texlive[59246] Master/texmf-dist: euclideangeometry (17may21)
commits+karl at tug.org
commits+karl at tug.org
Mon May 17 22:44:32 CEST 2021
Revision: 59246
http://tug.org/svn/texlive?view=revision&revision=59246
Author: karl
Date: 2021-05-17 22:44:32 +0200 (Mon, 17 May 2021)
Log Message:
-----------
euclideangeometry (17may21)
Modified Paths:
--------------
trunk/Master/texmf-dist/doc/latex/euclideangeometry/README.txt
trunk/Master/texmf-dist/doc/latex/euclideangeometry/euclideangeometry-man.pdf
trunk/Master/texmf-dist/doc/latex/euclideangeometry/euclideangeometry-man.tex
trunk/Master/texmf-dist/doc/latex/euclideangeometry/euclideangeometry.pdf
trunk/Master/texmf-dist/source/latex/euclideangeometry/euclideangeometry.dtx
trunk/Master/texmf-dist/tex/latex/euclideangeometry/euclideangeometry.sty
Modified: trunk/Master/texmf-dist/doc/latex/euclideangeometry/README.txt
===================================================================
--- trunk/Master/texmf-dist/doc/latex/euclideangeometry/README.txt 2021-05-17 20:44:18 UTC (rev 59245)
+++ trunk/Master/texmf-dist/doc/latex/euclideangeometry/README.txt 2021-05-17 20:44:32 UTC (rev 59246)
@@ -1,52 +1,29 @@
-%%
-%% This is file `README.txt',
-%% generated with the docstrip utility.
-%%
-%% The original source files were:
-%%
-%% euclideangeometry.dtx (with options: `readme')
-%%
-%% Copyright (C) 2020 Claudio Beccari all rights reserved.
-%% License information appended
-%%
File README.txt for package euclideangeometry
- [2020-04-15 v.0.1.8 Extension package for curve2e]
+ [2021-05-16 v.0.2.0 Extension package for curve2e]
-The package bundle euclideangeometry is composed of the following files
-euclideangeometry.dtx
-euclideangeometry.pdf
-euclideangeometry-man.tex
-euclideangeometry-man.pdf
-README.txt
+This work is "maintained"
+This work consists of files:
+1) euclideangeometry.dtx, and the derived files
+ euclideangeometry.sty and euclideangeometry.pdf,
+2) euclideangeometry-man.tex and the derived file
+ euclideangeometry-man.pdf,
+3) README.txt
+
euclideangeometry.dtx is the documented TeX source file of package
-euclideangeometry.sty; you get euclideangeometry.sty,
-euclideangeometry.pdf by running pdflatex on euclideangeometry.dtx.
+euclideangeometry.sty obtained by running pdflatex on euclideangeometry.dtx
+euclideangeometry.pdf obtained by running pdflatex on euclideangeometry.dtx.
README.txt, this file, contains general information.
euclideangeometry-man.tex and euclideangeometry-man.pdf are
-the source file and the readable document containing the end
-user manual.
+the source file and the readable document containing the
+end-user manual.
+
In other words euclideangeometry.pdf is oriented towards the
-developers and euclideangeometry-man.pdf to the end users.
+developers and euclideangeometry-man.pdf to the end-users.
Claudio Beccari
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 files:
-%% 1) euclideangeometry.dtx, and the derived files euclideangeometry.sty
-%% and euclideangeometry.pdf,
-%% 2) euclideangeometry-man.tex and the derived file euclideangeometry-man.pdf,
-%% 3) the auxiliary derived file README.txt
-%%
-%%
-%% End of file `README.txt'.
Modified: trunk/Master/texmf-dist/doc/latex/euclideangeometry/euclideangeometry-man.pdf
===================================================================
(Binary files differ)
Modified: trunk/Master/texmf-dist/doc/latex/euclideangeometry/euclideangeometry-man.tex
===================================================================
--- trunk/Master/texmf-dist/doc/latex/euclideangeometry/euclideangeometry-man.tex 2021-05-17 20:44:18 UTC (rev 59245)
+++ trunk/Master/texmf-dist/doc/latex/euclideangeometry/euclideangeometry-man.tex 2021-05-17 20:44:32 UTC (rev 59246)
@@ -6,8 +6,8 @@
\usepackage[utf8]{inputenc}
\usepackage[english]{babel}
\usepackage{lmodern,textcomp,mflogo}
-\usepackage{amsmath,fancyvrb,graphicx,verbatim,afterpage,trace}
-\usepackage{etoolbox,enumitem,xspace,xcolor,euclideangeometry}
+\usepackage{amsmath,fancyvrb,graphicx,afterpage,etoolbox,trace}
+\usepackage{enumitem,xspace,xcolor,euclideangeometry,pm-isomath}
\usepackage{url}
\providecommand\file{}
@@ -98,13 +98,12 @@
\def\hz{\hskip0pt}
\makeatletter
-\newwrite\example at out
\newlength\Wboxu \newlength\Wboxd
-% Attention!
+% Caution!
%
-% This is the latest version of the Esempio/Example environment
-% It differs from the previous versions because it accepts an optional
+% This is the latest version of the Esempio (Example) environment
+% It differs from the previous ones because it accepts an optional
% first argument asterisk; if the asterisk is not specified, the
% environment produces the code and the typeset result side by side.
% If the asterisk is specified, the code is typeset first, and its typeset
@@ -120,31 +119,44 @@
% When the asterisk is NOT specified, the \textwidth fraction for the
% code may be specified: default is (0.40); the remaining fraction minus
% \columnsep is used for the code typeset result.
+% For some reasons the optional code is not so optional, although the
+% argument descriptor is D()(0.40); it is not a burden to specify it
+% every time:
%
-\newwrite\example at out
-\DeclareDocumentEnvironment{Esempio}{s O{\normalsize} D(){0.40}}
-{\par\addvspace{3.0ex plus 0.8ex minus 0.5ex}\vskip -\parskip
-\Wboxu=#3\textwidth\relax
-\Wboxd=\dimexpr\linewidth-\columnsep-\Wboxu\relax
-\begingroup
-\@bsphack
-\immediate\openout\example at out\jobname-temp.tex
-\let\do\@makeother\dospecials\catcode`\^^M\active
-\def\verbatim at processline{%
- \immediate\write\example at out{\the\verbatim at line}}%
-\verbatim at start\relax}%
-{\immediate\closeout\example at out\@esphack\endgroup
-\begin{minipage}{\textwidth}%
-\IfBooleanTF{#1}{\begin{minipage}{\textwidth}}{\begin{minipage}{\Wboxu}}%
-#2\relax
-\verbatiminput{\jobname-temp.tex}
-\end{minipage}%
-\IfBooleanTF{#1}{\par\bigskip}{\hfill}%
-\IfBooleanTF{#1}{\begin{minipage}{\textwidth}}{\begin{minipage}{\Wboxd}}%
-\raggedleft
-\input{\jobname-temp}
-\end{minipage}
-\end{minipage}\par
+% Warning!
+% The \begin and \end statements must be on a line by themselves:
+%
+% Correct:
+% \begin{Esempio}*[...](...)
+% code
+% \end{Esempio}
+%
+% Wrong:
+% \begin{Esempio}*[...](...)
+% code\end{Esempio}
+%
+% The code end-of-line characters are part of the code to be saved
+% and reused
+
+\DeclareDocumentEnvironment{Esempio}{ s O{\normalsize} D(){0.40} }%
+{%
+ \par%\addvspace{3.0ex plus 0.8ex minus 0.5ex}\vskip -\parskip
+ \Wboxu=#3\textwidth
+ \Wboxd=\dimexpr\linewidth-\columnsep-\Wboxu\relax
+ \VerbatimOut{\jobname-temp.tex}%
+}{%
+ \endVerbatimOut
+ \begin{minipage}{\textwidth}%
+ \IfBooleanTF{#1}{\begin{minipage}{\textwidth}}{\begin{minipage}{\Wboxu}}%
+ #2\relax
+ \VerbatimInput{\jobname-temp.tex}
+ \end{minipage}%
+ \IfBooleanTF{#1}{\par\bigskip}{\hfill}%
+ \IfBooleanTF{#1}{\begin{minipage}{\textwidth}}{\begin{minipage}{\Wboxd}}%
+ \raggedleft
+ \input{\jobname-temp}
+ \end{minipage}
+ \end{minipage}\par
}
\makeatother
@@ -184,10 +196,10 @@
\end{titlepage}
\begin{abstract}
- This file further extends the functionalities of the \pack{curve2e}
- package, which, on turn, is an extension of the \pack{pict2e} package
- to the standard \env{picture} environment as defined in the \LaTeX\
- kernel source file.
+ The \pack{euclideangeometry} package further extends the functionalities
+ of the \pack{curve2e} package, which, on turn, is an extension of the
+ \pack{pict2e} package for the standard \env{picture} environment as
+ defined in the \LaTeX\ kernel source file.
The \pack{curve2e} package was upgraded a the beginning of 2020; the
material of this new package, might have been included in the former one,
@@ -195,7 +207,7 @@
package takes care of requesting the packages it depends from.
The purpose is to provide the tools to draw most of the geometrical
- constructions that a high school instructor or bachelor degree professor
+ constructions that a high school teacher or bachelor degree professor
might need in order to teach geometry. The connection to Euclide depends
on the fact that in its times calculations were made with ruler, compass,
and, apparently, also with ellipsograph.
@@ -203,7 +215,7 @@
The user of this package has available all the machinery provided by
the \pack{pict2e} and \pack{curve2e} packages, in order to define new
functionalities and build macros that draw the necessary lines, circles,
- and other such objects, as they would have done in the ancient times.
+ and other such objects, as they would have done in the old times.
Actually just one macro is programmed to solve a linear system of equations
\end{abstract}
@@ -219,7 +231,7 @@
\section{Introduction}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
The \pack{picture} environment has been available since the very beginning
- of \LaTeX in 1985. At that time it was a very simple environment
+ of \LaTeX in 1985. At that time it was a really simple environment
that allowed to draw very simple line graphics with many limitations.
When \LaTeX was upgraded from \LaTeX\!2.09 to \LaTeXe in 1994, Leslie
Lamport announced an upgrade that eventually became available in 2003
@@ -238,7 +250,16 @@
\pack{pict2e} and \pack{curve2e}, but extends the functionalities with a
very smart handling of coordinate systems, that allow to draw many line
drawings suitable for teaching geometry in high schools and introductory
- courses in the university bachelor degree programs.
