texlive[61944] Master/texmf-dist: fiziko (8feb22)
commits+karl at tug.org
commits+karl at tug.org
Tue Feb 8 22:49:28 CET 2022
Revision: 61944
http://tug.org/svn/texlive?view=revision&revision=61944
Author: karl
Date: 2022-02-08 22:49:28 +0100 (Tue, 08 Feb 2022)
Log Message:
-----------
fiziko (8feb22)
Modified Paths:
--------------
trunk/Master/texmf-dist/doc/metapost/fiziko/README
trunk/Master/texmf-dist/doc/metapost/fiziko/fiziko.pdf
trunk/Master/texmf-dist/doc/metapost/fiziko/fiziko.tex
trunk/Master/texmf-dist/metapost/fiziko/fiziko.mp
Modified: trunk/Master/texmf-dist/doc/metapost/fiziko/README
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/fiziko/README 2022-02-08 21:49:10 UTC (rev 61943)
+++ trunk/Master/texmf-dist/doc/metapost/fiziko/README 2022-02-08 21:49:28 UTC (rev 61944)
@@ -1,5 +1,5 @@
Name: fiziko
-Version: 0.1.3
+Version: 0.2.0
License: GNU GPLv3 or later
Author: Sergey Slyusarev
Repository: https://github.com/jemmybutton/fiziko
Modified: trunk/Master/texmf-dist/doc/metapost/fiziko/fiziko.pdf
===================================================================
(Binary files differ)
Modified: trunk/Master/texmf-dist/doc/metapost/fiziko/fiziko.tex
===================================================================
--- trunk/Master/texmf-dist/doc/metapost/fiziko/fiziko.tex 2022-02-08 21:49:10 UTC (rev 61943)
+++ trunk/Master/texmf-dist/doc/metapost/fiziko/fiziko.tex 2022-02-08 21:49:28 UTC (rev 61944)
@@ -1,10 +1,9 @@
-\documentclass{article}
+\documentclass{ltxdoc}
-\usepackage{luamplib}
+\usepackage{luamplib, listings, bxtexlogo, ccicons}
\everymplib{verbatimtex \leavevmode etex; input fiziko.mp; beginfig(1);}
\everyendmplib{endfig;}
-\usepackage{listings}
\lstset{
language=MetaPost,
numbers=left,
@@ -12,16 +11,14 @@
basicstyle=\scriptsize
}
-\usepackage{cclicenses}
-
\author{Sergey Slyusarev}
-\title{``fiziko'' v. 0.1.3 package for MetaPost}
+\title{``fiziko'' v. 0.2.0 package for \METAPOST}
\begin{document}
\maketitle
\begin{abstract}
-This document describes a bunch of macros provided by ``fiziko'' library for MetaPost.
+This document describes a bunch of macros provided by ``fiziko'' library for \METAPOST.
\end{abstract}
\begin{centering}
@@ -28,7 +25,7 @@
This document is distributed under CC-BY-SA 4.0 license
-\cc\bysa
+\ccbysa
https://github.com/jemmybutton/fiziko
@@ -35,10 +32,10 @@
\end{centering}
\section{Introduction}
-This MetaPost library was initially written to automate some elements of black and white illustrations for a physics textbook. First and foremost it provides functions to draw things like lines of variable width, shaded spheres and tubes of different kinds, which can be used to produce images of a variety of objects. The library also contains functions to draw some objects constructed from these primitives.
+This \METAPOST\ library was initially written to automate some elements of black and white illustrations for a physics textbook. First and foremost it provides functions to draw things like lines of variable width, shaded spheres and tubes of different kinds, which can be used to produce images of a variety of objects. The library also contains functions to draw some objects constructed from these primitives.
\section{Usage}
-Simply include this in the beginning of your MetaPost document:
+Simply include this in the beginning of your \METAPOST\ document:
\begin{lstlisting}
input fiziko.mp
@@ -113,12 +110,27 @@
endfor;
\end{mplibcode}
-\subsection{sphere.l (\emph{diameter, angle})}
+\subsection{sphere.s (\emph{diameter})}
+This macro returns a \texttt{picture} of a sphere with specified diameter shaded with stipples.
