#1}%
-\def\@tempB{#2}\unless\ifx\@tempB\empty\strip at semicolon#2\fi}
+\def\@tempB{#2}\unless\ifx\@tempB\empty \strip at semicolon#2\fi}
\def\strip at semicolon#1;{\def\@tempB{#1}}
% \end{macrocode}
-% By changing the tension values we can achieve different results: see
-% figure~14 in the user manual |curve2e-manual.pdf|.
+% By changing the tension values we can achieve
+% different results: see figure~14 in the user
+% manual |curve2e-manual.pdf|.
%
-% We use the formula we got for arcs~\eqref{equ:corda}, where the half
-% chord is indicated with $s$, and we derive the necessary distances:
+% We use the formula we got for
+% arcs~\eqref{equ:corda}, where the half chord is
+% indicated with $s$, and we derive the necessary
+% distances:
%\begin{subequations}\label{equ:Kzero-Kuno}
%\begin{align}
%K_0 &= \frac{4}{3} s\frac{1-\cos\theta_0}{\sin^2\theta_0}\\
%K_1 &=\frac{4}{3}s\frac{1-\cos\theta_1}{\sin^2\theta_1}
%\end{align}
-%\end{subequations}
+%\end{subequations}
%
-% We therefore start with getting the points and directions and
-% calculating the chord and its direction:
+% We therefore start with getting the points and
+% directions and calculating the chord and its
+% direction:
% \begin{macrocode}
\def\CurveTo#1WithDir#2{%
\def\@Tuno{1}\def\@Tzero{1}\relax
@@ -2821,8 +3514,8 @@
\bgroup\unless\ifx\@tempB\empty\GetCoord(\@tempB)\@Tzero\@Tuno\fi
\DistanceAndDirOfVect\@Puno minus\@Pzero to\@Chord and\@DirChord
% \end{macrocode}
-% Then we rotate everything about the starting point so as to bring the
-% chord on the real axis
+% Then we rotate everything about the starting
+% point so as to bring the chord on the real axis
% \begin{macrocode}
\Multvect{\@Dzero}*{\@DirChord}\@Dpzero
\Multvect{\@Duno}*{\@DirChord}\@Dpuno
@@ -2830,42 +3523,56 @@
\GetCoord(\@Dpuno)\@DXpuno\@DYpuno
\DivideFN\@Chord by2 to\@semichord
% \end{macrocode}
-% The chord needs not be actually rotated because it suffices its length
-% along the real axis; the chord length is memorised in |\@Chord| and
-% its half is saved in |\@semichord|.
+% The chord needs not be actually rotated because
+% it suffices its length along the real axis; the
+% chord length is memorised in |\@Chord| and its
+% half is saved in |\@semichord|.
%
-% We now examine the various degenerate cases, when either tangent is
-% perpendicular or parallel to the chord. Notice that we are calculating
-% the distances of the control points from the adjacent nodes using the
-% half chord length, not the full length. We also distinguish between the
-% computations relative to the arc starting point and those relative to
-% the end point. Notice that if the directions of two successive nodes are
-% identical, it is necessary to draw a line, not a third order
-% spline\footnote{Many thanks to John Hillas who spotted this bug, that
-% passed unnoticed for long time, because it is a very unusual situation.};
-% therefore it is necessary to make a suitable test that is more
-% comfortable to do after the chord has been rotated to be horizontal;
-% in facts, if the two directions are equal, the vertical components
-% of the directions are both vanishing values; probably, instead of
-% testing with respect to zero, it might be advisable to test the
-% absolute value with respect to a small number such as, for example,
-% “1.e-6.”
+% We now examine the various degenerate cases, when
+% either tangent is perpendicular or parallel to
+% the chord. Notice that we are calculating the
+% distances of the control points from the adjacent
+% nodes using the half chord length, not the full
+% length. We also distinguish between the
+% computations relative to the arc starting point
+% and those relative to the end point.
%
+% Notice that if the directions of two successive
+% nodes are identical, it is necessary to draw a
+% line, not a third order spline\footnote{Many
+% thanks to John Hillas who spotted this bug, that
+% passed unnoticed for a long time, because it is a
+% very unusual situation.}; therefore it is
+% necessary to make a suitable test that is more
+% comfortable to do after the chord has been
+% rotated to be horizontal; in facts, if the two
+% directions are equal, the vertical components of
+% the directions are both vanishing values;
+% probably, instead of testing with respect to
+% zero, it might be advisable to test the absolute
+% value with respect to a small number such as, for
+% example, “1.e-6.”
+%
% \begin{macrocode}
-\fptest{\@DYpuno=0 && \@DYpzero=0}{\GetCoord(\@Puno)\@tX\@tY
- \pIIe at lineto{\@tX\unitlength}{\@tY\unitlength}}%
-{\ifdim\@DXpzero\p@=\z@
- \@tdA=1.333333\p@
- \Numero\@KCzero{\@semichord\@tdA}%
-\fi
-\ifdim\@DYpzero\p@=\z@
- \@tdA=1.333333\p@
- \Numero\@Kpzero{\@semichord\@tdA}%
-\fi
+%
+\fptest{abs(\@DYpuno)<=0.01&& abs(\@DYpzero)<=0.01}
+{\GetCoord(\@Puno)\@tX\@tY
+ \pIIe at lineto{\@tX\unitlength}%
+ {\@tY\unitlength}%
+}{%
+ \fptestT{abs(\@DXpzero)<=0.01}%
+ {\@tdA=1.333333\p@
+ \Numero\@KCzero{\@semichord\@tdA}}%
+\fptestT{abs(\@DYpzero)<=0.01}%
+ {\@tdA=1.333333\p@
+ \Numero\@Kpzero{\@semichord\@tdA}}%
+%
% \end{macrocode}
-% The distances we are looking for are positive generally fractional
-% numbers; so if the components are negative, we take the absolute
-% values. Eventually we determine the absolute control point coordinates.
+% The distances we are looking for are positive
+% generally fractional numbers; so if the
+% components are negative, we take the absolute
+% values. Eventually we determine the absolute
+% control point coordinates.
% \begin{macrocode}
\unless\ifdim\@DXpzero\p@=\z@
\unless\ifdim\@DYpzero\p@=\z@
@@ -2881,12 +3588,14 @@
\ScaleVect\@Dzero by\@KCzero to\@CPzero
\AddVect\@Pzero and\@CPzero to\@CPzero
% \end{macrocode}
-% We now repeat the calculations for the arc end point, taking into
-% consideration that the end point direction points outwards, so that in
-% computing the end point control point we have to take this fact into
-% consideration by using a negative sign for the distance; in this way
-% the displacement of the control point from the end point takes place
-% in a backwards direction.
+% We now repeat the calculations for the arc end
+% point, taking into consideration that the end
+% point direction points outwards, so that in
+% computing the end point control point we have to
+% take this fact into consideration by using a
+% negative sign for the distance; in this way the
+% displacement of the control point from the end
+% point takes place in a backwards direction.
% \begin{macrocode}
\ifdim\@DXpuno\p@=\z@
\@tdA=-1.333333\p@
@@ -2910,19 +3619,25 @@
\ScaleVect\@Duno by\@KCuno to\@CPuno
\AddVect\@Puno and\@CPuno to\@CPuno
% \end{macrocode}
-% Now we have the four points and we can instruct the internal
-% \texttt{pict2e} macros to do the path drawing.
+% Now we have the four points and we can instruct
+% the internal \texttt{pict2e} macros to do the
+% path drawing.
% \begin{macrocode}
\GetCoord(\@Puno)\@XPuno\@YPuno
\GetCoord(\@CPzero)\@XCPzero\@YCPzero
\GetCoord(\@CPuno)\@XCPuno\@YCPuno
-\pIIe at curveto{\@XCPzero\unitlength}{\@YCPzero\unitlength}%
- {\@XCPuno\unitlength}{\@YCPuno\unitlength}%
- {\@XPuno\unitlength}{\@YPuno\unitlength}}\egroup
+\pIIe at curveto{\@XCPzero\unitlength}%
+ {\@YCPzero\unitlength}%
+ {\@XCPuno\unitlength}%
+ {\@YCPuno\unitlength}%
+ {\@XPuno\unitlength}%
+ {\@YPuno\unitlength}}\egroup
% \end{macrocode}
-% It does not have to stroke the curve because other Bézier splines
-% might still be added to the path. On the opposite it memorises the
-% final point to be used as the initial point of the next spline
+% It does not have to stroke the curve because
+% other Bézier splines might still be added to the
+% path. On the opposite it memorises the final
+% point to be used as the initial point of the next
+% spline
% \begin{macrocode}
\CopyVect\@Puno to\@Pzero
\CopyVect\@Duno to\@Dzero
@@ -2930,30 +3645,40 @@
% \end{macrocode}
%
%
-% We finally define the overall |\Curve| macro that has two flavours:
-% starred and unstarred; the former fills the curve path with the locally
-% selected color, while the latter just strokes the path. Both
-% recursively examine an arbitrary list of nodes and directions; node
-% coordinates are grouped within round parentheses while direction
-% components are grouped within angle brackets. Before testing for a
-% possible star, this initial command kills any space or glue that
-% might precede it\footnote{Thanks to John Hillas who spotted the
-% effects of this missing glue elimination.} The first call of the
-% macro initialises the drawing process and checks for the next node and
-% direction; if a second node is missing, it issues a warning message and
-% does not draw anything. It does not check for a change in direction,
-% because it would be meaningless at the beginning of a curve. The second
-% macro defines the path to the next point and checks for another node;
-% if the next list item is a square bracket delimited argument, it
-% interprets it as a change of direction, while if it is another
-% parenthesis delimited argument it interprets it as a new node-direction
-% specification; if the node and direction list is terminated, it issues
-% the stroking or filling command through |\CurveEnd|, and exits the
-% recursive process. The |\CurveEnd| control sequence has a different
-% meaning depending on the fact that the main macro was starred or
-% unstarred. The |@ChangeDir| macro is just an interface to execute the
-% regular |\ChangeDir| macro, but also for recursing again by recalling
-% |\@Curve|.
+% We finally define the overall |\Curve| macro that
+% has two flavours: starred and unstarred; the
+% former fills the curve path with the locally
+% selected color, while the latter just strokes the
+% path. Both recursively examine an arbitrary list
+% of nodes and directions; node coordinates are
+% grouped within round parentheses while direction
+% components are grouped within angle brackets.
+% Before testing for a possible star, this initial
+% command kills any space or glue that might
+% precede it\footnote{Thanks to John Hillas who
+% spotted the effects of this missing glue
+% elimination.} The first call of the macro
+% initialises the drawing process and checks for
+% the next node and direction; if a second node is
+% missing, it issues a warning message and does not
+% draw anything. It does not check for a change in
+% direction, because it would be meaningless at the
+% beginning of a curve. The second macro defines
+% the path to the next point and checks for another
+% node; if the next list item is a square bracket
+% delimited argument, it interprets it as a change
+% of direction, while if it is another parenthesis
+% delimited argument it interprets it as a new
+% node-direction specification; if the node and
+% direction list is terminated, it issues the
+% stroking or filling command through |\CurveEnd|,
+% and exits the recursive process. The |\CurveEnd|
+% control sequence has a different meaning
+% depending on the fact that the main macro was
+% starred or unstarred. The |@ChangeDir| macro is
+% just an interface to execute the regular
+% |\ChangeDir| macro, but also for recursing
+% again by recalling |\@Curve|.