+ courses in the university bachelor degree programs. It is worth mentioning
+ that an extension of \pack{TikZ}, called \pack{tkz-euclide} is also
+ available in a complete and updated \TeX system installation; at the
+ moment its documentation needs some refinements, at least to
+ consistently use a single language, without switching from English
+ to French and viceversa. It aims at the same readership, but it allows
+ to do many more geometrical constructions, than \pack{euclideangeometry}.
+ The real difference is that \pack{euclideangemetry} may be easily
+ expanded without the need of knowing the complex machinery and coding
+ of the \pack{tkz-euclide} underlaying \pack{TikZ} package.
This package \pack{euclideangeomery} apparently follows the same
path of \pack{xpicture}, but it avoids defining a new user language
@@ -248,7 +269,7 @@
It is worth mentioning that now \pack{curve2e} accepts coordinates in both
cartesian and polar form; it allows to identify specific points of the
drawing with macros, so the same macro can be used over and over again to
- address the same points. The package can draw lines, vectors, arcs
+ address the same point. The package can draw lines, vectors, arcs
with no arrow tips, or with one arrow tip, or with arrow tips at both ends,
arcs included. The macros for drawing poly lines, polygons, circles,
generic curves (by means of Bézier cubic or quadratic splines) are
@@ -262,8 +283,9 @@
This grid is useful also to the end user, while s/he is working on a
particular drawing, but when the drawing is finished, the user can
delete the grid command or comment out that line of code.
- For what regards the commands used to render the images, their codes can
- be found in the documented code file \pack{euclideangeometry.pdf}.
+ For what regards the commands used to render the images, their
+ \emph{codes} can be found in the documented code file
+ \pack{euclideangeometry.pdf}.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Installing \pack{euclideangeometry}}
@@ -273,9 +295,20 @@
installation, otherwise this package won't work; this means that
you have done your updating after 2020-01-18. And this package is already
present in any modern updated complete installation of the \TeX system.
- Otherwise the package will load \pack{curve2e} with an old version
- and file date, and this package will abort its own loading, besides
- aborting the whole job.
+ If \pack{curve2e} has a date earlier then 2020-01-018, the \pack{curve2e}
+ itself will load \pack{curve2ev161}, an older version, and this package
+ \pack{euclideangeomentry} will abort its own loading, besides
+ aborting the whole job.
+
+ We remember the package dependencies; the primary dependence is package
+ \pack{curve2e} with a version date more recent or equal to 2020-01-18.
+ On turn \pack{curve2e} requires packages \pack{xparse} and \pack{xfp};
+ missing these two package, it loads its own previous version, that does
+ not use such packages, but their absence forbids it working, so that,
+ after a very visible error message, it directly aborts. It also depends
+ on \pack{etoolbox}.
+ The chain of dependencies of the above first level packages may be
+ controlled directly on those packages documentation
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Loading \pack{euclideangeometry}}
@@ -286,7 +319,7 @@
\cs{usepackage}\oarg{options}\Marg{euclideangeomery}
\end{flushleft}
The package will take care of managing the possible \meta{options}
- and to call \pack{curve2e} with the such specified options; on turn
+ and to call \pack{curve2e} with such specified options; on turn
\pack{curve2e} calls \pack{pict2e} passing on the \meta{options}; such
\meta{options} are only those usable by \pack{pict2e} because neither
\pack{curve2e} nor \pack{euclideangeometry} use any option. If the
@@ -315,8 +348,8 @@
same restrictions; in particular there are the following improvements.
\begin{enumerate}[noitemsep]
\item Lines and vectors are drawn as usual by \cs{put}ting in place
- their forms, but their inclinations are not limited to a limited
- number of slope parameters, originally specified with reciprocally
+ their forms, but their inclinations are not limited to a small set of
+ slope parameters, originally specified with reciprocally
prime single digit values not exceeding~6 for lines, and~4 for vectors;
the length of these sloped objects is still their horizontal component;
now, the slopes may be described with any signed fractional number not
@@ -326,7 +359,7 @@
\item There is no restriction on the minimum length of lines and vectors.
%
\item Circles and dots can be drawn at any size, not at that dozen
- or so of finite sizes that were accepted with the original environment.
+ or so finite sizes that were accepted with the original environment.
%
\item Ovals may be specified the corner curvature; the default
size of the quarter circles that make up the oval corners may be
@@ -372,7 +405,7 @@
There were also the low level commands user interfaces to the various
drivers; these drivers really exist, but \pack{pict2e}
- knows how to detect the correct language of the necessary drive;
+ knows how to detect the correct language of the necessary driver;
the user is therefore allowed to pretend to ignore the existence
of such drivers, and s/he can simply use these low level commands; their
names are almost self explanatory.
@@ -390,7 +423,7 @@
initial point are among the specified arguments, but the reader should
check on the \pack{pict2e} documentation for the details.
-\item[]\mbox{\bfseries Attention!} Notice that these commands produce
+\item[]\mbox{\bfseries Warning!} Notice that these commands produce
just information to trace lines, but by themselves they do not trace
anything; in order to actually trace the curve or do other operations
with what has been done after the user finished describing the line to be
@@ -405,7 +438,7 @@
\item If a \cs{fillpath} command is used, the line loop is filled with
the current color. Notice, if the described line is not a closed loop,
- this filling command acts as if the line first point and last point were
+ this filling command acts as if the line first and last points were
joined by a straight line.
\end{enumerate}
@@ -444,7 +477,7 @@
better to declare the \cs{roundcap} for the whole document.
We do not go further in the description of the new \pack{pict2e}
- modified and new new commands; the reader unfamiliar with programmable
+ modified and new commands; the reader unfamiliar with programmable
drawing and the \pack{pic2e} extensions can consult that package
documentation. Actually all commands have been redefined or modified
by \pack{curve2e} in order to render them at least compatible with
@@ -454,7 +487,7 @@
\begin{figure}[!htb] \centering
\makebox[\textwidth]{\unitlength=0.009\textwidth
\begin{picture}(130,50)
- \GraphGrid(130,50)
+ \AutoGrid
\linethickness{4mm}
\buttcap\miterjoin
\put(10,10){\polyline[\miterjoin](0,0)(30,0)(30,30)
@@ -518,7 +551,7 @@
\end{align*}
Squares and square roots\footnote{The square root of a complex number
has two complex values; here we do not go into the details on how
- \pack{curve2e} choses one or the other value. In practice, the
+ \pack{curve2e} choses which value. In practice, the
\pack{curve2e} macros that use square roots, work mostly on scalars to
find magnitudes that are always positive.} are simply done with:
\begin{align*}
@@ -529,7 +562,7 @@
asterisk:
\[\text{if } z= x+\iu y \text{ then } z^\star = x- \iu y\]
and from these simple formal rules many results can be obtained;
- and therefore several macros must be defined.
+ and therefore several macros have been defined.
But let us summarise. Here is a short list with a minimum of
explanation of the commands functionalities introduced by
@@ -565,8 +598,8 @@
macros are used, instead of explicit numerical values, but for input
vector macros it is possible to use the comma or colon separated ordered
pair; “versor” means “unit vector”; angles are always expressed in
- degrees; output quantities are everything follows the key word
- \texttt{to}; output quantities are alway supposed to be in the form
+ degrees; output quantities are everything that follows the key word
+ \texttt{to}; output quantities are always supposed to be in the form
of control sequences.
\begin{itemize}\small
\item \cs{MakeVectorFrom}\meta{number,number}\meta{numeric macro} to\meta{vector macro}
@@ -629,7 +662,7 @@
\item Command \cs{polyline}, \cs{polygon} and \cs{polygon*} are redefined
to accept both coordinate kinds.
-\item Commands \cs{VECTOR}\parg{$P_1$}\parg{$P_2$} (and \cs{VVECTOR}, with the same syntax) draw vectors with one arrow tip at the end, or arrow tips at both ends respectively.
+\item Commands \cs{VECTOR}\parg{$P_1$}\parg{$P_2$} (and \cs{VVECTOR}, with the same syntax) draw vectors with one arrow tip at the end, or arrow tips at both ends respectively.l
\item New commands \cs{Arc}\parg{center}\parg{start}\marg{angle} and,
with the same syntax, \cs{VectorArc} and \cs{VectorARC} draw
@@ -646,19 +679,19 @@
\cs{multiput}\oarg{shift}\parg{origin}\parg{step}\marg{number}\marg{object}\oarg{handler}
\end{flushleft}
where, if you neglect the first and the last (optional) arguments,
- you have the original syntax; the \meta{origin} point is where the first
- \meta{object} is placed; \meta{step} is the displacement of a new
- \meta{object} relative to the previous one; \meta{number} is the
- total number of \meta{object}s put in place by the command; possibly
- the number may be an integer expression computed with the \cs{inteval}
- function of the L3~language, accessed through the \pack{xfp} package
- already loaded by \pack{curve2e}. The new features are \meta{shift},
- that is used to displace the whole drawing somewhere else (in case
- some fine tuning is required), and \meta{handler}; the latter is a
- powerful means to control both the object to be set in place and its
- position; further on there will be examples that show that the object
- can be put not only on straight paths, but also un other curves,
- including parabolas, circles, and other shapes.
+ you have the original syntax; the \meta{origin} point is where the
+ first \meta{object} is placed; \meta{step} is the displacement of a
+ new \meta{object} relative to the previous one; \meta{number} is the
+ total number of \meta{object}s put in place by the command; it is
+ possible to specify the number trough an integer expression computed
+ with the \cs{inteval} function of the L3~language, accessed through
+ the \pack{xfp} package already loaded by \pack{curve2e}. The new
+ features are \meta{shift}, that is used to displace the whole drawing
+ somewhere else (in case some fine tuning is required), and \meta{handler};
+ the latter is a powerful means to control both the object to be set in
+ place and its position; further on there will be examples that show
+ that the object can be put not only on straight paths, but also un
+ other curves, including parabolas, circles, and other shapes.