+
+\begin{lstlisting}
+ for i := 1 step 1 until 6:
+ draw sphere.s(i*1/4cm) shifted (1/2cm*(i*(i+1))/2, 0);
+ endfor;
+\end{lstlisting}
+
+\begin{mplibcode}
+ for i := 1 step 1 until 6:
+ draw sphere.s(i*1/4cm) shifted (1/2cm*(i*(i+1))/2, 0);
+ endfor;
+\end{mplibcode}
+
+\subsection{sphereLat (\emph{diameter, angle})}
This macro returns a \texttt{picture} of a shaded sphere with specified diameter. Unlike \texttt{sphere.c} macro, this one draws latitudinal strokes around axis rotated at specified \texttt{angle}.
\begin{lstlisting}
for i := 1 step 1 until 6:
- draw sphere.l(i*1/4cm, -90 + i*30)
+ draw sphereLat(i*1/4cm, -90 + i*30)
shifted (1/2cm*(i*(i+1))/2, 0);
endfor;
\end{lstlisting}
@@ -125,7 +137,7 @@
\begin{mplibcode}
for i := 1 step 1 until 6:
- draw sphere.l(i*1/4cm, -90 + i*30)
+ draw sphereLat(i*1/4cm, -90 + i*30)
shifted (1/2cm*(i*(i+1))/2, 0);
endfor;
\end{mplibcode}
@@ -160,6 +172,21 @@
draw tube.t (p)(1/2cm*sin(offsetPathLength*pi));
\end{mplibcode}
+\subsection{tube.s (\emph{path})(\emph{offset function})}
+This macro returns a \texttt{picture} of a shaded ``tube'' of variable width along given path, which is controlled by some arbitrary function, analogous to \texttt{offsetPath}. ``Tube'' drawn by this macro is shaded with stipples. Once tube is generated, you can call \texttt{tubeOutline} path global variable, if you need one.
+
+\begin{lstlisting}
+ path p;
+ p := (0,0){dir(30)}..(5cm, 0)..{dir(30)}(10cm, 0);
+ draw tube.s (p)(1/2cm*sin(offsetPathLength*pi));
+\end{lstlisting}
+
+\begin{mplibcode}
+ path p;
+ p := (0,0){dir(30)}..(5cm, 0)..{dir(30)}(10cm, 0);
+ draw tube.s (p)(1/2cm*sin(offsetPathLength*pi));
+\end{mplibcode}
+
\subsection{tube.e (\emph{path})(\emph{offset function})}
This macro returns the outline of a tube as a path.
@@ -200,7 +227,7 @@
endfor;
\end{lstlisting}
-\begin{mplibcode}
+\noindent\begin{mplibcode}
draw (-1/8cm, 0)--(12cm, 0);
for i := 1 step 1 until 6:
r := 1/7cm*i;
@@ -248,7 +275,8 @@
endfor;
\end{lstlisting}
-\begin{mplibcode}
+
+\noindent\begin{mplibcode}
draw (-1/8cm, 0)--(12cm, 0);
for i := 1 step 1 until 6:
r := 1/7cm*i;
@@ -267,7 +295,7 @@
draw (-1/8cm, 0)--(12cm, 0);
\end{lstlisting}
-\begin{mplibcode}
+\noindent\begin{mplibcode}
for i := 1 step 1 until 6:
draw weight.s(1/4cm + i*1/4cm) shifted (1/2cm*(i*(i+1))/2, 0);
endfor;
@@ -284,7 +312,7 @@
draw (12cm, 0)--(-1/8cm, 0);
\end{lstlisting}
-\begin{mplibcode}
+\noindent\begin{mplibcode}
for i := 1 step 1 until 6:
draw weight.h(1/4cm + i*1/4cm) shifted (1/2cm*(i*(i+1))/2, 0);
endfor;
@@ -333,6 +361,22 @@
\subsection{solid (\emph{path, angle, type})}
Fills given \texttt{path} with strokes of specific type at a given \texttt{angle}. \texttt{type} can be 0 (``solid'' strokes) and 1 (``glass'' strokes).