% \begin{macrocode}
\def\Curve{\@killglue\@ifstar{\let\fillstroke\fillpath\Curve@}%
{\let\fillstroke\strokepath\Curve@}}
@@ -2962,8 +3687,11 @@
\StartCurveAt#1WithDir{#2}%
\@ifnextchar\lp at r\@Curve{%
\PackageWarning{curve2e}{%
- Curve specifications must contain at least two nodes!\MessageBreak
- Please, control your \string\Curve\space specifications\MessageBreak}}}
+ Curve specifications must contain at least
+ two nodes!^^J
+ Please, control your \string\Curve\space
+ specifications^^J}}}
+
\def\@Curve(#1)<#2>{%
\CurveTo#1WithDir{#2}%
\@ifnextchar\lp at r\@Curve{%
@@ -2971,64 +3699,84 @@
\def\@ChangeDir[#1]{\ChangeDir<#1>\@Curve}
% \end{macrocode}
%
-% As a concluding remark, please notice that the |\Curve| macro is
-% certainly the most comfortable to use, but it is sort of frozen in its
-% possibilities. The user may certainly use the |\StartCurve|,
-% |\CurveTo|, |\ChangeDir|, and |\CurveFinish| or |\FillCurve| for a
-% more versatile set of drawing macros; evidently nobody forbids to
-% exploit the full power of the |\cbezier| original macro for cubic
-% splines; we made available macros |\CbezierTo| and the isolated arc
-% macro |\CbezierBetween| in order to use the general internal cubic
-% Bézier splines in a more comfortable way.
+% As a concluding remark, please notice that the
+% |\Curve| macro is certainly the most comfortable
+% to use, but it is sort of frozen in its
+% possibilities. The user may certainly use the
+% |\StartCurve|, |\CurveTo|, |\ChangeDir|, and
+% |\CurveFinish| or |\FillCurve| for a more
+% versatile set of drawing macros; evidently nobody
+% forbids to exploit the full power of the
+% |\cbezier| original macro for cubic splines; we
+% made available macros |\CbezierTo| and the
+% isolated Bézier arc macro% |\CbezierBetween| in
+% order to use the general internal cubic Bézier
+% splines in a more comfortable way.
%
-% As it can be seen in figure~15 of the |curve2e-manual.pdf| file, the
-% two diagrams should approximately
-% represent a sine wave. With Bézier curves, that resort on polynomials,
-% it is impossible to represent a transcendental function, but it is only
-% possible to approximate it. It is evident that the approximation
-% obtained with full control on the control points requires less arcs and
-% it is more accurate than the approximation obtained with the recursive
-% |\Curve| macro; this macro requires almost two times as many pieces of
-% information in order to minimise the effects of the lack of control on
-% the control points, and even with this added information the macro
-% approaches the sine wave with less accuracy. At the same time for many
-% applications the |\Curve| recursive macro proves to be much easier to
-% use than single arcs drawn with the |\CbezierBetween| macro.
+% As it can be seen in figure~15 of the
+% |curve2e-manual.pdf| file, the two diagrams
+% should approximately represent a sine
+% wave. With Bézier curves, that resort on
+% polynomials, it is impossible to represent a
+% transcendental function, but it is only possible
+% to approximate it. It is evident that the
+% approximation obtained with full control on the
+% control points requires less arcs and it is more
+% accurate than the approximation obtained with the
+% recursive |\Curve| macro; this macro requires
+% almost two times as many pieces of information
+% in order to minimise the effects of the lack of
+% control on the control points, and even with this
+% added information the macro approaches the sine
+% wave with less accuracy. At the same time for
+% many applications the |\Curve| recursive macro
+% proves to be much easier to use than single arcs
+% drawn with the |\CbezierBetween| macro.
%
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \subsection{Quadratic splines}
-%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% We want to create a recursive macro with the same properties as the
-% above described |\Curve| macro, but that uses quadratic splines; we
-% call it |\Qurve| so that the macro name initial letter reminds us of
-% the nature of the splines being used. For the rest they have an almost
-% identical syntax; with quadratic splines it is not possible to specify
-% the distance of the control points from the extrema, since quadratic
-% splines have just one control point that must lay at the intersection
-% of the two tangent directions; therefore with quadratic splines the
-% tangents at each point cannot have the optional part that starts with a
-% semicolon. The syntax, therefore, is just:
-%\begin{flushleft}
+%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% We want to create a recursive macro with the same
+% properties as the above described |\Curve| macro,
+% but that uses quadratic splines; we call it
+% |\Qurve| so that the macro name initial letter
+% reminds us of the nature of the splines being
+% used. For the rest they have an almost identical
+% syntax; with quadratic splines it is not possible
+% to specify the distance of the control points
+% from the extrema, since quadratic splines have
+% just one control point that must lay at the
+% intersection of the two tangent directions;
+% therefore with quadratic splines the tangents at
+% each point cannot have the optional part that
+% starts with a semicolon. The syntax, therefore,
+% is just:
+%\begin{Sintassi}
%\cs{Qurve}\parg{first point}\aarg{direction}...\parg{any point}\aarg{direction}...\parg{last point}\aarg{direction}
-%\end{flushleft}
-% As with |\Curve|, also with |\Qurve| there is no limitation on the
-% number of points, except for the computer memory size; it is advisable
-% not to use many arcs otherwise it might become very difficult to find
-% errors.
+%\end{Sintassi}
+% As with |\Curve|, also with |\Qurve| there is no
+% limitation on the number of points, except for
+% the computer memory size; it is advisable not to
+% use many arcs otherwise it might become very
+% difficult to find errors.
%
-% The first macros that set up the recursion are very similar to those we
-% wrote for |\Curve|:
+% The first macros that set up the recursion are
+% very similar to those we wrote for |\Curve|:
% \begin{macrocode}
-\def\Qurve{\@ifstar{\let\fillstroke\fillpath\Qurve@}%
-{\let\fillstroke\strokepath\Qurve@}}
+\def\Qurve{%
+ \@ifstar{\let\fillstroke\fillpath\Qurve@}%
+ {\let\fillstroke\strokepath\Qurve@}%
+}%
\def\Qurve@(#1)<#2>{%
\StartCurveAt#1WithDir{#2}%
\@ifnextchar\lp at r\@Qurve{%
\PackageWarning{curve2e}{%
- Quadratic curve specifications must contain at least
- two nodes!\MessageBreak
- Please, control your Qurve specifications\MessageBreak}}}%
+ Quadratic curve specifications must contain
+ at least two nodes!^^J
+ Please, control your Qurve
+ specifications^^J}}}%
\def\@Qurve(#1)<#2>{\QurveTo#1WithDir{#2}%
\@ifnextchar\lp at r\@Qurve{%
@@ -3037,45 +3785,54 @@
\def\@ChangeQDir[#1]{\ChangeDir<#1>\@Qurve}%
% \end{macrocode}
%
-% Notice that in case of long paths it might be better to use the single
-% macros |\StartCurveAt|, |\QurveTo|, |\ChangeDir| and |\CurveFinish|
-% (or |\FillCurve|), with their respective syntax, in such a way that a
-% long list of node-direction specifications passed to |\Qurve| may be
-% split into shorter input lines in order to edit the input data in a
-% more comfortable way.
+% Notice that in case of long paths it might be
+% better to use the single macros |\StartCurveAt|,
+% |\QurveTo|, |\ChangeDir| and |\CurveFinish| (or
+% |\FillCurve|), with their respective syntax, in
+% such a way that a long list of node-direction
+% specifications passed to |\Qurve| may be split
+% into shorter input lines in order to edit the
+% input data in a more comfortable way.
%
-%
-% The macro that does everything is |\QurveTo|. It starts by reading
-% its arguments received through the calling macro |\@Qurve|
+% The macro that does everything is |\QurveTo|. It
+% starts by reading its arguments received through
+% the calling macro |\@Qurve|
% \begin{macrocode}
\def\QurveTo#1WithDir#2{%
\edef\@Puno{#1}\DirOfVect#2to\@Duno\bgroup
\DistanceAndDirOfVect\@Puno minus\@Pzero to\@Chord and\@DirChord
% \end{macrocode}
-% It verifies if |\@Dpzero| and |\@Dpuno|, the directions at the two
-% extrema of the arc, are parallel or anti-parallel by taking their
-% ``scalar'' product (|\@Dpzero| times |\@Dpuno*|); if the imaginary
-% component of the scalar product vanishes the two directions are
-% parallel; in this case we produce an error message, but we continue by
-% skipping this arc destination point; evidently the drawing will not be
-% the desired one, but the job should not abort.
+% It verifies if |\@Dpzero| and |\@Dpuno|, the
+% directions at the two extrema of the arc, are
+% parallel or anti-parallel by taking their
+% “scalar” product (|\@Dpzero| times |\@Dpuno*|);
+% if the imaginary component of the scalar product
+% vanishes the two directions are parallel; in this
+% case we produce an error message, but we continue
+% by skipping this arc destination point; evidently
+% the drawing will not be the desired one, but
+% the job should not abort.
% \begin{macrocode}
\Multvect{\@Dzero}*{\@Duno}\@Scalar
\YpartOfVect\@Scalar to \@YScalar
\ifdim\@YScalar\p@=\z@
\PackageWarning{curve2e}%
- {Quadratic Bezier arcs cannot have their starting\MessageBreak
- and ending directions parallel or antiparallel with\MessageBreak
- each other. This arc is skipped and replaced with
- a dotted line.\MessageBreak}%
+ {Quadratic Bezier arcs cannot have their
+ starting^^J
+ and ending directions parallel or antiparallel
+ with each other.^^J
+ This arc is skipped and replaced with
+ a dotted line.^^J}%
\Dotline(\@Pzero)(\@Puno){2}\relax
\else
% \end{macrocode}
-% Otherwise we rotate everything about the starting point so as to bring
-% the chord on the real axis; we get also the components of the two
-% directions that, we should remember, are unit vectors, not generic
-% vectors, although the user can use the vector specifications that are
-% more understandable to him/her:
+% Otherwise we rotate everything about the starting
+% point so as to bring the chord on the real axis;
+% we get also the components of the two directions
+% that, we should remember, are unit vectors, not
+% generic vectors, although users can use the
+% vector specifications that are more
+% understandable to them:
% \begin{macrocode}
\Multvect{\@Dzero}*{\@DirChord}\@Dpzero
\Multvect{\@Duno}*{\@DirChord}\@Dpuno
@@ -3082,30 +3839,41 @@
\GetCoord(\@Dpzero)\@DXpzero\@DYpzero
\GetCoord(\@Dpuno)\@DXpuno\@DYpuno
% \end{macrocode}
-% We check if the two directions point to the same half plane; this
-% implies that these rotated directions point to different sides of the
-% chord vector; all this is equivalent to the fact that the two direction
-% Y components have opposite signs, so that their product is strictly
-% negative, while the two X components product is not negative.
+% We check if the two directions point to the same
+% half plane; this implies that these rotated
+% directions point to different sides of the chord
+% vector; all this is equivalent to the fact that
+% the two direction Y components have opposite
+% signs, so that their product is strictly
+% negative, while the two X components product is
+% not negative.