\item Another version of repetitive commands \cs{xmultiput} is very
similar to \cs{multiput} but the iterations are controlled in a
@@ -675,31 +708,34 @@
\cs{inteval}, it can use many mathematical functions, from square roots,
to exponentials, logarithms, trigonometric and hyperbolic direct and
inverse functions\footnote{The implementation of inverse hyperbolic
- function is on the L3~Team “to do” list.}, plus other ones. Normally
- fractional numbers are operated on decimal strings, with 16 fractional
- places, and 14 integer places but the L3~functions accept also scientific
- notation. The user can specify truncation or rounding to a specified
- number of digits. Such integer and fractional mathematical operations
- are already integrated in most computations performed by \pack{curve2e}.
+ function at the moment is on the L3~Team “to do” list.}, plus other ones.
+ Normally fractional numbers are operated on decimal strings, with 16
+ fractional places, and 14 integer places but the L3~functions accept also
+ scientific notation. The user can specify truncation or rounding to a
+ specified number of digits. Such integer and fractional mathematical
+ operations are already integrated in most computations performed by
+ \pack{curve2e}.
-\item \pack{curve2e} provides two more L3 functions: \cs{fptest} and
+\item \pack{curve2e} provides three more L3 functions: \cs{fptest} and
\cs{fpdowhile} with the following syntax:
\begin{flushleft}\obeylines
\cs{fptest}\marg{test}\marg{true}\marg{false}
\cs{fpdowhile}\marg{test}\marg{actions}
+\cs{fowhiledo}\marg{test}\marg{actions}
\end{flushleft}
- For both macros the \meta{test} is a logical F3~expression; its operands
- are logical constants, logical values, logical numeric comparisons; its
- operators are the typical \texttt{||}, \texttt{\&\&}, and \texttt{!},
- respectively for OR, AND, and NOT. The logical numerical comparisons
- are mathematical constants or expressions connected with relation
- operators, such as \texttt{>, =, <}; such operators may be negated with
- the NOT operator; therefore, for example, \texttt{!>} means “not greater
- than”, therefore “lower or equal to”.
+ For all these macros the \meta{test} is a logical L3~expression; its
+ operands are logical constants, logical values, logical numeric
+ comparisons; its operators are the typical \texttt{||}, \texttt{\&\&},
+ and \texttt{!}, respectively for OR, AND, and NOT. The logical numerical
+ comparisons are mathematical constants or expressions connected with
+ relation operators, such as \texttt{>, =, <}; such operators may be
+ negated with the NOT operator; therefore, for example, \texttt{!>} means
+ “not greater than”, therefore “lower or equal to”.
\item The above tests are very useful to control both \cs{fptest} and
- \cs{fpdowhile}. The logical \meta{test} result lets \cs{fptest} execute
- only the \meta{true} or the \meta{false} code. Before using \cs{fpdowhile}
+ \cs{fpdowhile} and \cs{fowhiledo}. The logical \meta{test} result lets
+ \cs{fptest} execute only the \meta{true} or the \meta{false} code.
+ Before using \cs{fpdowhile} or \cs{fpwhiledo}
the \meta{test} expression must be initialised to be \texttt{true};
the \meta{actions} should contain some code to be iteratively executed,
but they must contain some assignments, typically a change in an
@@ -707,11 +743,21 @@
expression becomes \texttt{false}. Lacking this assignments, the
loop continues to infinity, or better, until a fatal error message
is issued that informs that the program working memory is exhausted.
+ The difference between \cs{fpdowhile} and \cs{fpwhiledo} ie the order
+ in which the \meta{test} and the first\meta{action} is executed; in facts
+ \cs{fpdowhile} first does the \meta{action} then the \meta{test}, while
+ \cs{fpwhiledo} first executes the \meta{test} then the \meta{action}.
+ Since the modification of the test logical value is done by the commands
+ contained in the \meta{actions} this switching of the \meta{test} and
+ \meta{action} produces different results. Adjusting the \meta{test} it is
+ possible to get the same results, but the expressiveness of the \meta{test}
+ may be easier to understand in one way rather than the other. Some of the
+ examples show the such different \meta{test} syntaxes.
\item Such new commands are already used to code the \cs{multiput} and
\cs{xmultiput} commands, but they are available also to the user who can
operate in a very advanced way; further on, some examples will show
- some advanced drawings.
+ certain advanced drawings.
\item General curves can be drawn by \pack{pic2e} command \cs{curve}
that is sort of difficult to use, because the user has to specify
@@ -823,7 +869,7 @@
\begin{Esempio}[\setfontsize{7}](0.40)
\unitlength=0.005\linewidth
\begin{picture}(170,140)(0,-70)
-\GraphGrid(0,-70)(170,140)
+\AutoGrid
\VECTOR(0,0)(170,0)
\Pbox(170,0)[t]{x}[0]
\Pbox(100,0)[t]{\mathrm{1}}[2]
@@ -846,6 +892,7 @@
\end{Esempio}
\caption{The golden section $x_2$ and the golden number $x_1$}\label{fig:aureo}
\end{figure}
+
By the way figure~\ref{fig:aureo} shows also the code that is used
for the drawing done completely with the facilities available just with \pack{curv2e}. It is also a usage example of several commands.
@@ -855,7 +902,7 @@
Mathematicians in the classical times B.C. up to the artists in the
Renaissance, had no other means but to use geometrical constructions with
ruler and compass. Even today in schools where calculus is not yet
- taught as a normal subject, possibly not in certainly high school degree
+ taught as a normal subject, possibly not in certain high school degree
courses, but certainly not in elementary and junior high schools, the
instructors have to recourse to geometrical constructions. Sometimes, as
in Italy, access to public universities is open with no restrictions to
@@ -878,6 +925,9 @@
section~\ref{sec:examples} we show their usage by means examples.
\begin{enumerate}[noitemsep]
+%
+\item Command \cs{polyvector} is simple extension of the \cs{polyline} command introduced by \pack{pict2e}: draws a polyline with an arrow tip at its end; it turns out to be very handy while drawing block diagrams.
+%
\item Command \cs{IntersectionOfLines} is a fundamental one; its syntax is
the following:
\begin{ttsyntax}
@@ -886,9 +936,9 @@
\end{ttsyntax}
were each line is identified with its \meta{point} and its \emph{direction}
\meta{dir}; the intersection coordinates go to the output \meta{vector}.
-
+%
\item A second command\cs{IntersectionOfSegments} does almost the same
- work, but the coordinates of a segment define also its direction,
+ work, but the coordinates of a segment end points define also its direction,
which is the argument of the difference of the terminal nodes of each
segment; the syntax therefore is the following:
\begin{ttsyntax}
@@ -898,31 +948,35 @@
Again the intersection point coordinates go to the output \meta{vector}.
The first segment is between points 11 and 12, and, similarly, the second
segment is between points 21 and 22.
+%
\item Another “intersection” command is \cs{IntersectionsOfLine} to
determine the two intersection of a line with a circle. The syntax is:
\begin{ttsyntax}
-\cs{IntersectionsOfLine}\parg{point}\parg{dir}WithCircle\parg{center}\marg{radius}to\meta{int1} and\meta{int2}
+\cs{IntersectionsOfLine}\parg{point}\parg{dir}
+\qquad WithCircle\parg{center}\marg{radius}to\meta{int1} and\meta{int2}
\end{ttsyntax}
where \meta{point} and \meta{dir} identify a line with a given direction
and passing through a given point; the circle is identified with its
\meta{center} and \meta{radius}; the intersection points \meta{int1} and
- \meta{int2} are the coordinates of the intersection points; If the line
+ \meta{int2} are the coordinates of the intersection points; if the line
and circle do not intersect, a warning message is issued, shown in the
console and written to the \file{.log} file; the intersection points are
assigned the default values \texttt{0,0}, which evidently produce strange
results in the output document, so as to remind the user to give a look
to the \file{.log} file and to review his/her data.
+%
\item It is difficult to numerically determine the coordinates of the
intersection points of two circles; it becomes easier if one of the
- intersections is known; To this end, a macro to draw a circle with a
+ intersections is known; to this end, a macro to draw a circle with a
given center and passing through a given point is handy:
\begin{ttsyntax}
\cs{CircleThrough}\meta{point}WithCenter\marg{center}
\end{ttsyntax}
draws such circumference.
+%
\item With the above macro it becomes easy to draw two circumferences
with different centers and passing through the same point; therefore
- it becomes determine the other intersection point by means of the
+ it becomes easy to determine the other intersection point by means of the
following macro:
\begin{ttsyntax}
\cs{Segment}\parg{endpoint1}\parg{endpoint2}SymmetricPointOF\meta{p1}
@@ -932,6 +986,7 @@
symmetrical point \meta{p2} of \meta{p1} with respect to the segment
that joins the centers of the given circles intersecting one another
in \meta{p1}.
+%
\item It would be interesting to solve the same problem with help of
the following macro relating to right triangles identified with their
hypothenuse and one of its legs; the other leg is found by means of this
@@ -943,7 +998,7 @@
since the intersection points of two circles define their common chord;
this chord and the two circle centers define two isosceles triangles
with the same base; therefore the segment joining the circle radii,
- coincides whit the chord axis and divides each isosceles triangle in
+ coincides whith the chord axis and divides each isosceles triangle in
two right triangles, where the hypotenuse is one of two radii and the
first leg is the distance from the chord middle point, intersection of
the chord and the segment joining the circle centers; at this point the
@@ -950,7 +1005,8 @@
distance of the second point intersection from the chord middle point
and the coordinates of the second intersection may be easily computed;
of course this is a much clumsier way to determine the second
- intersection, but it is useful to solve this right triangle easy problem.
+ intersection, but it is useful to solve this right triangle easy problem.
+%
\item Command \cs{ThreePointCircle} draws a circle that goes through three
given points; the syntax is the following:
\begin{ttsyntax}
@@ -966,7 +1022,7 @@
\end{ttsyntax}
computes the three point circle center assigning its coordinates to
\meta{vector}.
-
+%
\item Command \cs{CircleWithCenter} draws a circle given its center and it
radius; in facts the syntax is the following:
\begin{ttsyntax}
@@ -974,7 +1030,7 @@
\end{ttsyntax}
This macro does not require the \cs{put} command to put the circle
in place.
-
+%
\item A similar macro \cs{Circlewithcenter} does almost the same; its
syntax is the following:
\begin{ttsyntax}
@@ -985,7 +1041,7 @@
modulus of which is computed and used as the radius; in the latter
command the \meta{radius} is a scalar and (its magnitude) is directly
used.