+\begin{lstlisting}
+ path p[];
+ p1 := unitsquare scaled 2cm;
+ p2 := p1 shifted (4cm, 0);
+ draw solid(p1, 45, 0);
+ draw solid(p2, -45, 1);
+\end{lstlisting}
+
+\begin{mplibcode}
+ path p[];
+ p1 := unitsquare scaled 2cm;
+ p2 := p1 shifted (4cm, 0);
+ draw solid(p1, 45, 0);
+ draw solid(p2, -45, 1);
+\end{mplibcode}
+
\subsection{woodBlock (\emph{width, height})}
Returns a \texttt{picture} of a rectangular block of wood with its bottom-left corner in the origin.
@@ -383,7 +427,7 @@
\end{mplibcode}
\subsection{Knots}
-There are two macros to handle knot drawing: \texttt{addStrandToKnot} and \texttt{knotFromStrands}. Currently the algorithm is not especially stable.
+There are two macros to handle knot drawing: \texttt{addStrandToKnot} and \texttt{knot\-From\-Strands}. Currently the algorithm is not especially stable.
\subsubsection{addStrandToKnot (\emph{knotName}) (\emph{path, ropeWidth, ropeType, intersectionOrder})}
This macro adds a strand to knot named \texttt{knotName} and returns nothing. Strand follows the given \texttt{path} and has a given \texttt{ropeWidth}. \texttt{ropeType} can be \texttt{"l"}, \texttt{"t"} (as in \texttt{tube.l} and \texttt{tube.t}) or \texttt{"e"} (for an unshaded strand). \texttt{intersectionOrder} is a string of comma separated numbers which represent a ``layer'' to which intersections along the strand go.
@@ -401,15 +445,15 @@
p3 := (fullcircle scaled 4cm);
addStrandToKnot (theknot) (p1 shifted (4cm, -4cm), 1/5cm, "l",
"-1,1,-1,1,-1,1,-1,1,-1");
- addStrandToKnot (theknot) (p2 shifted (4cm, -4cm), 1/6cm, "l",
+ addStrandToKnot (theknot) (p2 shifted (4cm, -4cm), 1/6cm, "s",
"");
- addStrandToKnot (theknot) (p3 shifted (4cm, -4cm), 1/7cm, "l",
+ addStrandToKnot (theknot) (p3 shifted (4cm, -4cm), 1/7cm, "e",
"-1,1");
draw knotFromStrands (theknot);
\end{lstlisting}
\begin{mplibcode}
- path p[]; path p[];
+ path p[];
p1 := (dir(90)*4/3cm) {dir(0)} .. tension 3/2
.. (dir(90 + 120)*4/3cm){dir(90 + 30)} .. tension 3/2
.. (dir(90 - 120)*4/3cm){dir(-90 - 30)} .. tension 3/2
@@ -418,13 +462,28 @@
p3 := (fullcircle scaled 4cm);
addStrandToKnot (theknot) (p1 shifted (4cm, -4cm), 1/5cm, "l",
"-1,1,-1,1,-1,1,-1,1,-1");
- addStrandToKnot (theknot) (p2 shifted (4cm, -4cm), 1/6cm, "l",
+ addStrandToKnot (theknot) (p2 shifted (4cm, -4cm), 1/6cm, "s",
"");
- addStrandToKnot (theknot) (p3 shifted (4cm, -4cm), 1/7cm, "l",
+ addStrandToKnot (theknot) (p3 shifted (4cm, -4cm), 1/7cm, "e",
"-1,1");
draw knotFromStrands (theknot);
\end{mplibcode}
+\subsection{Other 3D contraptions}
+Some macros can be used to shade 3D polygons. Currently only flat surfaces re supported
+
+\subsubsection{flatSurface\emph{\#@}(\emph{surface outline path, normal vector, hatch angle})}
+This macro returns a \texttt{picture} of a flat surface with the specified \texttt{surface outline path} with the given \texttt{normal vector}, illuminated from the direction determined by \texttt{lightDirection} and with hatches aligned at the andle \texttt{hatch angle}. If \texttt{\#@} is \texttt{".hatches"} then the surface is shaded with hatches, if it's \texttt{".stipples"}, then the surface is shaded with stipples.