% \begin{macrocode}
\MultiplyFN\@DXpzero by\@DXpuno to\@XXD
\MultiplyFN\@DYpzero by\@DYpuno to\@YYD
\unless\ifdim\@YYD\p@<\z@\ifdim\@XXD\p@<\z@
\PackageWarning{curve2e}%
- {Quadratic Bezier arcs cannot have inflection points\MessageBreak
- Therefore the tangents to the starting and ending arc\MessageBreak
- points cannot be directed to the same half plane.\MessageBreak
- This arc is skipped and replaced by a dotted line\MessageBreak}%
+ {Quadratic Bezier arcs cannot have
+ inflection points^^J
+ Therefore the tangents to the
+ starting and ending arc^^J
+ points cannot be directed to the
+ same half plane.^^J
+ This arc is skipped and replaced by
+ a dotted line^^J}%
\Dotline(\@Pzero)(\@Puno){2}\fi
\else
% \end{macrocode}
%
-% After these tests we should be in a ``normal'' situation. We first copy
-% the expanded input information into new macros that have more explicit
-% names: macros stating wit `S' denote the sine of the direction angle,
-% while those starting with `C' denote the cosine of that angle. We will
-% use these expanded definitions as we know we are working with the
-% actual values. These directions are those relative to the arc chord.
+% After these tests we should be in a “normal”
+% situation. We first copy the expanded input
+% information into new macros that have more
+% explicit names: macros starting with `S' denote
+% the sine of the direction angle, while those
+% starting with ‘C’ denote the cosine of that
+% angle. We will use these expanded definitions as
+% we know we are working with the actual values.
+% These directions are those relative to the arc
+% chord.
% \begin{macrocode}
\edef\@CDzero{\@DXpzero}\relax
\edef\@SDzero{\@DYpzero}\relax
@@ -3112,12 +3880,14 @@
\edef\@CDuno{\@DXpuno}\relax
\edef\@SDuno{\@DYpuno}\relax
% \end{macrocode}
-% Suppose we write the parametric equations of a straight line that
-% departs from the beginning of the chord with direction angle $\phi_0$
-% and the corresponding equation of the straight line departing from the
-% end of the chord (of length $c$) with direction angle $\phi_1$. We have
-% to find the coordinates of the intersection point of these two straight
-% lines.
+% Suppose we write the parametric equations of a
+% straight line that departs from the beginning of
+% the chord with direction angle $\phi_0$ and the
+% corresponding equation of the straight line
+% departing from the end of the chord (of length
+% $c$) with direction angle $\phi_1$. We have to
+% find the coordinates of the intersection point of
+% these two straight lines.
%\begin{subequations}
%\begin{align}
% t \cos\phi_0 - s \cos\phi_1 &= c\\
@@ -3124,34 +3894,38 @@
% t \sin\phi_0 - s \sin\phi_1 &= 0
%\end{align}
%\end{subequations}
-% The parameters $t$ and $s$ are just the running parameters; we have
-% to solve those simultaneous equations in the unknown variables $t$ and
-% $s$; these values let us compute the coordinates of the intersection
-% point:
+% The parameters $t$ and $s$ are just the running
+% parameters; we have to solve those simultaneous
+% equations in the unknown variables $t$ and $s$;
+% these values let us compute the coordinates of
+% the intersection point:
%\begin{subequations}\begin{align}
% X_C &=\dfrac{c\cos\phi_0\sin\phi_1}{\sin\phi_0\cos\phi_1 - \cos\phi_0\sin\phi_1} \\
% Y_C &=\dfrac{c\sin\phi_0\sin\phi_1}{\sin\phi_0\cos\phi_1 - \cos\phi_0\sin\phi_1}
%\end{align}\end{subequations}
%
-% Having performed the previous tests we are sure that the denominator is
-% not vanishing (direction are not parallel or anti-parallel) and that it
-% lays at the same side as the direction with angle $\phi_0$ with respect
-% to the chord.
+% Having performed the previous tests we are sure
+% that the denominator is not vanishing (directionw
+% are not parallel or anti-parallel) and that the
+% intersection point lays at the same side as the
+% direction with angle $\phi_0$ with respect to the
+% chord.
%
% The coding then goes on like this:
% \begin{macrocode}
-\MultiplyFN\@SDzero by\@CDuno to\@tempA
-\MultiplyFN\@SDuno by\@CDzero to\@tempB
+\MultiplY\@SDzero by\@CDuno to\@tempA
+\MultiplY\@SDuno by\@CDzero to\@tempB
\edef\@tempA{\strip at pt\dimexpr\@tempA\p at -\@tempB\p@}\relax
\@tdA=\@SDuno\p@ \@tdB=\@Chord\p@ \@tdC=\@tempA\p@
\edef\@tempC{\strip at pt\dimexpr \@tdA*\@tdB/\@tdC}\relax
-\MultiplyFN\@tempC by\@CDzero to \@XC
-\MultiplyFN\@tempC by\@SDzero to \@YC
+\MultiplY\@tempC by\@CDzero to \@XC
+\MultiplY\@tempC by\@SDzero to \@YC
\ModOfVect\@XC,\@YC to\@KC
% \end{macrocode}
-% Now we have the coordinates and the module of the intersection point
-% vector taking into account the rotation of the real axis; getting back
-% to the original coordinates before rotation, we get:
+% Now we have the coordinates and the module of the
+% intersection point vector taking into account the
+% rotation of the real axis; getting back to the
+% original coordinates before rotation, we get:
% \begin{macrocode}
\ScaleVect\@Dzero by\@KC to\@CP
\AddVect\@Pzero and\@CP to\@CP
@@ -3159,16 +3933,20 @@
\GetCoord(\@Puno)\@XPuno\@YPuno
\GetCoord(\@CP)\@XCP\@YCP
% \end{macrocode}
-% We have now the coordinates of the two end points of the quadratic
-% arc and of the single control point. Keeping in mind that the symbols
-% $P_0$, $P_1$ and $C$ denote geometrical points but also their coordinates
-% as ordered pairs of real numbers (i.e. they are complex numbers) we have
-% to determine the parameters of a cubic spline that with suitable
-% values gets simplifications in its parametric equation so that it
-% becomes a second degree function instead of a third degree one. It is
-% possible, even if it appears impossible that e cubic
-% form becomes a quadratic one; we should determine the values of $P_a$
-% and $P_b$ such that:
+% We have now the coordinates of the two end points
+% of the quadratic arc and of the single control
+% point. Keeping in mind that the symbols $P_0$,
+% $P_1$ and $C$ denote geometrical points but also
+% their coordinates as ordered pairs of real
+% numbers (i.e. they are complex numbers) we have
+% to determine the parameters of a cubic spline
+% that with suitable values gets simplifications in
+% its parametric equation so that it becomes a
+% second degree function instead of a third degree
+% one. It is possible, even if it appears
+% impossible that a cubic form becomes a quadratic
+% one; we should determine the values of $P_a$ and
+% $P_b$ such that:
%\[
% P_0(1-t)^3 +3P_a(1-t)^2t +3P_b(1-t)t^2 +P_1t^3
%\]
@@ -3182,9 +3960,12 @@
%\label{equ:spline3}
%\end{equation}
%
-% The transformations implied by equations~\eqref{equ:spline3} are
-% performed by the following macros already available from the |pict2e|
-% package; we use them here with the actual arguments used for this task:
+% The transformations implied by
+% equations~\eqref{equ:spline3}
+% are performed by the following macros already
+% available from the |pict2e| package; we use them
+% here with the actual arguments used for this
+% task:
% \begin{macrocode}
\@ovxx=\@XPzero\unitlength \@ovyy=\@YPzero\unitlength
\@ovdx=\@XCP\unitlength \@ovdy=\@YCP\unitlength
@@ -3195,11 +3976,14 @@
\pIIe at bezier@QtoC\@ydim\@ovdy\@clnht
% \end{macrocode}
%
-% We call the basic |pict2e| macro to draw a cubic spline and we finish
-% the conditional statements with which we started these calculations;
-% eventually we close the group we opened at the beginning and we copy
-% the terminal node information (position and direction) into the
-% zero-labelled macros that indicate the starting point of the next arc.
+% We call the basic |pict2e| macro to draw a cubic
+% spline and we finish the conditional statements
+% with which we started these calculations;
+% eventually we close the group we opened at the
+% beginning and we copy the terminal node
+% information (position and direction) into the
+% zero-labelled macros that indicate the starting
+% point of the next arc.
% \begin{macrocode}
\pIIe at curveto\@ovro\@ovri\@clnwd\@clnht\@xdim\@ydim
\fi\fi\egroup
@@ -3208,58 +3992,79 @@
\ignorespaces}
% \end{macrocode}
%
-% An example of usage is shown at the left in figure~16 of the user manual
-% |curve2e-manual.pdf| file\footnote{The commands \cs{legenda},
-% \cs{Pall} and \cs{Zbox} are specifically defined in the preamble of
-% this document; they must be used within a \texttt{picture} environment.
-% \cs{legenda} draws a framed legend made up of a single (short) math
-% formula; \cs{Pall} is just a shorthand to put a sized dot at a
-% specified position' \cs{Zbox} puts a symbol in math mode a little
-% displaced in the proper direction relative to a specified position.
-% They are just handy to label certain objects in a \texttt{picture}
-% diagram, but they are not part of the \texttt{curve2e} package.}
-% created with the code shown in the same page as the figure.
+% An example of usage is shown at the left in
+% figure~16 of the |curve2e-manual.pdf|
+% file\footnote{%
+% The commands \cs{legenda}, \cs{Pall} and
+% \cs{Zbox} are specifically defined in the
+% preamble of this document; they must be used
+% within a \texttt{picture} environment.
+% \cs{legenda} draws a framed legend made up of a
+% single (short) math formula; \cs{Pall} is just a
+% shorthand to put a sized dot at a specified
+% position; \cs{Zbox} puts a symbol in math mode a
+% little displaced in the proper direction relative
+% to a specified position. They are just handy to
+% label certain objects in a \texttt{picture}
+% diagram. They have been defined at the beginning
+% of the \texttt{curve2e.sty} code.} created with
+% the code shown in the same page as the figure.
%
-% Notice also that the inflexed line is made with two arcs that meet at
-% the inflection point; the same is true for the line that resembles
-% a sine wave. The cusps of the inner border of the green area are
-% obtained with the usual optional argument already used also with the
-% |\Curve| recursive macro.
+% Notice also that the inflexed line is made with
+% two arcs that meet at the inflection point; the
+% same is true for the line that resembles a sine
+% wave. The cusps of the inner border of the green
+% area are obtained with the usual optional
+% argument already used also with the |\Curve|
+% recursive macro.
%
-% The “circle” inside the square frame is visibly different from a real
-% circle, in spite of the fact that the maximum deviation from the true
-% circle is just about 6\% relative to the radius; a quarter circle
-% obtained with a single parabola is definitely a poor approximation of a
-% real quarter circle; possibly by splitting each quarter circle in three
-% or four partial arcs the approximation of a real quarter circle would be
-% much better. On the right of figure~16 of the user manual it is possible
-% to compare a “circle” obtained with quadratic arcs with the the internal
-% circle obtained with cubic arcs; the difference is easily seen even
-% without using measuring instruments.