-
+%
\item Command with syntax:
\begin{ttsyntax}
\cs{AxisOf}\meta{point1} and\meta{point2} to \meta{point3} and\meta{point4}
@@ -1004,7 +1060,7 @@
totally equivalent, aliases to one another; sometimes it is more
convenient to use a name, sometimes the other; it helps reading the
code and maintaining it.
-
+%
\item Given a triangle and a specific vertex, it is possible to determine
the middle point of the opposite side; it is not very difficult, but it
is very handy to have all the necessary elements to draw the median line.
@@ -1013,9 +1069,9 @@
\cs{TriangleMedianBase}\meta{vertex} on\meta{base1} and\meta{base2}
\qquad to\meta{base middle point}
\end{ttsyntax}
-
+%
\item A similar command \cs{TriangleHeightBase} is used to determine the
- intersection of the height segment from one vertex to the opposite base;
+ intersection of the height segment from one vertex to the opposite side;
with triangles that have an obtuse angle, the height base might lay
externally to one of the bases adjacent to such an angle. The syntax is
the following
@@ -1022,7 +1078,7 @@
\begin{ttsyntax}
\cs{TriangleHeigthtBase}\meta{vertex} on\meta{base1} and\meta{base2} to\meta{height base}
\end{ttsyntax}
-
+%
\item Similarly there is the \cs{TriangleBisectorBase} macro with
a similar syntax:
\begin{ttsyntax}
@@ -1029,7 +1085,7 @@
\cs{TriangleBisectorBase}\meta{vertex} on\meta{base1} and\meta{base2}
\qquad to\meta{bisector base}
\end{ttsyntax}
-
+%
\item A triangle \emph{barycenter} is the point where its median lines
intersect; command \cs{TriangleBarycenter} determines its coordinates
with the following syntax.
@@ -1036,7 +1092,7 @@
\begin{ttsyntax}
\cs{TriangleBarycenter}\parg{vertex1}\parg{vertex2}\parg{vertex3} to\meta{barycenter}
\end{ttsyntax}
-
+%
\item A triangle \emph{orthocenter} is the point where its height lines
intersect; command \cs{TriangleOrthocenter} determines its coordinates
with the following syntax:
@@ -1043,7 +1099,7 @@
\begin{ttsyntax}
\cs{TriangleOrthocenter}\parg{vertex1}\parg{vertex2}\parg{vertex3} to\meta{orthocenter}
\end{ttsyntax}
-
+%
\item A triangle \emph{incenter} is the point where its bisector lines
intersect; command \cs{TriangleIncenter} determines its coordinates
with the following syntax:
@@ -1050,7 +1106,7 @@
\begin{ttsyntax}
\cs{TriangleIncenter}\parg{vertex1}\parg{vertex2}\parg{vertex3} to\meta{incenter}
\end{ttsyntax}
-
+%
\item The distance of a specified point from a given segment or line is
computed with the following command
\begin{ttsyntax}
@@ -1059,7 +1115,7 @@
where \meta{point} specifies the point and \meta{point1} and \meta{point2}
identify two points on a segment or a line; \meta{distance} is a scalar
value.
-
+%
\item In a construction that will be examined in section~\ref{sec:examples}
we need to determine an ellipse axis if the other axis and the focal
distance are know; actually it solves the relation
@@ -1082,7 +1138,7 @@
again when dealing with the specific problem referred to at the
beginning of this list item; the description is going to be more
detailed and another macro is added to avoid possible errors.
-
+%
\item Given a segment, i.e. the coordinates of its end points, it is
useful to have a macro that computes its length; at the same time it is
useful to to compute its direction; this operation is not the same as to
@@ -1097,7 +1153,7 @@
+180^\circ$; it represents the argument of the vector that goes from
\meta{point1} to \meta{point2}, therefore the user must pay attention to
the order s/he enters the end point coordinates.
-
+%
\item The next command \cs{SymmetricalPointOf} is used to find the
reflection of a specified point with respect to a fixed point; of course
the latter is the middle point of the couple, but the unknown to be
@@ -1106,7 +1162,7 @@
\begin{ttsyntax}
\cs{SymmetricalPointOf}\meta{point1} respect\meta{fixed} to\meta{point2}
\end{ttsyntax}
-
+%
\item Command \cs{RegPolygon} draws a regular polygon inscribed within
a circle of given radius and center, with a specified number of sides;
optional arguments allow to specify color and thickness of the sides,
@@ -1136,8 +1192,9 @@
argument is specified, the polygon center is displaced accordingly.
The number of sides in theory may be very high, but it is not wise
to exceed a couple of dozen sides; if the number of sides is too
- high, a polygon (completely contained in an A4 page) may become undistinguishable from a circumference.
-
+ high, a polygon (completely contained in an A4 page) may become
+ undistinguishable from a circumference.
+%
\item Several macros are dedicated to ellipses; their names are spelled
in Italian, “ellisse”, because the name “ellipse” is already taken by
other packages; with an Italian user command names there should be no
@@ -1178,13 +1235,14 @@
\end{minipage}
\caption{The effect of shearing an ellipse with its bounding rectangle}\label{fig:shear}
\end{figure}
-
+%
\item The syntax of those six commands are the following:
\begin{ttsyntax}
\cs{Sellisse}\meta{$\star$}\marg{semiaxis-h}\marg{semiaxis-v}\oarg{shear}
\cs{ellisse}\meta{$\star$}\marg{semiaxis-h}\marg{semiaxis-v}
-\cs{XSellisse}\meta{$\star$}\parg{center}\oarg{angle}\aarg{shear}\marg{semiaxis-h}\%
-\qquad \marg{semiaxis-v}\meta{$\star$}\oarg{settings1}\oarg{settings2}
+\cs{XSellisse}\meta{$\star$}\parg{center}\oarg{angle}\%
+\qquad \aarg{shear}\marg{semiaxis-h}\marg{semiaxis-v}\meta{$\star$}\%
+\qquad \oarg{settings1}\oarg{settings2}
\cs{Xellisse}\meta{$\star$}\parg{center}\oarg{angle}\marg{semiaxis-h}\%
\qquad\marg{semiaxis-v}\oarg{settings1}\marg{settings2}
\cs{EllipseWithFocus}\meta{$\star$}\parg{vertex1}\parg{vertex2}\parg{vertex3}\parg{focus}
@@ -1193,7 +1251,7 @@
All require the semi axis lengths; the \meta{semiaxis-h} and
\meta{semiaxis-v} refer to the semi axes before possible rotation by
\meta{angle} degrees, and do not make assumptions on which axis is the
- bigger one. The optional parameter \meta{shear} is the angle in degrees
+ largger one. The optional parameter \meta{shear} is the angle in degrees
by which the vertical coordinate lines are slanted by effect of shearing.
If \meta{shear}, that by default equals zero, is not set
to another value, the asterisks of command \cs{Sellisse} and
@@ -1213,7 +1271,7 @@
requires less data, in the sense that such ellipse is unique; it
is the ellipse internally tangent to the triangle at its side middle
points.
-
+%
\end{enumerate}
@@ -1228,7 +1286,7 @@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Figure~\ref{fig:vectors} shows some vectors and vector arcs with the
- code used to draw them; as usual some points are described with cartesian
+ code used to draw them; some points are described with cartesian
coordinates and some with polar ones.
\begin{figure}[!htb]
@@ -1235,7 +1293,7 @@
\begin{Esempio}[\setfontsize{8.5}](0.45)
\unitlength=0.01\linewidth
\begin{picture}(100,60)
-\GraphGrid(100,60)
+\AutoGrid
\put(0,30){\vector(1,2){10}}
\put(20,30){\Vector(10,20)}
\VECTOR(40,30)(50,50)
@@ -1251,7 +1309,8 @@
\begin{figure*}[!tb]
-\begin{Esempio}*[\setfontsize{10}]\centering
+\begin{Esempio}*[\setfontsize{10}](0.40)
+\centering
\unitlength=0.006\linewidth\begin{picture}(120,90)
%
\RegPolygon(9,20){20}{6}<\linethickness{3pt}\color{red}>
@@ -1308,7 +1367,10 @@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Dashed and dotted lines}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- For dotted lines it is possible to specify the dot size;
+ For dashedl ines it is mandatory to specify the dash length, that
+ is just as long as the gap between dashes. For dotted lines it is
+ mandatory to specify the dot gap.
+ For dotted lines it is also possible to specify the dot size;
it can be specified with an explicit unit of measure, or, if no unit is
specified, it is assumed to be “points”. The \cs{Dotline} takes care
of transforming the implied or the explicit dimension in multiples of
@@ -1319,7 +1381,7 @@
\begin{Esempio}[\setfontsize{10}](0.45)
\unitlength=0.02\linewidth
\begin{picture}(40,40)
-\GraphGrid(40,40)
+\AutoGrid
\Dashline(0,0)(40,10){4}
\put(0,0){\circle*{1}}
\Dashline(40,10)(0,25){4}
@@ -1338,15 +1400,15 @@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Generic curves}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-With the \cs{Curve} macro it is possible to make line art or filled shapes. Figures~\ref{fig:hearts} show the same shape, the first just stroked and the second color filled.
+With the \cs{Curve} macro it is possible to make line art or filled shapes. The hearts drawn in figure~\ref{fig:hearts} show the same shape, the first just stroked and the second color filled.
-\begin{figure}[!htp]
+\begin{figure}[!htb]
\begin{Esempio}[\setfontsize{9}](0.65)
\unitlength=8mm\relax
\begin{picture}(5,5)
\put(0,0){\framebox(5,5){}}\thicklines\roundcap
\Curve(2.5,0)<0.1,1>(5,3.5)<0,1>%
- (4,5)<-1,0>(2.5,3.5)<-0.1,-1.2>[-0.1,1.2]%
+ (4,5)<-1,0>(2.5,3.5)<-0.01,-1.2>[-0.01,1.2]%
(1,5)<-1,0>(0,3.5)<0,-1>(2.5,0)<0.1,-1>
\end{picture}
\end{Esempio}
@@ -1359,7 +1421,7 @@
\put(0,0){\framebox(5,5){}}\thicklines\roundcap
\color{orange}\relax
\Curve*(2.5,0)<0.1,1>(5,3.5)<0,1>%
-(4,5)<-1,0>(2.5,3.5)<-0.1,-1.2>[-0.1,1.2]%
+(4,5)<-1,0>(2.5,3.5)<-0.01,-1.2>[-0.01,1.2]%
(1,5)<-1,0>(0,3.5)<0,-1>(2.5,0)<0.1,-1>
\end{picture}
\end{Esempio}
@@ -1379,13 +1441,13 @@
the green filled squares are along a sloping down line inclined by
$15^\circ$ as specified by the polar coordinates of the \meta{increment};
the blue filled triangles are distributed along a parabola; the red
- stroked diamonds are distributed along a half sine wave.