+
+\begin{mplibcode}
+ path p[];
+ p1 := unitsquare xscaled 1cm yscaled 2cm;
+ p2 := p1 shifted (1cm, 0);
+ draw flatSurface.hatches(p1, (-1,0,1), 45);
+ draw flatSurface.hatches(p2, (1,0,1), 45);
+draw p1; draw p2;
+\end{mplibcode}
+
\section{Other macros}
Some macros that are not directly related to drawing are listed below
@@ -473,10 +532,10 @@
Some macros that not related to physical problems at all are listed below.
\subsection{\emph{picture} maskedWith \emph{path}}
-This macro masks a part of a \texttt{picture} with closed \texttt{path}. In fact this is inversion of metapost's built-in \texttt{clip} but, in contrast to the latter, it does not modify original image. Note that it requires that counter-clockwise \texttt{path} to work properly.
+This macro masks a part of a \texttt{picture} with closed \texttt{path}. In fact this is inversion of \METAPOST's built-in \texttt{clip} but, in contrast to the latter, it does not modify original image. Note that it requires that counter-clockwise \texttt{path} to work properly.
\subsection{\emph{path} firstIntersectionTimes \emph{path}}
-This macro is similar to metapost's \texttt{intersectiontimes} but it returns intersection times with smallest time on first path.
+This macro is similar to \METAPOST's \texttt{intersectiontimes} but it returns intersection times with smallest time on first path.
\subsection{pathSubdivide \emph{path, n}}
This macro returns original \texttt{path} with \texttt{n}-times more points.
@@ -824,7 +883,7 @@
.. (-4/3cm, 0) .. (-1/2cm, -2/3cm) .. (1/2cm, 0)
.. (-1/2cm, 3/2cm) .. cycle;
p2 := p2 scaled 6/5;
- addStrandToKnot (primeTwo) (p2, 1/4cm, "l", "1, -1, 1, -1, 1");
+ addStrandToKnot (primeTwo) (p2, 1/4cm, "s", "1, -1, 1, -1, 1");
draw knotFromStrands (primeTwo) shifted (4cm, -2cm);
p3 := (dir(0)*3/2cm) .. (dir(1*72)*2/3cm)
.. (dir(2*72)*3/2cm) .. (dir(3*72)*2/3cm)
@@ -833,7 +892,7 @@
.. (dir(3*72)*3/2cm) .. (dir(4*72)*2/3cm)
.. cycle;
p3 := (p3 rotated (72/4)) scaled 6/5;
- addStrandToKnot (primeThree) (p3, 1/4cm, "l", "-1, 1, -1, 1, -1");
+ addStrandToKnot (primeThree) (p3, 1/4cm, "e", "-1, 1, -1, 1, -1");
draw knotFromStrands (primeThree) shifted (8cm, 0);
\end{mplibcode}
Modified: trunk/Master/texmf-dist/metapost/fiziko/fiziko.mp
===================================================================
--- trunk/Master/texmf-dist/metapost/fiziko/fiziko.mp 2022-02-08 21:49:10 UTC (rev 61943)
+++ trunk/Master/texmf-dist/metapost/fiziko/fiziko.mp 2022-02-08 21:49:28 UTC (rev 61944)
@@ -1,6 +1,6 @@
-% fiziko 0.1.3
+% fiziko 0.2.0
% MetaPost library for physics textbook illustrations
-% Copyright 2019 Sergey Slyusarev
+% Copyright 2022 Sergey Slyusarev
%
% This program is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
@@ -63,7 +63,7 @@
primarydef i maskedWith p =
begingroup
- save q, invertedmask, resultimage;
+ save q, invertedmask, resultimage, breakpoint;
pair q[];
path invertedmask;
picture resultimage;
@@ -72,8 +72,8 @@
q3 := lrcorner(i) shifted (1, -1);
q2 := (xpart(q3), ypart(q1));
q4 := (xpart(q1), ypart(q3));
- bp := ypart((ulcorner(p)--llcorner(p)) firstIntersectionTimes p);
- invertedmask := (subpath (bp, length(p) + bp) of p) -- q1 -- q2 -- q3 -- q4 -- q1 -- cycle;
+ breakpoint := ypart((ulcorner(p)--llcorner(p)) firstIntersectionTimes p);
+ invertedmask := (subpath (breakpoint, length(p) + breakpoint) of p) -- q1 -- q2 -- q3 -- q4 -- q1 -- cycle;
clip resultimage to invertedmask;
resultimage
endgroup
@@ -128,7 +128,33 @@
endgroup
enddef;
+% rotation in radians
+
+primarydef somethingToRotate radRotated radAngle =
+ somethingToRotate rotated ((radAngle/pi)*180)
+enddef;
+
%
+% some 3D stuff
+%
+
+% this one's from byrne.mp
+
+primarydef colorone dotprodXYZ colortwo =
+begingroup
+ save xp, yp, zp;
+ numeric xp[], yp[], zp[];
+ xp1 := (redpart colorone);
+ yp1 := (greenpart colorone);
+ zp1 := (bluepart colorone);
+ xp2 := (redpart colortwo);
+ yp2 := (greenpart colortwo);
+ zp2 := (bluepart colortwo);
+ xp1*xp2 + yp1*yp2 + zp1*zp2
+endgroup
+enddef;
+
+%
% sometimes it's useful to put some arrows along the path. this macro puts them
% in the middles of the segments that have length no less than midArrowLimit;
%
@@ -188,7 +214,7 @@
% We don't want to display strokes that are too thin to print. Default value
% is subject to change when needed.