+% The “circle” inside the square frame is visibly
+% different from a real circle, in spite of the
+% fact that the maximum deviation from the true
+% circle is just about 6\% relative to the radius;
+% a quarter circle obtained with a single parabola
+% is definitely a poor approximation of a real
+% quarter circle; possibly by splitting each
+% quarter circle in three or four partial arcs the
+% approximation of a real quarter circle would be
+% much better. On the right of figure~16 of the
+% user manual it is possible to compare a “circle”
+% obtained with quadratic arcs with the the
+% internal circle obtained with cubic arcs; the
+% difference is easily seen even without using
+% measuring instruments.
%
-% With quadratic arcs we decided to avoid defining specific macros
-% similar to |\CurveBetween| and |\CbezierBetween|; the first macro would
-% not save any typing to the operator; furthermore it may be questionable
-% if it was really useful even with cubic splines; the second macro with
-% quadratic arcs is meaningless, since with quadratic arcs there is just
-% one control point and there is no choice on its position.
+% With quadratic arcs we decided to avoid defining
+% specific macros similar to |\CurveBetween| and
+% |\CbezierBetween|; the first macro would not save
+% any typing to the user; furthermore it may be
+% questionable if it was really useful even with
+% cubic splines; the second macro with quadratic
+% arcs is meaningless, since with quadratic arcs
+% there is just one control point and there is no
+% choice on its position.
%
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \section{Conclusion}
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% I believe that the set of new macros provided by this package can
-% really help users to draw their diagrams with more agility; it
-% will be the accumulated experience to decide if this is true.
+% I believe that the set of new macros provided by
+% this package can really help users to draw their
+% diagrams with more agility; it will be the
+% accumulated experience to decide if this is true.
%
-% As a personal experience I found very comfortable to draw ellipses and
-% to define macros to draw not only such shapes or filled elliptical
-% areas, but also to create “legends” with coloured backgrounds and
-% borders. But this is just an application of the functionality
-% implemented in this package. In 2020 I added to CTAN another
-% specialised package, |euclideangeometry.sty| with its manual
-% |euclideangeometry-man.pdf| that uses the facilities of |curve2e|
-% to draw complex diagrams that plot curves, and other facilities that
-% solve some geometrical problems dealing with ellipses.
+% As a personal experience I found very comfortable
+% to draw ellipses and to define macros to draw not
+% only such shapes or filled elliptical areas, but
+% also to create “legends” with coloured
+% backgrounds and borders. But this is just an
+% application of the functionality implemented in
+% this package. In 2020 I added to CTAN another
+% specialised package,
+% |euclideangeometry.sty| with its manual
+% |euclideangeometry-man.pdf| that uses the
+% facilities of |curve2e| to draw complex diagrams
+% that plot curves, and other facilities that solve
+% some geometrical problems dealing with ellipses.
%
%\iffalse
%</package>
@@ -3270,11 +4075,12 @@
%<*readme>
%\fi
% \section{The \texttt{README.txt} file}
-% The following is the text that forms the contents of the |README.txt|
-% file that accompanies the package. We found it handy to have it in
-% the documented source, because in this way certain pieces of
-% information don't need to be repeated again and again in different
-% files.
+% The following is the text that forms the contents
+% of the |README.txt| file that accompanies the
+% package. We found it handy to have it in the
+% documented source, because in this way certain
+% pieces of information don't need to be repeated
+% again and again in different files.
% \begin{macrocode}
The package bundle curve2e is composed of the following files
@@ -3307,7 +4113,7 @@
The curve2e-manual files contains the user manual; in
this way the long preliminary descriptive part of the previous versions
-curve2e.pdf file has been transferred to shorter dedicated file, and the
+curve2e.pdf file has been transferred to a shorter dedicated file, and the
"normal" user should have enough information to use the package. The
curve2e.pdf file, extracted from the .dtx one, contains the code
documentation and is intended for the developers, or for the curious
@@ -3328,8 +4134,8 @@
and vectors with any non integer slope parameters, to draw dashed and
dotted lines of any slope, to draw arcs and curved vectors, to draw
curves where just the interpolating nodes are specified together with
-the slopes at such nodes; closed paths of any shape can be filled with
-color; all coordinates are treated as ordered pairs, i.e. "complex
+the tangent directions at such nodes; closed paths of any shape can be
+filled with color; all coordinates are treated as ordered pairs, i.e. "complex
numbers"; coordinates may be expressed also in polar form. Coordinates
may be specified with macros, so that editing any drawing is rendered
much simpler: any point specified with a macro is modified only once
@@ -3351,8 +4157,7 @@
Curve2e solves a conflict with package eso-pic.
-This version of curve2e is almost fully compatible with pict2e dated
-2014/01/12 version 0.2z and later.
+This version of curve2e is almost fully compatible with pict2e version 0.4z and later.
If you specify
@@ -3400,9 +4205,9 @@
%<*v161>
%\fi
% \section{The roll-back package version \texttt{curve2e-v161}}
-% this is the fall-back version of |curve2e-v161.sty| to which the main
-% file |curve2e.sty| falls back in case the interface package |xfp| is
-% not available.
+% This is the fall-back version of |curve2e-v161.sty| to which
+% the main file |curve2e.sty| falls back in case the interface
+% packages |xfp| and |xparse| are not available.
% \begin{macrocode}
\NeedsTeXFormat{LaTeX2e}[2016/01/01]
\ProvidesPackage{curve2e-v161}%
@@ -3994,28 +4799,24 @@
{\@sPunX\unitlength}{\@sPunY\unitlength}%
\fi}
\def\VectorArc(#1)(#2)#3{\begingroup
-\@tdA=#3\p@ \ifdim\@tdA=\z@\else
- \@VArc(#1)(#2)%
-\fi
-\endgroup\ignorespaces}%
+\edef\tempG{#3}\@tdA=#3\p@
+\fptestF{#3=0}{\@VArc(#1)(#2)}}%
+
\def\VectorARC(#1)(#2)#3{\begingroup
-\@tdA=#3\p@
-\ifdim\@tdA=\z@\else
- \@VARC(#1)(#2)%
-\fi
-\endgroup\ignorespaces}%
+\edef\tempG{#3}\@tdA=#3\p@
+\fptestF{#3=0}{\@VArc(#1)(#2)}}%
+
\def\@VArc(#1)(#2){%
-\ifdim\@tdA>\z@
- \let\Segno+%
-\else
- \@tdA=-\@tdA \let\Segno-%
-\fi \Numero\@gradi\@tdA
-\ifdim\@tdA>360\p@
- \PackageWarning{curve2e}{The arc aperture is \@gradi\space degrees
- and gets reduced\MessageBreak%
- to the range 0--360 taking the sign into consideration}%
- \@whiledim\@tdA>360\p@\do{\advance\@tdA-360\p@}%
-\fi
+\fptest{\tempG>\z@}{\let\Segno+}%
+ {\edef\tempG={-\tempG}\let\Segno-}%
+\fptestT{\tempG>360}{%
+\PackageWarning{curve2e}{The arc aperture is \tempG\space degrees
+ and gets reduced^^J%
+ to the range 0--360 taking the sign into
+ consideration}%
+ \edef\tempG{\Modulo{\tempG}{360}}}%
+\@tdA=\tempG\p@
+\Numero\@gradi\@tdA
\SubVect#1from#2to\@V \ModOfVect\@V to\@Raggio \CopyVect#2to\@pPun
\@tdE=\pIIe at FAW\@wholewidth \@tdE=\pIIe at FAL\@tdE
\DividE\@tdE by \@Raggio\unitlength to\DeltaGradi
@@ -4024,13 +4825,13 @@
\@tdD=\ifx\Segno--\fi\@gradi\p@ \Numero\@tempa\@tdD
\DirFromAngle\@tempa to\@Dir
\MultVect\@V by\@Dir to\@sPun
-\edef\@tempA{\ifx\Segno-\m at ne\else\@ne\fi}%
+\edef\@tempA{\ifx\Segno--\@ne\fi}%
\MultVect\@sPun by 0,\@tempA to\@vPun
\DirOfVect\@vPun to\@Dir
\AddVect\@sPun and #1 to \@sPun
\GetCoord(\@sPun)\@tdX\@tdY
\@tdD\ifx\Segno--\fi\DeltaGradi\p@
-\@tdD=.5\@tdD \Numero\DeltaGradi\@tdD
+\@tdD=0.5\@tdD \Numero\DeltaGradi\@tdD
\DirFromAngle\DeltaGradi to\@Dird
\MultVect\@Dir by*\@Dird to\@Dir
\GetCoord(\@Dir)\@xnum\@ynum
@@ -4038,20 +4839,20 @@
\@tdE =\ifx\Segno--\fi\DeltaGradi\p@
\advance\@tdA -\@tdE \Numero\@gradi\@tdA
\CopyVect#1to\@Cent \GetCoord(\@pPun)\@pPunX\@pPunY
-\@@Arc
-\strokepath\ignorespaces}%
+\@@Arc\strokepath\endgroup\ignorespaces}%
+
\def\@VARC(#1)(#2){%
-\ifdim\@tdA>\z@
- \let\Segno+%
-\else
- \@tdA=-\@tdA \let\Segno-%
-\fi \Numero\@gradi\@tdA
-\ifdim\@tdA>360\p@
- \PackageWarning{curve2e}{The arc aperture is \@gradi\space degrees
- and gets reduced\MessageBreak%
- to the range 0--360 taking the sign into consideration}%
- \@whiledim\@tdA>360\p@\do{\advance\@tdA-360\p@}%
-\fi
+\fptest{\tempG>\z@}{\let\Segno+}%
+ {\edef\tempG={-\tempG}\let\Segno-}%
+\@tdA=\tempG\p@
+\Numero\@gradi\@tdA
+\fptestT{\tempG>360}{%
+ \PackageWarning{curve2e}{The arc aperture is \tempG\space degrees
+ and gets reduced^^J%
+ to the range 0--360 taking the sign into
+ consideration}%
+ \edef\tempG{\Modulo{\tempG}{360}}%
+}
\SubVect#1from#2to\@V \ModOfVect\@V to\@Raggio \CopyVect#2to\@pPun
\@tdE=\pIIe at FAW\@wholewidth \@tdE=0.8\@tdE
\DividE\@tdE by \@Raggio\unitlength to\DeltaGradi
@@ -4202,6 +5003,7 @@
\PackageWarning{curve2e}{%
Curve specifications must contain at least two nodes!\MessageBreak
Please, control your Curve specifications\MessageBreak}}}
+
\def\@Curve(#1)<#2>{%
\CurveTo#1WithDir{#2}%
\@ifnextchar\lp at r\@Curve{%
Modified: trunk/Master/texmf-dist/tex/latex/curve2e/curve2e-v161.sty
===================================================================
--- trunk/Master/texmf-dist/tex/latex/curve2e/curve2e-v161.sty 2024-11-13 21:11:32 UTC (rev 72841)
+++ trunk/Master/texmf-dist/tex/latex/curve2e/curve2e-v161.sty 2024-11-13 21:11:45 UTC (rev 72842)
@@ -6,9 +6,11 @@
%%
%% curve2e.dtx (with options: `v161')
%%
-%% Copyright (C) 2005--2023 Claudio Beccari all rights reserved.