+ stroked diamonds are distributed along a half sine wave.\enlargethispage*{\baselineskip}
\noindent\begin{figure}[!htb]
\begin{Esempio}[\setfontsize{8}](0.55)
\unitlength=0.01\linewidth
\begin{picture}(100,100)
-\GraphGrid(100,100)
+\AutoGrid
\multiput(0,0)(10,10){11}{\circle*{2}}
\color{blue!70!white}
\multiput(0,0)(10,0){11}{%
@@ -1415,7 +1477,7 @@
\begin{Esempio}[\setfontsize{9.5}](0.525)
\unitlength=0.0095\linewidth
\begin{picture}(100,100)
-\GraphGrid(100,100)
+\AutoGrid
\put(50,50){\thicklines\circle{100}}
\xmultiput[50,50](60:35)(-30:1){12}%
{\makebox(0,0){\circle*{2}}}%
@@ -1448,10 +1510,10 @@
do the job with \cs{xmultiput}.
\begin{figure*}[!tp]
-\begin{Esempio}[\setfontsize{9}](0.5)%
+\begin{Esempio}[\setfontsize{9}](0.5)
\unitlength=0.008\linewidth
\begin{picture}(100,100)
-\GraphGrid(100,100)
+\AutoGrid
\VECTOR(0,0)(100,0)\Pbox(100,0)[tr]{x}[0]
\VECTOR(0,0)(0,100)\Pbox(0,100)[tr]{y}[0]
\Pbox(0,0)[r]{O}[3pt]
@@ -1480,7 +1542,7 @@
A heart shaped mathematical function taken from the internet
\footnote{\url{http://mathworld.wolfram.com/HeartCurve.html} reports
several formulas, including the cardioid, but the one we use here is
- a different function} is the following
+ a different function.} is the following
\begin{align*}
x(t) &= \sin^3(t)\\
y(t) &= \dfrac{13\cos(t)-5\cos(2t)-2\cos(3t)-\cos(4t)}{16}
@@ -1508,7 +1570,7 @@
% Drawing
\unitlength=0,005\linewidth
\begin{picture}(200,200)(-100,-100)
-\GraphGrid(-100,-100)(200,200)
+\AutoGrid
\VECTOR(-100,0)(100,0)\Pbox(100,0)[tr]{x}[0]
\VECTOR(0,-100)(0,100)\Pbox(0,100)[tl]{y}[0]
\Pbox(0,0)[tr]{O}\linethickness{1pt}\bgroup
@@ -1531,7 +1593,7 @@
%
\unitlength=0,005\linewidth
\begin{picture}(200,200)(-100,-100)
-\GraphGrid(-100,-100)(200,200)
+\AutoGrid
\VECTOR(-100,0)(100,0)\Pbox(100,0)[tr]{x}[0]
\VECTOR(0,-100)(0,100)\Pbox(0,100)[tl]{y}[0]
\Pbox(0,0)[tr]{O}\linethickness{1pt}\bgroup
@@ -1554,8 +1616,8 @@
Figure~\ref{fig:circle-and-line} shows the simple geometrical construction that leads to the determination of the intersections; one of the lines is tangent to the circle and the intersection points $P_3$ and $P_4$ coincide.
-\begin{figure}
-\begin{Esempio}[\setfontsize{9}]
+\begin{figure}[!htb]
+\begin{Esempio}[\setfontsize{9}](0,40)
\unitlength=0.007\linewidth
\begin{picture}(100,100)
\AutoGrid
@@ -1584,8 +1646,8 @@
Figure~\ref{fig:two-intersecting-circles} shows the geometrical construction to determine the second intersection point $P_2$ of two circles that already have a first common point $P_1$. The common chord and the segment joining the centers are not shown, but the code, although with “strange” point names, shows all the steps necessary to find the second intersection point
-\begin{figure}\centering
-\begin{Esempio}[\setfontsize{9}]
+\begin{figure}[!htb]\centering
+\begin{Esempio}[\setfontsize{9}](0.40)
\unitlength0.007\linewidth
\begin{picture}(100,100)
\AutoGrid
@@ -1605,24 +1667,25 @@
\caption{Second intersection point $P_2$ of two circles sharing a first intersection point $P_1$}\label{fig:two-intersecting-circles}
\end{figure}
-The following macro allows to determine both intersections, if they exist, of two generic circles; of corse the maro is a little more complicated than the above macro need to find the second intersection when one is already known. Even the reasoning behind the macro is quite different and slightly “creative”.
+The following macro allows to determine both intersections, if they exist, of two generic circles; of course the macro is a little more complicated than the above macro that has to find the second intersection when one is already known. Even the reasoning behind the macro is quite different and slightly “creative”.
In facts the reasoning is to avoid any or most analytical computations; analytically it would be quite simple to set up a system of two second degree polynomial equations; after processing such a system it is necessary to solve a second degree equation, but in order to control if there are intersections it should be necessary to discuss the value and sign of the discriminant; it is nothing special when doing all this by hand, but it involves a complicated code in terms of the \LaTeX\ language.
-It is much simpler to reason geometrically; imagine to draw two circles; let $a$ be the distance of their centers, and let $R_1$ and $R_2$ be their radii. Then if
+
+It is much simpler to reason geometrically; imagine to draw two circles; let $a>0$ be the distance of their centers\footnote{If $a=0$ the circles are concentric and do not intersect.}, and let $R_1$ and $R_2$ be their radii. Then if
\[
-|R_1 -R_2| \leq a \leq R_1+R_2
+|R_1 - R_2| \leq a \leq R_1 + R_2
\]
-the intersections do exist, even if it is possible that the circles are tangent to one another and the two intersection points become a (double) one; this takes place when either ‘equals’ sign applies. I f the left boundary is not satisfied the centers are too close one another and the internal circle is too small compared to the external one. On the opposite if the upper bound is not satisfied the second circle is outside the first one and too far away.
+the intersections do exist, even if it is possible that the circles are tangent to one another and the two intersection points become a (double) one; this takes place when either ‘equals’ sign applies. If the left boundary is not satisfied the centers are too close to one another and the internal circle is too small compared to the external one. On the opposite if the upper bound is not satisfied the second circle is outside the first one and too far away.
-The macro controls the above range, and if the the input data do not satisfy the range boundaries, there are no intersections: a warning message is issued, but computations go on with non sense values for both output coordinates; may be other errors or produced, but in any case the successive drawing lines will not be acceptable; a good sign to the user who may have not noticed the warning message in his/her console, but is immediately “forced” to consult this manual and find out this explanation; s/he will then review his/her code in oder to change the drawing data.
+The macro controls the above range, and if the the input data do not satisfy the range boundaries, there are no intersections: a warning message is issued, but computations go on with non sense values for both output coordinates; may be other errors are produced, but in any case the successive drawing lines will not be acceptable; a good sign to the user who may have not noticed the warning message in his/her console, but is immediately “forced” to consult this manual and find out this explanation; s/he will then review his/her code in oder to change the drawing data.
-If the data cope with the above range, the computations go on along this simple reasoning, that it drawn in the left part of figure~\ref{fig;Intersections-of-two-circles}. There you see the segment that joins the two centers, and the intersection points to be found. They are the end points of the chord common to both circles; using as vertices the two centers and such chord as the base, two isosceles triangles are formed; the segment joining the centers bisects both triangles forming four right triangles where the hypotenuse is formed by the pertinent radius, and one leg is half the chord; with reference to the right triangles $IC_1P_1$ and $IC_2P_1$, Pithagoras' theorem lets us determine the relation between the common leg $IP_1$ and the other triangle sides; this s the small analytical computation we have to execute, so as to compute the distance $c$ from the center $C_1$ and the common leg length $h$. These two values are sufficient, together with the direction of segment $C_1C_2$ to find the intersection points coordinates.
+If the data cope with the above range, the computations go on along this simple reasoning, that it drawn in the left part of figure~\ref{fig;Intersections-of-two-circles}. There you see the segment that joins the two centers, and the intersection points to be found. They are the end points of the chord common to both circles; using as vertices the two centers and such chord as the base, two isosceles triangles are formed; the segment joining the centers bisects both triangles forming four right triangles where the hypotenuse is formed by the pertinent radius, and one leg is half the chord; with reference to the triangles $IC_1P_1$ and $IC_2P_1$, Pithagoras' theorem lets us determine the relation between the common leg $IP_1$ and the other triangle sides; this is the small analytical computation we have to execute, so as to compute the distance $c$ from the center $C_1$ and the common leg length $h$. These two values are sufficient, together with the direction of segment $C_1C_2$ to find the intersection points coordinates.
The syntax il the following
\begin{ttsyntax}
\cs{TwoCirclesIntersections}\parg{C1}\parg{C2}withradii\marg{R1} and\marg{R2} to\meta{P1} and\meta{P2}
\end{ttsyntax}
-Th symbols are self explanatory; as usual, input data (those entered before the keyword \texttt{to}) may be control sequences defined with the necessary data, or explicit data; on the opposite the output ones must be control sequences.