minStrokeWidth := msw;
- maxShadingStrokeWidth := 2minStrokeWidth;
+ maxShadingStrokeWidth := 3/2minStrokeWidth;
% At some point it's useless to display even dashes
minDashStrokeWidth := 1/3minStrokeWidth;
@@ -201,12 +227,18 @@
% all the shading algorithms need to know how close lines should be packed
shadingDensity := 3maxShadingStrokeWidth;
+ stippleSize := 3/2minStrokeWidth;
+ minStippleStep := 1/2stippleSize;
+ stippleShadingDensity := 3minStippleStep;
+ minStippleStrokeWidth := 1/20stippleSize;
+
% here are some pens
- pen thinpen, thickpen, fatpen;
+ pen thinpen, thickpen, fatpen, stipplepen;
thinpen := pencircle scaled minStrokeWidth;
thickpen := pencircle scaled 3minStrokeWidth;
fatpen := pencircle scaled 6minStrokeWidth;
+ stipplepen := pencircle scaled stippleSize;
enddef;
defineMinStrokeWidth(1/5pt);
@@ -214,11 +246,33 @@
% here we set global light direction
def defineLightDirection (expr ldx, ldy) =
- pair lightDirection, lightDirectionVector;
+ pair lightDirection;
+ color lightDirectionVectorXYZ;
lightDirection := (ldx, ldy);
- lightDirectionVector := (sin(xpart(lightDirection)), sin(ypart(lightDirection)));
+ lightDirectionVectorXYZ := (0, 0, 1);
+ lightDirectionVectorXYZ := rotateXYZaround.x(lightDirectionVectorXYZ, ldy);
+ lightDirectionVectorXYZ := rotateXYZaround.y(lightDirectionVectorXYZ, ldx);
enddef;
+vardef rotateXYZaround@# (expr p, a) =
+ save partProj, rv;
+ pair partProj;
+ color rv;
+ if str @# = "x":
+ partProj := (greenpart(p), bluepart(p)) radRotated -a;
+ rv := (redpart(p), xpart(partProj), ypart(partProj));
+ elseif str @# = "y":
+ partProj := (redpart(p), bluepart(p)) radRotated -a;
+ rv := (xpart(partProj), greenpart(p), ypart(partProj));
+ elseif str @# = "z":
+ partProj := (redpart(p), greenpart(p)) radRotated -a;
+ rv := (xpart(partProj), ypart(partProj), bluepart(p));
+ else:
+ errmessage("What axis is " & str @# & "?");
+ fi;
+ rv
+enddef;
+
defineLightDirection(-1/8pi, 1/8pi);
boolean shadowsEnabled;
@@ -373,9 +427,9 @@
def brushGenerate (expr p, q, i) =
begingroup
- save w, bp, bt, t;
+ save w, brushPath, bt, t;
numeric w[], t[];
- path bp[], bt;
+ path brushPath[], bt;
bt := q;
w0 := (ypart(urcorner(bt)));
w1 := (ypart(lrcorner(bt)));
@@ -391,9 +445,9 @@
elseif (arclength(p) > 0):
if (w0 > 99/100minStrokeWidth)
and (w1 > 99/100minStrokeWidth):
- bp1 := offsetPathGenerate (p, q yscaled 1/2, 0);
- bp2 := offsetPathGenerate (p, q yscaled -1/2, 0);
- fill bp1 -- reverse(bp2) -- cycle;
+ brushPath1 := offsetPathGenerate (p, q yscaled 1/2, 0);
+ brushPath2 := offsetPathGenerate (p, q yscaled -1/2, 0);
+ fill brushPath1 -- reverse(brushPath2) -- cycle;
elseif (w0 < 101/100minStrokeWidth) and (w1 < 101/100minStrokeWidth):
thinBrushGenerate (p, q, 0)
fi;
@@ -405,31 +459,67 @@
% macro for thin lines which are actually dashed