+%% Copyright (C) 2005--2024 Claudio Beccari all
+%% rights reserved.
%% License information appended
%%
+
\NeedsTeXFormat{LaTeX2e}[2016/01/01]
\ProvidesPackage{curve2e-v161}%
[2019/02/07 v.1.61 Extension package for pict2e]
@@ -599,28 +601,24 @@
{\@sPunX\unitlength}{\@sPunY\unitlength}%
\fi}
\def\VectorArc(#1)(#2)#3{\begingroup
-\@tdA=#3\p@ \ifdim\@tdA=\z@\else
- \@VArc(#1)(#2)%
-\fi
-\endgroup\ignorespaces}%
+\edef\tempG{#3}\@tdA=#3\p@
+\fptestF{#3=0}{\@VArc(#1)(#2)}}%
+
\def\VectorARC(#1)(#2)#3{\begingroup
-\@tdA=#3\p@
-\ifdim\@tdA=\z@\else
- \@VARC(#1)(#2)%
-\fi
-\endgroup\ignorespaces}%
+\edef\tempG{#3}\@tdA=#3\p@
+\fptestF{#3=0}{\@VArc(#1)(#2)}}%
+
\def\@VArc(#1)(#2){%
-\ifdim\@tdA>\z@
- \let\Segno+%
-\else
- \@tdA=-\@tdA \let\Segno-%
-\fi \Numero\@gradi\@tdA
-\ifdim\@tdA>360\p@
- \PackageWarning{curve2e}{The arc aperture is \@gradi\space degrees
- and gets reduced\MessageBreak%
- to the range 0--360 taking the sign into consideration}%
- \@whiledim\@tdA>360\p@\do{\advance\@tdA-360\p@}%
-\fi
+\fptest{\tempG>\z@}{\let\Segno+}%
+ {\edef\tempG={-\tempG}\let\Segno-}%
+\fptestT{\tempG>360}{%
+\PackageWarning{curve2e}{The arc aperture is \tempG\space degrees
+ and gets reduced^^J%
+ to the range 0--360 taking the sign into
+ consideration}%
+ \edef\tempG{\Modulo{\tempG}{360}}}%
+\@tdA=\tempG\p@
+\Numero\@gradi\@tdA
\SubVect#1from#2to\@V \ModOfVect\@V to\@Raggio \CopyVect#2to\@pPun
\@tdE=\pIIe at FAW\@wholewidth \@tdE=\pIIe at FAL\@tdE
\DividE\@tdE by \@Raggio\unitlength to\DeltaGradi
@@ -629,13 +627,13 @@
\@tdD=\ifx\Segno--\fi\@gradi\p@ \Numero\@tempa\@tdD
\DirFromAngle\@tempa to\@Dir
\MultVect\@V by\@Dir to\@sPun
-\edef\@tempA{\ifx\Segno-\m at ne\else\@ne\fi}%
+\edef\@tempA{\ifx\Segno--\@ne\fi}%
\MultVect\@sPun by 0,\@tempA to\@vPun
\DirOfVect\@vPun to\@Dir
\AddVect\@sPun and #1 to \@sPun
\GetCoord(\@sPun)\@tdX\@tdY
\@tdD\ifx\Segno--\fi\DeltaGradi\p@
-\@tdD=.5\@tdD \Numero\DeltaGradi\@tdD
+\@tdD=0.5\@tdD \Numero\DeltaGradi\@tdD
\DirFromAngle\DeltaGradi to\@Dird
\MultVect\@Dir by*\@Dird to\@Dir
\GetCoord(\@Dir)\@xnum\@ynum
@@ -643,20 +641,20 @@
\@tdE =\ifx\Segno--\fi\DeltaGradi\p@
\advance\@tdA -\@tdE \Numero\@gradi\@tdA
\CopyVect#1to\@Cent \GetCoord(\@pPun)\@pPunX\@pPunY
-\@@Arc
-\strokepath\ignorespaces}%
+\@@Arc\strokepath\endgroup\ignorespaces}%
+
\def\@VARC(#1)(#2){%
-\ifdim\@tdA>\z@
- \let\Segno+%
-\else
- \@tdA=-\@tdA \let\Segno-%
-\fi \Numero\@gradi\@tdA
-\ifdim\@tdA>360\p@
- \PackageWarning{curve2e}{The arc aperture is \@gradi\space degrees
- and gets reduced\MessageBreak%
- to the range 0--360 taking the sign into consideration}%
- \@whiledim\@tdA>360\p@\do{\advance\@tdA-360\p@}%
-\fi
+\fptest{\tempG>\z@}{\let\Segno+}%
+ {\edef\tempG={-\tempG}\let\Segno-}%
+\@tdA=\tempG\p@
+\Numero\@gradi\@tdA
+\fptestT{\tempG>360}{%
+ \PackageWarning{curve2e}{The arc aperture is \tempG\space degrees
+ and gets reduced^^J%
+ to the range 0--360 taking the sign into
+ consideration}%
+ \edef\tempG{\Modulo{\tempG}{360}}%
+}
\SubVect#1from#2to\@V \ModOfVect\@V to\@Raggio \CopyVect#2to\@pPun
\@tdE=\pIIe at FAW\@wholewidth \@tdE=0.8\@tdE
\DividE\@tdE by \@Raggio\unitlength to\DeltaGradi
@@ -807,6 +805,7 @@
\PackageWarning{curve2e}{%
Curve specifications must contain at least two nodes!\MessageBreak
Please, control your Curve specifications\MessageBreak}}}
+
\def\@Curve(#1)<#2>{%
\CurveTo#1WithDir{#2}%
\@ifnextchar\lp at r\@Curve{%
@@ -886,15 +885,17 @@
%%
-%% Distributable under the LaTeX Project Public License,
-%% version 1.3c or higher (your choice). The latest version of
-%% this license is at: http://www.latex-project.org/lppl.txt
+%% Distributable under the LaTeX Project Public
+%% License, version 1.3c or higher (your choice).
+%% The latest version of this license is at:
+%% http://www.latex-project.org/lppl.txt
%%
%% This work is "maintained"
%%
-%% This work consists of file curve2e.dtx, and the derived files
-%% curve2e.sty and curve2e.pdf, plus the auxiliary derived files
-%% README.txt and curve2e-v161.sty.
+%% This work consists of file curve2e.dtx, and the
+%% derived files curve2e.sty and curve2e.pdf, plus
+%% the auxiliary derived files README.txt and
+%% curve2e-v161.sty.
%%
%%
%% End of file `curve2e-v161.sty'.
Modified: trunk/Master/texmf-dist/tex/latex/curve2e/curve2e.sty
===================================================================
--- trunk/Master/texmf-dist/tex/latex/curve2e/curve2e.sty 2024-11-13 21:11:32 UTC (rev 72841)
+++ trunk/Master/texmf-dist/tex/latex/curve2e/curve2e.sty 2024-11-13 21:11:45 UTC (rev 72842)
@@ -6,12 +6,14 @@
%%
%% curve2e.dtx (with options: `package')
%%
-%% Copyright (C) 2005--2023 Claudio Beccari all rights reserved.
+%% Copyright (C) 2005--2024 Claudio Beccari all
+%% rights reserved.
%% License information appended
%%
\NeedsTeXFormat{LaTeX2e}[2019/01/01]
\ProvidesPackage{curve2e}%
- [2023-07-04 v.2.3.1 Extension package for pict2e]
+[2024-11-13 v.2.6.0 Extension package for pict2e]
+
\IfFileExists{xfp.sty}{%
\RequirePackage{graphicx,color}
\RequirePackageWithOptions{pict2e}[2014/01/01]
@@ -35,11 +37,21 @@
\ExplSyntaxOn
\AtBeginDocument{%
\ProvideExpandableDocumentCommand\fptest{m m m}{%
- \fp_compare:nTF{#1}{#2}{#3}\ignorespaces}
+ \fp_compare:nTF{#1}{#2}{#3}}
+\ProvideExpandableDocumentCommand\fptestT{m m}{%
+ \fp_compare:nTF{#1}{#2}{\relax}}
+\ProvideExpandableDocumentCommand\fptestF{m m}{%
+ \fp_compare:nTF{#1}{\relax}{#2}}
\ProvideExpandableDocumentCommand\fpdowhile{m m}{%
- \fp_do_while:nn{#1}{#2}\ignorespaces}
+ \fp_do_while:nn{#1}{#2}}
\ProvideExpandableDocumentCommand\fpwhiledo{m m}{%
- \fp_while_do:nn{#1}{#2}\ignorespaces}
+ \fp_while_do:nn{#1}{#2}}
+\ProvideExpandableDocumentCommand\Modulo{m m}{%
+ \inteval{\int_mod:nn{#1}{#2}}}
+\ProvideExpandableDocumentCommand\Ifodd{m m m}{%
+ \int_if_odd:nTF{#1}{#2}{#3}}
+\ProvideExpandableDocumentCommand\Ifequal{m m m m}%
+ {\str_if_eq:eeTF{#1}{#2}{#3}{#4}}
}
\ExplSyntaxOff
@@ -259,35 +271,64 @@
\ignorespaces}}
\def\@picture(#1,#2)(#3,#4){%
- \edef\pict at urcorner{#1,#2}% New statement
- \edef\pict at llcorner{#3,#4}% New statement
+ \edef\pict at dimen{#1,#2} % New 2.4.0
+ \edef\pict at offset{#3,#4}% New 2.4.0
\@picht#2\unitlength
\setbox\@picbox\hb at xt@#1\unitlength\bgroup
\hskip -#3\unitlength
\lower #4\unitlength\hbox\bgroup
\ignorespaces}
-\def\Gr at phGrid(#1,#2){\bgroup\textcolor{red}{\linethickness{.1\p@}%
-\RoundUp#1modulo10to\@GridWd \RoundUp#2modulo10to\@GridHt
-\@tempcnta=\@GridWd \divide\@tempcnta10\relax \advance\@tempcnta\@ne
-\multiput(0,0)(10,0){\@tempcnta}{\line(0,1){\@GridHt}}%
-\@tempcnta=\@GridHt \divide\@tempcnta10\advance\@tempcnta\@ne
-\multiput(0,0)(0,10){\@tempcnta}{\line(1,0){\@GridWd}}\thinlines}%
+
+\newif\ifinnerlines \let\ifinnerlines\iftrue
+\def\noinnerlines{\let\ifinnerlines\iffalse}
+
+\newcommand\griglia[2]{%
+\linethickness{#1\p@}%
+\edef\ggllx{\Goffx}
+\fpdowhile{\ggllx!>\GridWd}{%
+\fptest{\ggllx=\fpeval{#2*(round(\ggllx/#2,0))}}%
+{\segment(\ggllx,\Goffy)(\ggllx,\GridHt)}{\relax}%