+Th symbols are self explanatory; as usual, input data (those entered before the keyword \texttt{to}) may be control sequences (defined with the necessary data), or explicit data; on the opposite the output ones must be control sequences.
\begin{figure}[!htb]
\begin{minipage}{0.475\linewidth}
@@ -1675,7 +1738,7 @@
The code for drawing figure~\ref{fig;Intersections-of-two-circles} is the following.
\begin{Verbatim}
-\begin{minipage}{0.475\linewidth}
+\begin{minipage}{0.475\linewidth}% Geometrical construcion
\unitlength0.01\linewidth
\begin{picture}(100,100)(-50,-50)
\AutoGrid
@@ -1689,7 +1752,7 @@
\thinlines
\TwoCirclesIntersections(\Kuno)(\Kdue)withradii\RKuno
and\RKdue to\Puno and\Pdue
-\Pbox(\Kuno)[br]{C_1}[4] \Pbox(\Kdue)[bl]{C_2}[4]
+\Pbox(\Kuno)[br]{C_1}[4] \Pbox(\Kdue)[bl]{C_2}[4]
\Pbox(\Puno)[tl]{P_1}[4] \Pbox(\Pdue)[bc]{P_2}[4]
\put(\Kuno){\Vector(-45:\RKuno)}\Pbox(5,-27)[bl]{R_1}[0]
\put(\Kdue){\Vector(-45:\RKdue)}\Pbox(25, 3)[bl]{R_2}[0]
@@ -1701,7 +1764,7 @@
\end{picture}
\end{minipage}
\hfill
-\begin{minipage}{0.475\linewidth}
+\begin{minipage}{0.475\linewidth}% Clean final result
\unitlength0.01\linewidth
\begin{picture}(100,100)(-50,-50)
\AutoGrid
@@ -1736,7 +1799,7 @@
special lines relative to a specific vertex. Thanks to the macros
described earlier in this list, this drawing is particularly simple; most
of the code is dedicated to labelling the various points and to
- assign coordinate values to the macros that are going to be use
+ assign coordinate values to the macros that are going to be used
in a symbolic way. The generic triangle (not a regular polygon) requires
one line of code, and the determination of the intersections of the lines
with the suitable triangle side, and their tracing requires two code lines
@@ -1746,20 +1809,20 @@
\begin{Esempio}[\setfontsize{6.9}](0.4)
\unitlength=0.008\linewidth
\begin{picture}(100,100)(0,-10)
-\GraphGrid(0,-10)(100,100)
-\def\Puno{0,0} \def\Pdue{0,80} \def\Ptre{100,60}
+\AutoGrid
+\def\Puno{0,0} \def\Pdue{0,80} \def\Ptre{100,55}
{\thicklines\polygon(\Puno)(\Pdue)(\Ptre)}%
- \Pbox(\Puno)[tc]{P_1}[1]
-\Pbox(\Pdue)[bc]{P_2}[1]\Pbox(\Ptre)[bc]{P_3}[1]
- % Median
+ \Pbox(\Puno)[tc]{P_1}[2]
+\Pbox(\Pdue)[bc]{P_2}[2]\Pbox(\Ptre)[bc]{P_3}[2]
+% Median
\TriangleMedianBase\Puno on \Pdue and \Ptre to\M
- \Pbox(\M)[bc]{M}[1.5]\segment(\Puno)(\M)
+ \Pbox(\M)[bc]{M}[2]\segment(\Puno)(\M)
% Height
\TriangleHeightBase\Puno on \Pdue and\Ptre to\H
\Dotline(\Puno)(\H){2}[1.5]\Pbox(\H)[bc]{H}[1.5]
% Bisector
\TriangleBisectorBase\Puno on\Pdue and\Ptre to\B
- \Dashline(\Puno)(\B){3}\Pbox(\B)[b]{B}[1.5]
+ \Dashline(\Puno)(\B){1.5}\Pbox(\B)[b]{B}[2]
\end{picture}
\end{Esempio}
\caption{A triangle with the median, the height, and the bisector lines
@@ -1787,8 +1850,8 @@
\begin{Esempio}[\setfontsize{6.5}](0.45)
\unitlength=0.008\linewidth
\begin{picture}(100,100)(0,-10)
-\GraphGrid(0,-10)(100,100)
-\def\Puno{0,0}\def\Pdue{0,80}\def\Ptre{100,60}
+\AutoGrid
+\def\Puno{0,0}\def\Pdue{0,80}\def\Ptre{100,55}
{\linethickness{0.6pt}\polygon(\Puno)(\Pdue)(\Ptre)}%
\Pbox(\Puno)[tl]{P_1}[1.5]%
\Pbox(\Pdue)[bl]{P_2}[1.5]\Pbox(\Ptre)[bc]{P_3}[1.5]
@@ -1809,8 +1872,8 @@
\begin{Esempio}[\setfontsize{6.5}](0.45)
\unitlength=0.008\linewidth
\begin{picture}(100,100)(0,-10)
-\GraphGrid(0,-10)(100,100)
-\def\Puno{0,0}\def\Pdue{0,80}\def\Ptre{100,60}
+\AutoGrid
+\def\Puno{0,0}\def\Pdue{0,80}\def\Ptre{100,55}
{\linethickness{0.6pt}\polygon(\Puno)(\Pdue)(\Ptre)}%
\Pbox(\Puno)[tl]{P_1}[1.5]%
\Pbox(\Pdue)[bl]{P_2}[1.5]\Pbox(\Ptre)[bc]{P_3}[1.5]
@@ -1831,8 +1894,8 @@
\begin{Esempio}[\setfontsize{6}](0.45)
\unitlength=0.008\linewidth
\begin{picture}(100,100)(0,-10)
-\GraphGrid(0,-10)(100,100)
-\def\Puno{0,0}\def\Pdue{0,80}\def\Ptre{100,60}
+\AutoGrid
+\def\Puno{0,0}\def\Pdue{0,80}\def\Ptre{100,55}
{\linethickness{0.6pt}%
\polygon(\Puno)(\Pdue)(\Ptre)}%
\Pbox(\Puno)[tl]{P_1}[1.5]%
@@ -1858,7 +1921,7 @@
\begin{Esempio}[\setfontsize{6.25}](0.45)
\unitlength=0.01\linewidth
\begin{picture}(100,110)
-\GraphGrid(100,110)
+\AutoGrid
\CopyVect20,10to\Pu \Pbox(\Pu)[t]{P_1}
\CopyVect10,90to\Pd \Pbox(\Pd)[br]{P_2}
\CopyVect100,70to\Pt \Pbox(\Pt)[l]{P_3}
@@ -1870,20 +1933,21 @@
\AddVect\Mu and\Du to\Du\Dotline(\Mu)(\Du){3}[2]
\AddVect\Md and\Dd to\Dd\Dotline(\Md)(\Dd){3}[2]
\AddVect\Mt and\Dt to\Dt\Dotline(\Mt)(\Dt){3}[2]
-\Pbox(\C)[t]{C}[2.5]
+\Pbox(\C)[l]{C}[3.5]
\ThreePointCircle*(\Pu)(\Pd)(\Pt)
-\end{picture}\end{Esempio}
+\end{picture}
+\end{Esempio}
\caption{Determination of the circumcenter and of the circumcircle}\label{fig:circumcenter}
\end{figure}
- Although these examples require some new simple macros, described
- in the previous sections; some more more examples can be made that require
- more complex macros. Even these macros are just examples. For other
- applications it is probably necessary to add even more macros.
+ These examples require some new simple macros, described in the previous
+ sections; some more more examples can be made that require more complex
+ macros. Even these macros are just examples. For other applications it is
+ probably necessary to add even more macros.
Let us proceed with the construction of the Steiner ellipse: given a
triangle, there exists only one ellipse that is internally tangent to
- the side middle points.
+ the side mid-points.
The geometrical construction goes on this way; suppose you have to draw
the Steiner ellipse of triangle $T$; finding the side middle points
@@ -1910,9 +1974,10 @@
\begin{Esempio}[\setfontsize{8}](0.5)
\unitlength=0.01\linewidth
\begin{picture}(100,110)
-\GraphGrid(100,110)%
+\AutoGrid
\SteinerEllipse(10,10)(90,20)(60,105)[2]
-\end{picture}\end{Esempio}
+\end{picture}
+\end{Esempio}
\caption{The Steiner ellipse of a given triangle}
\label{fig:Steiner-finale}
\end{figure}
@@ -1924,9 +1989,10 @@
\begin{Esempio}[\setfontsize{8}](0.5)
\unitlength=0.01\linewidth
\begin{picture}(100,110)(0,-10)
-\GraphGrid(0,-10)(100,110)%
+\AutoGrid
\SteinerEllipse*(10,10)(90,20)(60,105)[2]
-\end{picture}\end{Esempio}
+\end{picture}
+\end{Esempio}
\caption{The construction of the Steiner ellipse of a given triangle}
\label{fig:Steiner-intermedio}
\end{figure}
@@ -1934,10 +2000,13 @@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{The tangent to an ellipse}\label{ssec:diretriz}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-Ellipses have mani interesting properties. One that I was not able to find anywhere in the documentation I examined (of course not the totality of available on ellipses, except an on-line document written in Portuguese by Sergio Alvez, \url{https://docplayer.com.br/345411-Elipses-inscritas-num-triangulo.html}, is the \emph{director circumference}, literal translation of the Portuguese definition \emph{circunfência diretriz}.
+Ellipses have many interesting properties. One that I was not able to find anywhere in the documentation I examined (of course not the totality of available documents on ellipses) except an on-line document written in Portuguese by Sergio Alvez,
+\begin{flushleft}\setfontsize{10}%
+\url{https://docplayer.com.br/345411-Elipses-inscritas-num-triangulo.html}\end{flushleft}
+is the \emph{director circumference}, literal translation of the Portuguese definition \emph{circunfência diretriz}.
Consider an ellipse with its foci $F$ en $F'$, and a generic point $P$ on its contour.
-Trace a segment from $F\,P$ and another segment for $P\,F'$; these segments measure the distanced from point $P$ to each focus: their sum is the length of the main ellipse axis $2a$, being $a$ the semi axis. Now lengthen the segment $P\,F'$ to point $S$ by the length of $F\,P$; the length of $S\,F'$ is therefore equal to $2a$; now trace the circumference with center in $F'$ and radius $2a$; this is the \emph{director circumference}, that is labelled with~$\Gamma$.
+Trace a segment from $F\,P$ and another segment for $P\,F'$; these segments measure the distances from point $P$ to each focus: their sum is the length of the main ellipse axis $2a$, where $a$ is the semi axis. Now lengthen the segment $P\,F'$ to point $S$ by the length of $F\,P$; the length of $S\,F'$ is therefore equal to $2a$; now trace the circumference with center in $F'$ and radius $2a$; this is the \emph{director circumference}, that is labelled with~$\Gamma$.