%
-def thinBrushGenerate (expr p, q, i) =
+vardef thinBrushGenerate@#(expr p, q, i) =
begingroup
- save w, bp, bt, t, h, linecap;
+ save w, brushPath, bt, t, h, minLength, minWidth, dashPatternImage;
numeric w[], t[];
- path bp[], bt;
+ path brushPath[], bt;
+ picture dashPatternImage;
bt := q;
w0 := (ypart(urcorner(bt)));
w1 := (ypart(lrcorner(bt)));
w2 := floor((1/2(w0 + w1))/dashStrokeWidthStep)*dashStrokeWidthStep;
t := cutPathTime(bt, w2);
- bp1 := subpath (0, t) of p;
- bp2 := subpath (t, length(p)) of p;
+ brushPath1 := subpath (0, t) of p;
+ brushPath2 := subpath (t, length(p)) of p;
+ if (str @# = "") or (str @# = "hatches"):
+ minLength := minDashStrokeLength;
+ minWidth := minDashStrokeWidth;
+ elseif str @# = "stipples":
+ minLength := minStippleStep;
+ minWidth := minStippleStrokeWidth;
+ fi;
if (((w0 - w1) > dashStrokeWidthStep) and (i < 15))
- and ((arclength(bp1) > minDashStrokeLength)
- or (arclength(bp2) > minDashStrokeLength)):
- thinBrushGenerate (bp1, subpath (0, t) of q, i + 1);
- thinBrushGenerate (bp2, subpath (t, length(q)) of q, i + 1);
+ and ((arclength(brushPath1) > minLength)
+ or (arclength(brushPath2) > minLength)):
+ thinBrushGenerate@#(brushPath1, subpath (0, t) of q, i + 1);
+ thinBrushGenerate@#(brushPath2, subpath (t, length(q)) of q, i + 1);
else:
- linecap := butt;
- if (w2 > minStrokeWidth):
- w2 := minStrokeWidth;
+ if (str @# = "") or (str @# = "hatches"):
+ if (w2 > minStrokeWidth):
+ w2 := minStrokeWidth;
+ fi;
+ if (w2 >= minWidth) and (arclength(p) > 0):
+ draw p withpen thinpen dashed thinBrushPattern(w2, arclength(p));
+ fi;
+ elseif str @# = "stipples":
+ begingroup
+ interim linecap := rounded;
+ save stippleSizeVar;
+ stippleSizeVar := stippleSize;
+ save stippleSize;
+ w2 := 1/3w2;
+ if (w2 >= minWidth) and (arclength(p) > 0):
+ stippleSize := stippleSizeVar * (0.9 + uniformdeviate(0.3));
+ dashPatternImage := stipplesBrushPattern(w2, arclength(p));
+ if urcorner(dashPatternImage) <> (0,0):
+ brushPath1 := offsetPathGenerate (p, (q yscaled 0) shifted (0, 1/3stippleShadingDensity), 0);
+ draw brushPath1 withpen (pencircle scaled stippleSize) dashed dashPatternImage;
+ fi;
+ stippleSize := stippleSizeVar * (0.9 + uniformdeviate(0.3));
+ dashPatternImage := stipplesBrushPattern(w2, arclength(p));
+ if urcorner(dashPatternImage) <> (0,0):
+ brushPath2 := offsetPathGenerate (p, (q yscaled 0) shifted (0, -1/3stippleShadingDensity), 0);
+ draw brushPath2 withpen (pencircle scaled stippleSize) dashed dashPatternImage;
+ fi;
+ stippleSize := stippleSizeVar * (0.9 + uniformdeviate(0.3));
+ dashPatternImage := stipplesBrushPattern(w2, arclength(p));
+ if urcorner(dashPatternImage) <> (0,0):
+ draw p withpen (pencircle scaled stippleSize) dashed dashPatternImage;
+ fi;
+ fi;