+\edef\ggllx{\fpeval{\ggllx+#2}}}%
+\edef\gglly{\Goffy}
+\fpdowhile{\gglly!>\GridHt}{%
+\fptest{\gglly=\fpeval{#2*(round(\gglly/#2,0))}}%
+{\segment(\Goffx,\gglly)(\GridWd,\gglly)}{\relax}
+\edef\gglly{\fpeval{\gglly+#2}}}}
+
+\NewDocumentCommand\Gr at phGrid{d() d()}{\bgroup
+\color{\GridColor}
+\edef\Gdim{#1}\edef\Goff{#2}
+\GetCoord(\Gdim)\Gllx\Glly
+\GetCoord(\Goff)\Goffx\Goffy
+\edef\GridWd{\fpeval{\Gllx+\Goffx}}%
+\edef\GridHt{\fpeval{\Glly+\Goffy}}%
+\griglia{1.0}{10}
+\ifinnerlines
+ \griglia{0.70}{5}%
+ \unless\ifdim \unitlength < 1mm
+ \griglia{0.70}{5}%
+ \griglia{0.35}{1}%
+ \fi
+\fi
+\egroup
+\ignorespaces}
+
+\NewDocumentCommand\AutoGrid%
+{D(){\pict at dimen} D(){\pict at offset} O{cyan!50!white}}{\bgroup
+\def\GridColor{#3}%
+\put(0,0){\Gr at phGrid(#1)(#2)}%
\egroup\ignorespaces}
-\NewDocumentCommand\AutoGrid{d() d()}{\bgroup%
-\put(\pict at llcorner){\expandafter\Gr at phGrid\expandafter(\pict at urcorner)}%
+\NewDocumentCommand\GraphGrid%
+{R(){\pict at dimen} D(){\pict at offset} O{cyan!50!white}}
+{\bgroup
+\def\GridColor{#3}%
+\put(#2){\Gr at phGrid(#1)(#2)}%
\egroup\ignorespaces}
-\NewDocumentCommand\GraphGrid{r() d()}{%
-\IfValueTF{#2}{\put(#1){\Gr at phGrid(#2)}}%
- {\put(0,0){\Gr at phGrid(#1)}}}
-
\def\RoundUp#1modulo#2to#3{\edef#3{\fpeval{(ceil(#1/#2,0))*#2}}}%
\def\Integer#1.#2??{#1}%
-%%
-%%
-%%
-%%
+
\providecommand\Pbox{}
\newlength\PbDim
\RenewDocumentCommand\Pbox{D(){0,0} O{cc} m O{0.5ex} s D<>{0}}{%
@@ -294,9 +335,9 @@
\put(#1){\rotatebox{#6}{\makebox(0,0){%
\settowidth\PbDim{#2}%
\edef\Rapp{\fpeval{\PbDim/{1ex}}}%
-\fptest{\Rapp > 1.5}{\fboxsep=0.5ex}{\fboxsep=0.75ex}%
+\fptest{\Rapp>1.5}{\fboxsep=0.5ex}{\fboxsep=0.75ex}%
\IfBooleanTF{#5}{\fboxrule=0.4pt}{\fboxrule=0pt}%
-\fptest{#4 = 0sp}%
+\fptest{#4=0sp}%
{\makebox(0,0)[#2]{\fbox{$\relax#3\relax$}}}%
{\edef\Diam{\fpeval{(#4)/\unitlength}}%
\makebox(0,0){\circle*{\Diam}}%
@@ -311,9 +352,9 @@
\providecommand\legenda{}
\newbox\legendbox
-\RenewDocumentCommand\legenda{ D(){0,0} m}{\put(#1){%
+\RenewDocumentCommand\legenda{D(){0,0} m}{\put(#1){%
\setbox\legendbox\hbox{$\relax#2\relax$}%
- \edef\@tempA{\fpeval{(\wd\legendbox + 3\p@)/\unitlength}}%
+ \edef\@tempA{\fpeval{(\wd\legendbox+3\p@)/\unitlength}}%
\edef\@tempB{\fpeval{(\ht\legendbox+\dp\legendbox+3\p@)/\unitlength}}%
\framebox(\@tempA,\@tempB){\box\legendbox}}\ignorespaces}
@@ -323,24 +364,23 @@
\let\DivideFN\DividE
\def\MultiplY#1by#2to#3{\edef#3{\fpeval{#1 * #2}}}\relax
\let\MultiplyFN\MultiplY
-\unless\ifdefined\Numero
- \def\Numero#1#2{\edef#1{\fpeval{round(#2,6)}}\ignorespaces}%
-\fi
+\providecommand\Numero[2]{\edef#1{\fpeval{round(#2,6)}}}
\def\SinOf#1to#2{\edef#2{\fpeval{round(sind#1,6)}}}\relax
\def\CosOf#1to#2{\edef#2{\fpeval{round(cosd#1,6)}}}\relax
\def\ArgOfVect#1to#2{\GetCoord(#1){\t at X}{\t at Y}%
-\fptest{\t at X=\z@ && \t at Y=\z@}{\edef#2{0}%
-\PackageWarning{curve2e}{Null vector}{Check your data\MessageBreak
-Computations go on, but the results may be meaningless}}{%
-\edef#2{\fpeval{round(atand(\t at Y,\t at X),6)}}}\ignorespaces}
-\def\MakeVectorFrom#1#2to#3{\edef#3{#1,#2}\ignorespaces}%
+\fptest{\t at X=\z@&&\t at Y=\z@}{\edef#2{0}%
+\PackageWarning{curve2e}{Null vector}{%
+Check your data\MessageBreak
+Computations go on, but the results may be meaningless}%
+}{\edef#2{\fpeval{round(atand(\t at Y,\t at X),6)}}}%
+\ignorespaces}
+\def\MakeVectorFrom#1#2to#3{\edef#3{#1,#2}}%
\def\CopyVect#1to#2{\edef#2{#1}\ignorespaces}%
\def\ModOfVect#1to#2{\GetCoord(#1)\t at X\t at Y
-\edef#2{\fpeval{round(sqrt(\t at X*\t at X + \t at Y*\t at Y),6)}}%
-\ignorespaces}%
+\edef#2{\fpeval{round(sqrt(\t at X*\t at X + \t at Y*\t at Y),6)}}\ignorespaces}%
\def\DirOfVect#1to#2{\GetCoord(#1)\t at X\t at Y
\ModOfVect#1to\@tempa
-\fptest{\@tempa=\z@}{}{%
+\fptestF{\@tempa=\z@}{%
\edef\t at X{\fpeval{round(\t at X/\@tempa,6)}}%
\edef\t at Y{\fpeval{round(\t at Y/\@tempa,6)}}%
}\MakeVectorFrom\t at X\t at Y to#2\ignorespaces}%
@@ -350,10 +390,8 @@
\def\DistanceAndDirOfVect#1minus#2to#3and#4{%
\SubVect#2from#1to\@tempa
\ModAndDirOfVect\@tempa to#3and#4\ignorespaces}%
-\def\XpartOfVect#1to#2{%
-\GetCoord(#1)#2\@tempa\ignorespaces}%
-\def\YpartOfVect#1to#2{%
-\GetCoord(#1)\@tempa#2\ignorespaces}%
+\def\XpartOfVect#1to#2{\GetCoord(#1)#2\@tempa\ignorespaces}%
+\def\YpartOfVect#1to#2{\GetCoord(#1)\@tempa#2\ignorespaces}%
\def\DirFromAngle#1to#2{%
\edef\t at X{\fpeval{round(cosd#1,6)}}%
\edef\t at Y{\fpeval{round(sind#1,6)}}%
@@ -363,8 +401,7 @@
\edef\t at Y{\fpeval{#2 * \t at Y}}%
\MakeVectorFrom\t at X\t at Y to#3\ignorespaces}%
\def\ConjVect#1to#2{\GetCoord(#1)\t at X\t at Y
-\edef\t at Y{-\t at Y}%
-\MakeVectorFrom\t at X\t at Y to#2\ignorespaces}%
+\edef\t at Y{-\t at Y}\MakeVectorFrom\t at X\t at Y to#2\ignorespaces}%
\def\AddVect#1and#2to#3{\GetCoord(#1)\tu at X\tu at Y
\GetCoord(#2)\td at X\td at Y
\edef\t at X{\fpeval{\tu at X + \td at X}}%
@@ -378,69 +415,75 @@
\def\ModAndAngleOfVect#1to#2and#3{\ModOfVect#1to#2\relax
\ArgOfVect#1to#3\ignorespaces}
\newcount\MV at C
-\NewDocumentCommand\Multvect{m s m s m}{%
-\MV at C=0
-\ModAndAngleOfVect#1to\MV at uM and\MV at uA
+\NewDocumentCommand\Multvect{m s m s m}%
+{\ModAndAngleOfVect#1to\MV at uM and\MV at uA
\ModAndAngleOfVect#3to\MV at dM and\MV at dA
-\IfBooleanT{#2}{\MV at C=1}\relax
-\IfBooleanT{#4}{\MV at C=1}\relax
-\unless\ifnum\MV at C=0\edef\MV at dA{-\MV at dA}\fi
-\edef\MV at rM{\fpeval{round((\MV at uM * \MV at dM),6)}}%
-\edef\MV at rA{\fpeval{round((\MV at uA + \MV at dA),6)}}%
-\GetCoord(\MV at rA:\MV at rM)\t at X\t at Y
-\MakeVectorFrom\t at X\t at Y to#5}
-\def\MultVect#1by{\@ifstar{\let\MV at c\@ne\@MultVect#1by}%
- {\let\MV at c\empty\@MultVect#1by}}
+\fptestT{%
+\IfBooleanTF{#2}{1}{0}+\IfBooleanTF{#4}{1}{0}!=0}%
+{\edef\MV at dA{-\MV at dA}}%
+\edef\MV at rM{\fpeval{round((\MV at uM*\MV at dM),6)}}%
+\edef\MV at rA{\fpeval{round((\MV at uA+\MV at dA),6)}}%
+\edef#5{\fpeval{\MV at rM*cosd\MV at rA},\fpeval{\MV at rM*sind\MV at rA}}}
+\def\MultVect#1by{\@ifstar{\let\MV at c1\@MultVect#1 by}{\let\MV at c0\@MultVect#1by}}
+
\def\@MultVect#1by#2to#3{%
- \unless\ifx\MV at c\empty\Multvect{#1}{#2}*{#3}\else
- \Multvect{#1}{#2}{#3}\fi}
+ \fptest{\MV at c!=0}{\Multvect{#1}{#2}*{#3}}%
+ {\Multvect{#1}{#2}{#3}}%
+}%
\def\DivVect#1by#2to#3{\Divvect{#1}{#2}{#3}}
-\NewDocumentCommand\Divvect{ m m m }{%
-\ModAndDirOfVect#2to\@Mod and\@Dir
-\edef\@Mod{\fpeval{1 / \@Mod}}%
-\ConjVect\@Dir to\@Dir
-\ScaleVect#1by\@Mod to\@tempa
-\Multvect{\@tempa}{\@Dir}#3\ignorespaces}%
+\NewDocumentCommand \Divvect{m m m}%
+{\ModOfVect#2to\DV at dD
+\fptest{\DV at dD=0}{\PackageWarning{curve2e}{^^J%
+******************************************^^J%
+Division by zero!^^J%
+Result set to maxdimen in scaled points^^J%
+******************************************^^J}%
+\edef#3{\fpeval{\maxdimen*2**16},0}}%
+{\edef\DV at sF{\fpeval{1/\DV at dD**2}}%
+\Multvect{#2}{\DV at sF,0}{\DV at dD}%
+\Multvect{#1}{\DV at dD}*{#3}}}%
\def\Arc(#1)(#2)#3{\begingroup
-\@tdA=#3\p@