By construction, then, the circle $\gamma$ centred in $F$ and radius equal to $F\,P$ is tangent to $\Gamma$ in $S$ and passes through $F$. This allows to say that:
\begin{itemize}[noitemsep]
@@ -1944,31 +2013,41 @@
\item the ellipse is the locus of the centres of all circles passing through focus $F$ and internally tangent to the circle $\Gamma$ centred in the other focus $F'$ and with radius $2a$;
\item the axis of segment $S\,F$ is tangent to the ellipse;
\item the tangency point is the point $P$;
-\item since this axis passes through the midpoint $M$ of segment $S\,F$ and it is perpendicular to it, the segment $M\,P$ has the same direction of the tangent to the ellipse;
+\item since this axis passes through the midpoint $M$ of segment $S\,F$ and it is perpendicular to it, the segment $M\,P$ determines the direction of the tangent to the ellipse;
\item notice that points $S$ and $F$ are symmetrical with respect to the tangent in point $P$.
\end{itemize}
Such properties can be viewed and controlled in figure~\ref{fig:diretriz}.
-\begin{figure}[!tb]\centering
+\begin{figure}[!tbp]\centering
\begin{Esempio}*[\setfontsize{8.2}](0.40)
\unitlength=0.005\linewidth
\begin{picture}(170,160)(-60,-80)
-\GraphGrid(-60,-80)(170,160)
+\AutoGrid
\VECTOR(0,-80)(0,80)\Pbox(0,80)[r]{y}[0]
\VECTOR(-60,0)(110,0)\Pbox(110,0)[t]{x}[0]
+% Ellipse with given semi axes
\edef\A{40}\edef\B{30}\Xellisse{\A}{\B}[\thicklines]
+% Point P on the ellipse
\edef\X{\fpeval{\A*cosd(120)}}\edef\Y{\fpeval{\B*sind(120)}}
\edef\P{\X,\Y}\Pbox(\P)[b]{P}[3]
-\edef\C{\fpeval{sqrt(\A**2-\B**2)}}% Inter focal semi distance
+% Foci coordinates
+\edef\C{\fpeval{sqrt(\A**2-\B**2)}}
\CopyVect-\C,0 to\F \CopyVect\C,0 to\Fp\Pbox(\Fp)[t]{F'}[3]
\Pbox(\F)[t]{F}[3]\Pbox(0,0)[tr]{O}[3]
-\edef\Raggio{\fpeval{2*\A}}\Circlewithcenter\Fp radius\Raggio
-\SegmentLength(\P)(\F)to\raggio\Circlewithcenter\P radius\raggio
+% Director circumference
+\edef\Raggio{\fpeval{2*\A}}
+\Circlewithcenter\Fp radius\Raggio \Pbox(80,60)[tr]{\ISOGamma{lmss}}[0]
+% Tangent construction
+\SegmentLength(\P)(\F)to\raggio
+\Circlewithcenter\P radius\raggio \Pbox(-10,50)[bl]{\ISOgamma{lmss}}[0]
\SegmentArg(\Fp)(\P)to\Arg\AddVect\Fp and\Arg:\Raggio to\S
\segment(\Fp)(\S)\Pbox(\S)[br]{S}[3]
\segment(\F)(\S)\SegmentCenter(\F)(\S)to\M
\Pbox(\M)[r]{M}[3]\SegmentArg(\F)(\S)to\Arg
-\edef\Arg{\fpeval{\Arg-90}}\AddVect\M and \Arg:50 to\D\segment(\M)(\D)
+% Tangent
+\edef\Arg{\fpeval{\Arg-90}}
+\AddVect\M and \Arg:50 to\D \Pbox(\D)[l]{D}[3]
+\segment(\M)(\D)
\end{picture}
\end{Esempio}
\caption{The director circumference}\label{fig:diretriz}
@@ -1982,7 +2061,7 @@
It is possible to draw an ellipse that is internally tangent to
a triangle if one of its foci is specified; without this specification
- the problem is not definite, and the number o such ellipses is countless.
+ the problem is not definite, and the number of such ellipses is countless.
But with the focus specification, just one ellipse exists with that
tangency constraint. It suffices to find the other focus and at least
one point of tangency, because the focal distance and the sum of
@@ -1989,16 +2068,17 @@
distances of that tangency point from the foci, is sufficient to
determine all the parameters required to draw the ellipse.
- As seen in the previous subsection~\ref{ssec:diretriz}, it is sufficient to find the threes symmetrical point of The given focus with respect to to the three sides, i.e. the three lines that pass through the triangle vertices; and the constructions gives simultaneously the major axis length and the three tangency points, therefore all the elements required to draw the ellipse. to draw
+ As seen in the previous subsection~\ref{ssec:diretriz}, it is sufficient to find the three symmetrical points of the given focus with respect to the three sides, i.e. the three lines that pass through the triangle vertices; and the constructions gives simultaneously the major axis length and the three tangency points, therefore all the elements required to draw the ellipse to be drawn.
\begin{figure}[!tb]\centering
\begin{Esempio}[\setfontsize{7}](0.375)
\unitlength=0.0065\linewidth
\begin{picture}(150,150)(-30,-20)
-\GraphGrid(-30,-20)(150,150)
+\AutoGrid
\EllipseWithFocus%
(10,40)(110,10)(0,110)(20,60)
-\end{picture}\end{Esempio}
+\end{picture}
+\end{Esempio}
\caption{An ellipse internally tangent to a triangle, given a focus}
\label{fig:ellisse-interna-finale}
\end{figure}
@@ -2007,22 +2087,23 @@
\begin{Esempio}[\setfontsize{7}](0.375)
\unitlength0.0065\linewidth
\begin{picture}(150,150)(-30,-20)
-\GraphGrid(-30,-20)(150,150)
+\AutoGrid
\EllipseWithFocus*%
(10,40)(110,10)(0,110)(20,60)
-\end{picture}\end{Esempio}
+\end{picture}
+\end{Esempio}
\caption{Construction of the ellipse of figure~\ref{fig:ellisse-interna-finale}}\label{fig:ellisse-interna}
\end{figure}
- The geometrical construction with help of what has been explained in
- subsection~\ref{ssub:diretriz} is easy; the steps to follow, therefore
+ The geometrical construction, with help of what has been explained in
+ subsection~\ref{ssec:diretriz}, is easy; the steps to follow, therefore
are the following:\enlargethispage*{\baselineskip}
\begin{itemize}[noitemsep]
\item draw the triangle and the given focus $\mathsf{F}$;
-\item Find the symmetrical points $\mathsf S_i$ of this
+\item find the symmetrical points $\mathsf S_i$ of this
focus with respect to the sides of the triangle;
\item use these three points $\mathsf S_i$ as the vertices of a triangle
@@ -2035,7 +2116,7 @@
with the triangle sides; they represent the tangency points of the
ellipse to be drawn;
-\item the radius of the director circumference is the ellipse major axix;
+\item the radius of the director circumference is the ellipse major axis;
\item equation~\eqref{equ:axes-foci} allows to find the second axis
length; the segment that joins the foci has the required inclination
@@ -2068,8 +2149,8 @@
difficult the problem, the greater the satisfaction in solving it.
-\begin{center}
- Have fun with \LaTeX and its potential applications!
+\begin{center}\bfseries
+ Have fun with \LaTeX and its possible applications!
\end{center}
\end{document}
\ No newline at end of file
Modified: trunk/Master/texmf-dist/doc/latex/euclideangeometry/euclideangeometry.pdf
===================================================================
(Binary files differ)
Modified: trunk/Master/texmf-dist/source/latex/euclideangeometry/euclideangeometry.dtx
===================================================================
--- trunk/Master/texmf-dist/source/latex/euclideangeometry/euclideangeometry.dtx 2021-05-17 20:44:18 UTC (rev 59245)
+++ trunk/Master/texmf-dist/source/latex/euclideangeometry/euclideangeometry.dtx 2021-05-17 20:44:32 UTC (rev 59246)
@@ -6,30 +6,18 @@
\keepsilent
\preamble
- Copyright (C) 2020 Claudio Beccari all rights reserved.
- License information appended
+ Copyright (C) 2020-2021 Claudio Beccari all rights reserved.
+ 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
+
\endpreamble
-\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
-
-This work is "maintained"
-
-This work consists of files:
-1) euclideangeometry.dtx, and the derived files euclideangeometry.sty
- and euclideangeometry.pdf,
-2) euclideangeometry-man.tex and the derived file euclideangeometry-man.pdf,
-3) the auxiliary derived file README.txt
-
-\endpostamble
\askforoverwritefalse
\generate{\file{euclideangeometry.sty}{\from{euclideangeometry.dtx}{package}}}
-\generate{\file{README.txt}{\from{euclideangeometry.dtx}{readme}}}
+%\generate{\file{README.txt}{\from{euclideangeometry.dtx}{readme}}}
\def\tmpa{plain}
\ifx\tmpa\fmtname\endgroup\expandafter\bye\fi
@@ -45,7 +33,7 @@
%<package>\ProvidesPackage{euclideangeometry}%
%<readme>File README.txt for package euclideangeometry
%<*package|readme>
- [2020-04-15 v.0.1.8 Extension package for curve2e]
+ [2021-05-016 v.0.2.0 Extension package for curve2e]
%</package|readme>
%<*driver>
\documentclass{ltxdoc}\errorcontextlines=100
@@ -93,7 +81,9 @@
\fontfamily{lmr}\fontseries{m}\fontshape{sc}\selectfont
g\raisebox{-0.715ex}{\kern-0.26em u}\kern-0.13em\I\kern-0.14em t}\xspace}
\RequirePackage{etoolbox}
+
\makeatletter
+
\AfterEndPreamble{%
\DeclareRobustCommand{\TeX}{T\kern-.1667em
\lower.5ex\hbox{E}\kern-.125emX\@\xspace}
@@ -108,6 +98,7 @@
\kern-.15em%
\TeX}}
\makeatother
+
\DeclareRobustCommand*\TeXLive{\TeX\ Live\xspace}
\DeclareRobustCommand*\MikTeX{Mik\TeX}
\DeclareRobustCommand*\MacTeX{Mac\TeX}
@@ -130,6 +121,7 @@
\IfValueTF{#2}{\put(#1){\originalGraphGrid(#2)}}%
{\put(0,0){\originalGraphGrid(#1)}}}\fi
+
\begin{document}\errorcontextlines=100
\GetFileInfo{euclideangeometry.dtx}
\title{The \textsf{euclideangeometry} package}
@@ -154,7 +146,7 @@
% installed with your updated complete \TeX system installation.