+ endgroup
fi;
- if (w2 >= minDashStrokeWidth) and (arclength(p) > 0):
- draw p withpen thinpen dashed thinBrushPattern(w2, arclength(p));
- fi;
fi;
endgroup
enddef;
@@ -443,9 +533,9 @@
brushGenerate (p,
offsetPathTemplate (p, 0) (
1/2minStrokeWidth + 2*minStrokeWidth
- * angleToLightness(
- sphereAngleToAbsoulteAngle(
- (angleRad(direction offsetPathTime of p), 1/2)
+ * normalVectorToLightness(
+ sphereAnglesToNormalVector(
+ (angleRad(point offsetPathTime of p), arcsin(1/2))
), 0, point offsetPathTime of p
)
), 0);
@@ -482,7 +572,52 @@
fi
enddef;
+
%
+% Stipples are also dashes
+%
+
+vardef stipplesBrushPattern (expr w, l) =
+ save d, n, rn, rv, ss;
+ ss := 1/1000;
+ numeric d[];
+ picture rv;
+ %if w > stippleSize:
+ % d0 := minStippleStep;
+ %else:
+ n := (w*l)/(stippleSize**2);
+ rn := floor(n);
+ if rn > 0:
+ d0 := l/rn;
+ fi;
+ %fi;
+ if rn > 0:
+ d1 := uniformdeviate(d0);
+ d2 := d0-d1;
+ if rn >=3:
+ d3 := uniformdeviate(d0);
+ d4 := d0-d3;
+ %if uniformdeviate(2) > 1:
+ % d5 := uniformdeviate(d0);
+ % d6 := d0-d5;
+ % rv := dashpattern (off d1 on ss off (d2+d5)-ss on ss off (d4+d6)-ss on ss off d3-ss);
+ %else:
+ rv := dashpattern (off d1 on ss off (d2+d3)-ss on ss off d4-ss);
+ %fi;
+ else:
+ rv := dashpattern (off d1 on ss off d2-ss);
+ fi;
+ else:
+ if uniformdeviate(1) < n:
+ rv := dashpattern (off uniformdeviate(l-ss) on ss off l);
+ else:
+ rv := image();
+ fi;
+ fi;
+ rv
+enddef;
+
+%
% macro that actually draws line of variable width
%
@@ -493,25 +628,39 @@
enddef;
%
+% same, but only for thin brushes
+%
+
+vardef thinBrush@#(expr p) (text offsetFunction) =
+ image(
+ thinBrushGenerate@#(p, offsetPathTemplate(p, 0)(offsetFunction), 0);
+ )
+enddef;
+
+%
% This macro generates tube between paths p and q, of variable width d
% Tube is subdivided into segments in such a way that within every segment
% we need 2**n lines to generate even fill
%
-def tubeGenerate (expr p, q, d, i) =
-begingroup
- save w, bw, k, t, tubeWidth, sp, currentPath, currentTubePath, currentDepth;
+vardef tubeGenerate@#(expr p, q, d, i) =
+ save w, bw, k, t, tubeWidth, sp, currentPath, currentTubePath, currentDepth, lineDensity;
numeric w[], bw[], t, currentDepth;
path tubeWidth, sp, currentPath, currentTubePath;
tubeWidth := d yscaled 2;
+ if (str @# = "") or (str @# = "hatches"):
+ lineDensity := shadingDensity;
+ elseif (str @# = "stipples"):
+ lineDensity := stippleShadingDensity;
+ fi;
w0 := (ypart(urcorner(tubeWidth))) - 1/1000;
w1 := (ypart(lrcorner(tubeWidth))) + 1/1000;
- w2 := ceiling(log(w0/shadingDensity, 2));
- w3 := ceiling(log(w1/shadingDensity, 2));
+ w2 := ceiling(log(w0/lineDensity, 2));
+ w3 := ceiling(log(w1/lineDensity, 2));
if ((w2 > w3) and (i<20)):
- t := cutPathTime(tubeWidth, shadingDensity*(2**(w2-1)));