-\unless\ifdim\@tdA=\z@
- \@Arc(#1)(#2)%
-\fi
-\endgroup\ignorespaces}%
+\edef\tempG{#3}%
+\fptestF{#3=0}{\@Arc(#1)(#2)}}%
+
\def\@Arc(#1)(#2){%
-\ifdim\@tdA>\z@
- \let\Segno+%
-\else
- \@tdA=-\@tdA \let\Segno-%
-\fi
-\Numero\@gradi\@tdA
-\ifdim\@tdA>360\p@
- \PackageWarning{curve2e}{The arc aperture is \@gradi\space degrees
- and gets reduced\MessageBreak%
- to the range 0--360 taking the sign into consideration}%
- \@whiledim\@tdA>360\p@\do{\advance\@tdA-360\p@}%
-\fi
+\fptest{\tempG>\z@}%
+ {\let\Segno+}%
+ {\let\Segno-%
+ \edef\tempG{\fpeval{abs(\tempG)}}%
+ }%
+\fptestT{\tempG>360}{%
+ \PackageWarning{curve2e}%
+ {The arc aperture is \tempG\space degrees
+ and gets reduced^^J%
+ to the interval 0--360 taking the sign into
+ consideration}%
+ \edef\tempG{\Modulo{\tempG}{360}}%
+ }%
\GetCoord(#2)\@pPunX\@pPunY
\ifCV at polare
\ModOfVect#2to\@Raggio
\CopyVect#1to\@Cent
- \AddVect#2and#1to\@pPun% punto da cui parte l'arco
+ \AddVect#2and#1to\@pPun% starting point
\GetCoord(\@pPun)\@pPunX\@pPunY
\else
- \SubVect#2from#1to\@V \ModOfVect\@V to\@Raggio
+ \SubVect#2from#1to\@V
+ \ModOfVect\@V to\@Raggio
\CopyVect#2to\@pPun
- \CopyVect#1to\@Cent \GetCoord(\@pPun)\@pPunX\@pPunY
+ \CopyVect#1to\@Cent
+ \GetCoord(\@pPun)\@pPunX\@pPunY
\fi
-\@@Arc\strokepath\ignorespaces}%
-\def\@@Arc{\pIIe at moveto{\@pPunX\unitlength}{\@pPunY\unitlength}%
-\ifdim\@tdA>180\p@
- \advance\@tdA-180\p@
- \Numero\@gradi\@tdA
+\@@Arc\strokepath\endgroup\ignorespaces}%
+\def\@@Arc{%
+\pIIe at moveto{\@pPunX\unitlength}%
+ {\@pPunY\unitlength}%
+\fptestT{\tempG>180}{%
+ \edef\tempG{\fpeval{\tempG-180}}%
\SubVect\@pPun from\@Cent to\@V
\AddVect\@V and\@Cent to\@sPun
- \Multvect{\@V}{0,-1.3333333}\@V
+ \Multvect{\@V}{0,-1.3333333}{\@V}%
\if\Segno-\ScaleVect\@V by-1to\@V\fi
\AddVect\@pPun and\@V to\@pcPun
\AddVect\@sPun and\@V to\@scPun
@@ -447,21 +490,25 @@
\GetCoord(\@pcPun)\@pcPunX\@pcPunY
\GetCoord(\@scPun)\@scPunX\@scPunY
\GetCoord(\@sPun)\@sPunX\@sPunY
- \pIIe at curveto{\@pcPunX\unitlength}{\@pcPunY\unitlength}%
- {\@scPunX\unitlength}{\@scPunY\unitlength}%
- {\@sPunX\unitlength}{\@sPunY\unitlength}%
- \CopyVect\@sPun to\@pPun
-\fi
-\ifdim\@tdA>\z@
- \DirFromAngle\@gradi to\@Dir \if\Segno-\ConjVect\@Dir to\@Dir \fi
+ \pIIe at curveto{\@pcPunX\unitlength}%
+ {\@pcPunY\unitlength}%
+ {\@scPunX\unitlength}%
+ {\@scPunY\unitlength}%
+ {\@sPunX\unitlength}%
+ {\@sPunY\unitlength}%
+ \CopyVect\@sPun to\@pPun}%
+\fptestT{\tempG>0}{%
+ \DirFromAngle\tempG to\@Dir
+ \if\Segno-\ConjVect\@Dir to\@Dir \fi
\SubVect\@Cent from\@pPun to\@V
\Multvect{\@V}{\@Dir}\@V
\AddVect\@Cent and\@V to\@sPun
- \@tdA=.5\@tdA \Numero\@gradi\@tdA
- \DirFromAngle\@gradi to\@Phimezzi
+ \edef\tempG{\fpeval{\tempG/2}}%
+ \DirFromAngle\tempG to\@Phimezzi
\GetCoord(\@Phimezzi)\@cosphimezzi\@sinphimezzi
\@tdB=1.3333333\p@ \@tdB=\@Raggio\@tdB
- \@tdC=\p@ \advance\@tdC -\@cosphimezzi\p@ \Numero\@tempa\@tdC
+ \@tdC=\p@ \advance\@tdC -\@cosphimezzi\p@
+ \Numero\@tempa\@tdC
\@tdB=\@tempa\@tdB
\DividE\@tdB by\@sinphimezzi\p@ to\@cZ
\ScaleVect\@Phimezzi by\@cZ to\@Phimezzi
@@ -481,39 +528,36 @@
\GetCoord(\@pcPun)\@pcPunX\@pcPunY
\GetCoord(\@scPun)\@scPunX\@scPunY
\GetCoord(\@sPun)\@sPunX\@sPunY
- \pIIe at curveto{\@pcPunX\unitlength}{\@pcPunY\unitlength}%
- {\@scPunX\unitlength}{\@scPunY\unitlength}%
- {\@sPunX\unitlength}{\@sPunY\unitlength}%
-\fi}
+ \pIIe at curveto{\@pcPunX\unitlength}%
+ {\@pcPunY\unitlength}%
+ {\@scPunX\unitlength}%
+ {\@scPunY\unitlength}%
+ {\@sPunX\unitlength}%
+ {\@sPunY\unitlength}%
+}}%
\def\VectorArc(#1)(#2)#3{\begingroup
-\@tdA=#3\p@ \ifdim\@tdA=\z@\else
- \@VArc(#1)(#2)%
-\fi
-\endgroup\ignorespaces}%
-\def\VectorARC(#1)(#2)#3{\begingroup
-\@tdA=#3\p@
-\ifdim\@tdA=\z@\else
- \@VARC(#1)(#2)%
-\fi
-\endgroup\ignorespaces}%
-\let\VVectorArc\VectorARC
+\def\tempG{#3}%
+\fptestF{#3=0}{\@VArc(#1)(#2)}}%
\def\@VArc(#1)(#2){%
-\ifdim\@tdA>\z@
- \let\Segno+%
-\else
- \@tdA=-\@tdA \let\Segno-%
-\fi \Numero\@gradi\@tdA
-\ifdim\@tdA>360\p@
- \PackageWarning{curve2e}{The arc aperture is \@gradi\space degrees
- and gets reduced\MessageBreak%
- to the range 0--360 taking the sign into consideration}%
- \@whiledim\@tdA>360\p@\do{\advance\@tdA-360\p@}%
-\fi
+\fptest{\tempG>\z@}%
+ {\let\Segno+}%
+ {\let\Segno-%
+ \edef\tempG{\fpeval{abs(\tempG)}}}%
+\let\@gradi\tempG
+\fptestT{\tempG>360}
+ {\PackageWarning{curve2e}%
+ {The arc aperture is \tempG\space degrees
+ and gets reduced^^J%
+ to the range 0--360 taking the sign into
+ consideration}%
+ \edef\tempG{\Modulo{\tempG}{360}}%
+ }%
+\let\@gradi\tempG
\GetCoord(#2)\@pPunX\@pPunY
\ifCV at polare
\ModOfVect#2to\@Raggio \CopyVect#2to\@V
\CopyVect#1to\@Cent
- \AddVect#2and#1to\@pPun% punto da cui parte l'arco
+ \AddVect#2and#1to\@pPun% punto iniziale
\GetCoord(\@pPun)\@pPunX\@pPunY
\else
\SubVect#1from#2to\@V \ModOfVect\@V to\@Raggio
@@ -542,24 +586,31 @@
\advance\@tdA -\@tdE \Numero\@gradi\@tdA
\CopyVect#1to\@Cent \GetCoord(\@pPun)\@pPunX\@pPunY
\@@Arc
-\strokepath\ignorespaces}%
+\strokepath\endgroup\ignorespaces}%
+\def\VectorARC(#1)(#2)#3{\begingroup
+\def\tempG{#3}%
+ \fptestF{#3=0}{\@VARC(#1)(#2)}}%
+\let\VVectorArc\VectorARC% alias
+
\def\@VARC(#1)(#2){%
-\ifdim\@tdA>\z@
- \let\Segno+%
-\else
- \@tdA=-\@tdA \let\Segno-%
-\fi \Numero\@gradi\@tdA
-\ifdim\@tdA>360\p@
- \PackageWarning{curve2e}{The arc aperture is \@gradi\space degrees
+\fptest{\tempG>\z@}%
+ {\let\Segno+}%
+ {\let\Segno-%
+ \edef\tempG{\fpeval{abs(\tempG)}}}%
+\let\@gradi\tempG
+\fptestT{\tempG>360}{%
+ \PackageWarning{curve2e}%
+ {The arc aperture is \@gradi\space degrees
and gets reduced\MessageBreak%
- to the range 0--360 taking the sign into consideration}%
- \@whiledim\@tdA>360\p@\do{\advance\@tdA-360\p@}%
-\fi
+ to the range 0--360 taking the sign into
+ consideration}%
+ \edef\tempG{\Modulo{\tempG}{360}\p@}}
+ \@tdA=\tempG\p@ \let\@gradi\tempG
\GetCoord(#2)\@pPunX\@pPunY
\ifCV at polare
\ModOfVect#2to\@Raggio \CopyVect#2to\@V
\CopyVect#1to\@Cent
- \AddVect#2and#1to\@pPun% punto da cui parte l'arco
+ \AddVect#2and#1to\@pPun% punto iniziale
\GetCoord(\@pPun)\@pPunX\@pPunY
\else
\SubVect#1from#2to\@V \ModOfVect\@V to\@Raggio
@@ -568,11 +619,10 @@
\fi
\@tdE=\pIIe at FAW\@wholewidth \@tdE=\pIIe at FAL\@tdE
\DividE\@tdE by \@Raggio\unitlength to\DeltaGradi
-\@tdD=\DeltaGradi\p@
-\@tdD=57.29578\@tdD \Numero\DeltaGradi\@tdD
+\edef\DeltaGradi{\fpeval{57.29578*\DeltaGradi}}
\@tdD=\if\Segno--\fi\@gradi\p@ \Numero\@tempa\@tdD
\DirFromAngle\@tempa to\@Dir
-\Multvect{\@V}{\@Dir}\@sPun% corrects the end point
+\Multvect{\@V}{\@Dir}\@sPun% correct the end point
\edef\@tempA{\if\Segno--\fi1}%
\Multvect{\@sPun}{0,\@tempA}\@vPun
\DirOfVect\@vPun to\@Dir
@@ -593,7 +643,7 @@
\@tdE\if\Segno--\fi\DeltaGradi\p@
\Numero\@tempB{0.5\@tdE}%
\DirFromAngle\@tempB to\@Dird
-\Multvect{\@vPun}{\@Dird}\@vPun% corrects the starting point
+\Multvect{\@vPun}{\@Dird}\@vPun% correct the starting point
\DirOfVect\@vPun to\@Dir\GetCoord(\@Dir)\@xnum\@ynum
\put(\@pPunX,\@pPunY){\vector(\@xnum,\@ynum){0}}% starting point arrow tip