% Please refer to the user manual before using this package.
-% \CheckSum{1296}
+% \CheckSum{1294}
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\StopEventually{}
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -167,7 +159,7 @@
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% \subsection{Checking the date of a sufficiently recent \texttt{curve2e}
+% \subsection{Test the date of a sufficiently recent \texttt{curve2e}
% package}
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% This package has been already identified by the commands extracted
@@ -175,7 +167,7 @@
% In any case, if the test checks that the |curve2e| file date is too old;
% it warns the user with an emphasised error message on the console,
% loading this |euclideangeometry| package is stopped and the whole
-% job aborts. The emphasised error message appears like this:
+% job aborts. The emphasised error message appears like this:\\~
%\begin{flushleft}\ttfamily\obeylines
%*************************************************************
%Package curve2e too old
@@ -205,10 +197,10 @@
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% While doing any graphical geometrical drawing it is necessary to label
-% points, lines, angles and other such items. Non measurable labels should
-% be in upright sans serif font, according to the ISO regulations, but here
-% we are dealing witt point identified by macros the contain their
-% (cartesian or polar) coordinates that very often are both labels
+% points, lines, angles and other such items. Non measurable labels
+% should be in upright sans serif font, according to the ISO regulations,
+% but here we are dealing with point identified by macros the contain
+% their (cartesian or polar) coordinates that very often are both labels
% and math variables.
%
% Here we provide a versatile macro that can do several things. Its name
@@ -228,20 +220,21 @@
% incoherent, as well as \texttt{lr}), but in absence of this optional
% specification, the couple \texttt{cc} is assumed; most often than
% not, the label position becomes such that when the user reviews the
-% document drafts, s/he understands immediately that s/he forgot to specify
-% some reasonable \meta{alignment} codes; in any case the \texttt{cc} code
-% works fine to just put the dot of a specified diameter but with an empty
-% label. Think of the \meta{alignment}
+% document drafts, s/he understands immediately that s/he forgot to
+% specify some reasonable \meta{alignment} codes; in any case the
+% \texttt{cc} code works fine to just put the dot of a specified
+% diameter but with an empty label. Think of the \meta{alignment}
% letters as the position of the reference point with respect to the
% the \meta{label} optical center. The optional \meta{angle} argument
% produces a rotation of the whole label by that angle; it may be used
% in several circumstances, especially when the label is just text, to
% produce, for example, a sideways legend. It is useful also when the
-% labels are produced within a rotated box, in order to counterrotate them.
+% labels are produced within a rotated box, in order to counterrotate
+% them.
%
-% The optional asterisk draws a frame around the \emph{label}. Notice that
-% the separator between the visible or the invisible frame and the box
-% contents varies according the the fact that the \meta{alignment}
+% The optional asterisk draws a frame around the \emph{label}. Notice
+% that the separator between the visible or the invisible frame and the
+% box contents varies according the the fact that the \meta{alignment}
% specification contains just one or two letter codes; this is useful,
% because the diagonal position of the label should be optically equal
% to the gap that exists between the reference point and the \meta{label}
@@ -264,7 +257,6 @@
% a sloping line.
% \begin{macrocode}
\providecommand\Pbox{}
-\newlength\PbDim
\RenewDocumentCommand\Pbox{D(){0,0} O{cc} m O{0.5ex} s D<>{0}}{%
\put(#1){\rotatebox{#6}{\makebox(0,0){%
\settowidth\PbDim{#2}%
@@ -296,11 +288,11 @@
% fonts; with Type~1 fonts the only scalable fonts I know of, are the
% LibertinusMath fonts, usable through the LibertinusT1math package, are
% also the only ones that have 8~bit encoded math fonts (256
-% glyph fonts), while the standard default Type~1 math fonts are just
+% glyph fonts), while the standard default math fonts are just
% 7~bit encoded (128 glyphs fonts).
%
% Another useful labelling command is |Zbox|; this command is an
-% evolution of a command that I been using for years in several
+% evolution of a command that I have been using for years in several
% documents of mine. It uses some general text, not necessarily
% connected to a particular point of the |picture| environment,
% as a legend; It can draw short text as a simple horizontal box,
@@ -310,7 +302,7 @@
%\begin{ttsyntax}
%\cs{Zbox}\parg{position}\parg(dimensions)\oarg{alignment}\marg{text}
%\end{ttsyntax}
-% where \meta{position} is where the reference point of the box has
+% where \meta{position} is where the box reference point has
% to be put in the picture; \meta{dimensions} are optional; if not
% specified, the box is a horizontal one, and it is as wide as its
% contents; if it is specified, it must be a comma separated list
@@ -753,7 +745,7 @@
\edef\TCIdiffR{\fpeval{\Runo-\Rdue}}\edef\TCIsumR{\fpeval{\Runo+\Rdue}}
\fptest{\TCIdiffR > \A || \A > \TCIsumR}{%
\edef#5{0,0}\edef#6{0,0}% Valori assurdi se i cerchi non si intersecano
- \PackageWarning{TestFP}{%
+ \PackageWarning{euclideangeometry}{%
***********************************\MessageBreak
Circles do not intersect \MessageBreak
Check centers and radii and retry \MessageBreak
@@ -1513,65 +1505,27 @@
% document |euclideangeometry-man.pdf| describes much clearly with
% examples what you can do with the macros described in this package.
% In facts, this file just describes the package macros, and it gives
-% some ideas on how to extend the ability of |curve2e| to draw geometrical
-% diagrams.
+% some ideas on how to extend the ability of |curve2e| to draw
+% geometrical diagrams.
% The users who would like to modify or to add some functionalities
% are invited to do so; I will certainly acknowledge their contributions
% and even add their names to the list of authors.
%
-% As long as I can, I enjoy playing with \LaTeX and its wonderful
+% As long as I can, I enjoy playing with \LaTeX\ and its wonderful
% facilities; but, taking into consideration my age, I would invite
% the users to consider the possibility of assuming the maintenance
% of this package.
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%\section*{Aknowledgements}
+%\section{Acknowledgements}
%^^A%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% I am very grateful to Enrico Gregorio who let me know the several
% glitches I made in my first version; besides being a real \TeX wizard,
% he is a wise person and suggested me several things that was important
-% to change, because they could offer risks of confusion with other packages.
+% to change, because they could offer risks of confusion with other
+% packages.
%
%\iffalse
%</package>
%\fi
-%
-%\iffalse
-%<*readme>
-%^^A\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.
-% \begin{macrocode}
-The package bundle euclideangeometry is composed of the following files
-
-euclideangeometry.dtx
-euclideangeometry.pdf
-euclideangeometry-man.tex
-euclideangeometry-man.pdf
-README.txt
-
-euclideangeometry.dtx is the documented TeX source file of package
-euclideangeometry.sty; you get euclideangeometry.sty,
-euclideangeometry.pdf by running pdflatex on euclideangeometry.dtx.
-
-README.txt, this file, contains general information.
-
-euclideangeometry-man.tex and euclideangeometry-man.pdf are
-the source file and the readable document containing the end
-user manual.
-In other words euclideangeometry.pdf is oriented towards the
-developers and euclideangeometry-man.pdf to the end users.
-
-
-Claudio Beccari
-
-claudio dot beccari at gmail dot com
-% \end{macrocode}
-%^^A\iffalse
-%</readme>
-%\fi
% \Finale
-%^^A <driver>\endinput
+%
\ No newline at end of file
Modified: trunk/Master/texmf-dist/tex/latex/euclideangeometry/euclideangeometry.sty
===================================================================
--- trunk/Master/texmf-dist/tex/latex/euclideangeometry/euclideangeometry.sty 2021-05-17 20:44:18 UTC (rev 59245)
+++ trunk/Master/texmf-dist/tex/latex/euclideangeometry/euclideangeometry.sty 2021-05-17 20:44:32 UTC (rev 59246)
@@ -6,12 +6,15 @@
%%
%% euclideangeometry.dtx (with options: `package')
%%
-%% Copyright (C) 2020 Claudio Beccari all rights reserved.
-%% License information appended
+%% Copyright (C) 2020-2021 Claudio Beccari all rights reserved.
%%
+%% 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
+%%
\NeedsTeXFormat{LaTeX2e}[2019/01/01]
\ProvidesPackage{euclideangeometry}%
- [2020-04-15 v.0.1.8 Extension package for curve2e]
+ [2021-05-016 v.0.2.0 Extension package for curve2e]
\RequirePackage{curve2e}
\@ifpackagelater{curve2e}{2020/01/18}{}%
@@ -26,7 +29,6 @@
}%
\providecommand\Pbox{}
-\newlength\PbDim
\RenewDocumentCommand\Pbox{D(){0,0} O{cc} m O{0.5ex} s D<>{0}}{%
\put(#1){\rotatebox{#6}{\makebox(0,0){%
\settowidth\PbDim{#2}%
@@ -168,7 +170,7 @@
\edef\TCIdiffR{\fpeval{\Runo-\Rdue}}\edef\TCIsumR{\fpeval{\Runo+\Rdue}}
\fptest{\TCIdiffR > \A || \A > \TCIsumR}{%
\edef#5{0,0}\edef#6{0,0}% Valori assurdi se i cerchi non si intersecano
- \PackageWarning{TestFP}{%
+ \PackageWarning{euclideangeometry}{%
***********************************\MessageBreak
Circles do not intersect \MessageBreak
Check centers and radii and retry \MessageBreak
@@ -423,18 +425,6 @@
\VECTOR(0,-20)(0,130)\Pbox(0,130)[r]{y}[0]\Pbox(0,0)[tr]{O}[1.5pt]
\egroup\ignorespaces}
\let\EllisseConFuoco\EllipseWithFocus
-%%
-%% 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 files:
-%% 1) euclideangeometry.dtx, and the derived files euclideangeometry.sty
-%% and euclideangeometry.pdf,
-%% 2) euclideangeometry-man.tex and the derived file euclideangeometry-man.pdf,
-%% 3) the auxiliary derived file README.txt
-%%
+\endinput
%%
%% End of file `euclideangeometry.sty'.
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