\edef\@tempa{\if\Segno--\fi\DeltaGradi}%
@@ -603,7 +653,7 @@
\AddVect\@Cent and\@V to\@pPun
\GetCoord(\@pPun)\@pPunX\@pPunY
\@@Arc
-\strokepath\ignorespaces}%
+\strokepath\endgroup\ignorespaces}%
\def\CurveBetween#1and#2WithDirs#3and#4{%
\StartCurveAt#1WithDir{#3}\relax
@@ -623,7 +673,7 @@
\CopyVect\@tempa,\@tempb to\@Dzero
\DirOfVect\@Dzero to\@Dzero
\ignorespaces}
-\def\CurveFinish{\strokepath\endgroup\ignorespaces}%
+\def\CurveFinish{\strokepath\endgroup\ignorespaces}
\def\FillCurve{\fillpath\endgroup\ignorespaces}
\def\CurveEnd{\fillstroke\endgroup\ignorespaces}
\def\CbezierTo#1WithDir#2AndDists#3And#4{%
@@ -636,18 +686,18 @@
\GetCoord(\@Cuno)\@XCuno\@YCuno
\GetCoord(\@Puno)\@XPuno\@YPuno
\pIIe at curveto{\@XCzero\unitlength}{\@YCzero\unitlength}%
- {\@XCuno\unitlength}{\@YCuno\unitlength}%
- {\@XPuno\unitlength}{\@YPuno\unitlength}%
+ {\@XCuno\unitlength}%
+ {\@YCuno\unitlength}%
+ {\@XPuno\unitlength}%
+ {\@YPuno\unitlength}%
\CopyVect\@Puno to\@Pzero
\CopyVect\@Duno to\@Dzero
\ignorespaces}%
-\def\CbezierBetween#1And#2WithDirs#3And#4UsingDists#5And#6{%
-\StartCurveAt#1WithDir{#3}\relax
+\def\CbezierBetween#1And#2WithDirs#3And#4UsingDists#5And#6{\StartCurveAt#1WithDir{#3}\relax
\CbezierTo#2WithDir#4AndDists#5And{#6}\CurveFinish}
-
\def\@isTension#1;#2!!{\def\@tempA{#1}%
-\def\@tempB{#2}\unless\ifx\@tempB\empty\strip at semicolon#2\fi}
+\def\@tempB{#2}\unless\ifx\@tempB\empty \strip at semicolon#2\fi}
\def\strip at semicolon#1;{\def\@tempB{#1}}
\def\CurveTo#1WithDir#2{%
@@ -661,16 +711,17 @@
\GetCoord(\@Dpzero)\@DXpzero\@DYpzero
\GetCoord(\@Dpuno)\@DXpuno\@DYpuno
\DivideFN\@Chord by2 to\@semichord
-\fptest{\@DYpuno=0 && \@DYpzero=0}{\GetCoord(\@Puno)\@tX\@tY
- \pIIe at lineto{\@tX\unitlength}{\@tY\unitlength}}%
-{\ifdim\@DXpzero\p@=\z@
- \@tdA=1.333333\p@
- \Numero\@KCzero{\@semichord\@tdA}%
-\fi
-\ifdim\@DYpzero\p@=\z@
- \@tdA=1.333333\p@
- \Numero\@Kpzero{\@semichord\@tdA}%
-\fi
+\fptest{abs(\@DYpuno)<=0.01&& abs(\@DYpzero)<=0.01}
+{\GetCoord(\@Puno)\@tX\@tY
+ \pIIe at lineto{\@tX\unitlength}%
+ {\@tY\unitlength}%
+}{%
+ \fptestT{abs(\@DXpzero)<=0.01}%
+ {\@tdA=1.333333\p@
+ \Numero\@KCzero{\@semichord\@tdA}}%
+\fptestT{abs(\@DYpzero)<=0.01}%
+ {\@tdA=1.333333\p@
+ \Numero\@Kpzero{\@semichord\@tdA}}%
\unless\ifdim\@DXpzero\p@=\z@
\unless\ifdim\@DYpzero\p@=\z@
\edef\@CosDzero{\ifdim\@DXpzero\p@<\z@ -\fi\@DXpzero}%
@@ -708,9 +759,12 @@
\GetCoord(\@Puno)\@XPuno\@YPuno
\GetCoord(\@CPzero)\@XCPzero\@YCPzero
\GetCoord(\@CPuno)\@XCPuno\@YCPuno
-\pIIe at curveto{\@XCPzero\unitlength}{\@YCPzero\unitlength}%
- {\@XCPuno\unitlength}{\@YCPuno\unitlength}%
- {\@XPuno\unitlength}{\@YPuno\unitlength}}\egroup
+\pIIe at curveto{\@XCPzero\unitlength}%
+ {\@YCPzero\unitlength}%
+ {\@XCPuno\unitlength}%
+ {\@YCPuno\unitlength}%
+ {\@XPuno\unitlength}%
+ {\@YPuno\unitlength}}\egroup
\CopyVect\@Puno to\@Pzero
\CopyVect\@Duno to\@Dzero
\ignorespaces}%
@@ -721,23 +775,29 @@
\StartCurveAt#1WithDir{#2}%
\@ifnextchar\lp at r\@Curve{%
\PackageWarning{curve2e}{%
- Curve specifications must contain at least two nodes!\MessageBreak
- Please, control your \string\Curve\space specifications\MessageBreak}}}
+ Curve specifications must contain at least
+ two nodes!^^J
+ Please, control your \string\Curve\space
+ specifications^^J}}}
+
\def\@Curve(#1)<#2>{%
\CurveTo#1WithDir{#2}%
\@ifnextchar\lp at r\@Curve{%
\@ifnextchar[\@ChangeDir\CurveEnd}}
\def\@ChangeDir[#1]{\ChangeDir<#1>\@Curve}
-\def\Qurve{\@ifstar{\let\fillstroke\fillpath\Qurve@}%
-{\let\fillstroke\strokepath\Qurve@}}
+\def\Qurve{%
+ \@ifstar{\let\fillstroke\fillpath\Qurve@}%
+ {\let\fillstroke\strokepath\Qurve@}%
+}%
\def\Qurve@(#1)<#2>{%
\StartCurveAt#1WithDir{#2}%
\@ifnextchar\lp at r\@Qurve{%
\PackageWarning{curve2e}{%
- Quadratic curve specifications must contain at least
- two nodes!\MessageBreak
- Please, control your Qurve specifications\MessageBreak}}}%
+ Quadratic curve specifications must contain
+ at least two nodes!^^J
+ Please, control your Qurve
+ specifications^^J}}}%
\def\@Qurve(#1)<#2>{\QurveTo#1WithDir{#2}%
\@ifnextchar\lp at r\@Qurve{%
@@ -751,10 +811,12 @@
\YpartOfVect\@Scalar to \@YScalar
\ifdim\@YScalar\p@=\z@
\PackageWarning{curve2e}%
- {Quadratic Bezier arcs cannot have their starting\MessageBreak
- and ending directions parallel or antiparallel with\MessageBreak
- each other. This arc is skipped and replaced with
- a dotted line.\MessageBreak}%
+ {Quadratic Bezier arcs cannot have their
+ starting^^J
+ and ending directions parallel or antiparallel
+ with each other.^^J
+ This arc is skipped and replaced with
+ a dotted line.^^J}%
\Dotline(\@Pzero)(\@Puno){2}\relax
\else
\Multvect{\@Dzero}*{\@DirChord}\@Dpzero
@@ -765,10 +827,14 @@
\MultiplyFN\@DYpzero by\@DYpuno to\@YYD
\unless\ifdim\@YYD\p@<\z@\ifdim\@XXD\p@<\z@
\PackageWarning{curve2e}%
- {Quadratic Bezier arcs cannot have inflection points\MessageBreak
- Therefore the tangents to the starting and ending arc\MessageBreak
- points cannot be directed to the same half plane.\MessageBreak
- This arc is skipped and replaced by a dotted line\MessageBreak}%
+ {Quadratic Bezier arcs cannot have
+ inflection points^^J
+ Therefore the tangents to the
+ starting and ending arc^^J
+ points cannot be directed to the
+ same half plane.^^J
+ This arc is skipped and replaced by
+ a dotted line^^J}%
\Dotline(\@Pzero)(\@Puno){2}\fi
\else
\edef\@CDzero{\@DXpzero}\relax
@@ -775,13 +841,13 @@
\edef\@SDzero{\@DYpzero}\relax
\edef\@CDuno{\@DXpuno}\relax
\edef\@SDuno{\@DYpuno}\relax
-\MultiplyFN\@SDzero by\@CDuno to\@tempA
-\MultiplyFN\@SDuno by\@CDzero to\@tempB
+\MultiplY\@SDzero by\@CDuno to\@tempA
+\MultiplY\@SDuno by\@CDzero to\@tempB
\edef\@tempA{\strip at pt\dimexpr\@tempA\p at -\@tempB\p@}\relax
\@tdA=\@SDuno\p@ \@tdB=\@Chord\p@ \@tdC=\@tempA\p@
\edef\@tempC{\strip at pt\dimexpr \@tdA*\@tdB/\@tdC}\relax
-\MultiplyFN\@tempC by\@CDzero to \@XC
-\MultiplyFN\@tempC by\@SDzero to \@YC
+\MultiplY\@tempC by\@CDzero to \@XC
+\MultiplY\@tempC by\@SDzero to \@YC
\ModOfVect\@XC,\@YC to\@KC
\ScaleVect\@Dzero by\@KC to\@CP
\AddVect\@Pzero and\@CP to\@CP
@@ -802,15 +868,17 @@
\ignorespaces}
%%
-%% Distributable under the LaTeX Project Public License,
-%% version 1.3c or higher (your choice). The latest version of
-%% this license is at: http://www.latex-project.org/lppl.txt
+%% Distributable under the LaTeX Project Public
+%% License, version 1.3c or higher (your choice).
+%% The latest version of this license is at:
+%% http://www.latex-project.org/lppl.txt
%%
%% This work is "maintained"
%%
-%% This work consists of file curve2e.dtx, and the derived files
-%% curve2e.sty and curve2e.pdf, plus the auxiliary derived files
-%% README.txt and curve2e-v161.sty.
+%% This work consists of file curve2e.dtx, and the
+%% derived files curve2e.sty and curve2e.pdf, plus
+%% the auxiliary derived files README.txt and
+%% curve2e-v161.sty.
%%
%%
%% End of file `curve2e.sty'.
More information about the tex-live-commits
mailing list.