- tubeGenerate (subpath (0, t) of p, subpath (0, t) of q, subpath (0, t) of d, i + 1);
- tubeGenerate (subpath (t, length(p)) of p, subpath (t, length(q)) of q, subpath (t, length(d)) of d, i + 1);
+ t := cutPathTime(tubeWidth, lineDensity*(2**(w2-1)));
+ tubeGenerate@#(subpath (0, t) of p, subpath (0, t) of q, subpath (0, t) of d, i + 1);
+ tubeGenerate@#(subpath (t, length(p)) of p, subpath (t, length(q)) of q, subpath (t, length(d)) of d, i + 1);
else:
if (arclength(p) > 0) and (arclength(q) > 0):
bw1 := 2**w2;
@@ -518,27 +667,47 @@
currentTubePath := interpath (1/2, q, p);
for k := 0 upto bw1:
currentPath := interpath (k/bw1, q, p);
- angleOnTube := arccos(((k/bw1)*2) - 1);
- currentDepth := -abs((1-sin(angleOnTube))*w0);
+ angleOnTube := arcsin(((k/bw1)*2) - 1);
+ currentDepth := -abs((1-sin(angleOnTube + 1/2pi))*w0);
if shadowsEnabled:
currentPath := shadowCut(currentPath, currentDepth);
fi;
- brushGenerate (currentPath,
- offsetPathTemplate(currentPath, 0)(
- maxShadingStrokeWidth
- if odd (k): * (abs(ypart(point offsetPathTime of tubeWidth)/bw1) - 1/2shadingDensity) fi
- %* orderFade(xpart(unitvector(direction offsetPathTime of tubeWidth yscaled 1/2cos(angleOnTube))), k) % why was it even here?
- * angleToLightness(
- tubeAngleToAbsoulteAngle((
- angleOnTube,
- angleRad(direction offsetPathTime of currentTubePath),
- angleRad(direction offsetPathTime of tubeWidth yscaled 1/2)
- )), currentDepth, point offsetPathTime of currentPath)
- ), 0);
+ if (str @# = "") or (str @# = "hatches"):
+ brushGenerate (currentPath,
+ offsetPathTemplate(currentPath, 0)(
+ maxShadingStrokeWidth
+ if odd (k): * (abs(ypart(point offsetPathTime of tubeWidth)/bw1) - 1/2lineDensity) fi
+ * normalVectorToLightness(
+ tubeAnglesToNormalVector((
+ angleOnTube,
+ angleRad(direction offsetPathTime of currentTubePath),
+ angleRad(direction offsetPathTime of (tubeWidth yscaled 1/2))
+ )), currentDepth, point offsetPathTime of currentPath)
+ ), 0);
+ elseif (str @# = "stipples"):
+ begingroup
+ save stippleShadingDensity;
+ if w2 > 0:
+ stippleShadingDensity := 2w0/(2**w2); % When the distance between the lines changes, wtipples should spread further apart
+ else:
+ stippleShadingDensity := w0;
+ fi;
+ thinBrushGenerate.@#(currentPath,
+ offsetPathTemplate(currentPath, 0)(
+ stippleSize
+ if odd (k): * (abs(ypart(point offsetPathTime of tubeWidth)/bw1) - 1/2lineDensity) fi
+ * normalVectorToLightness(
+ tubeAnglesToNormalVector((
+ angleOnTube,
+ angleRad(direction offsetPathTime of currentTubePath),
+ angleRad(direction offsetPathTime of (tubeWidth yscaled 1/2))
+ )), currentDepth, point offsetPathTime of currentPath)
+ ), 0);
+ endgroup
+ fi;
endfor;
fi;
fi;
-endgroup
enddef;
%
@@ -587,12 +756,12 @@
offsetPathTemplate(currentPath, 0)(
maxShadingStrokeWidth
* orderFade(offsetPathLength[1/l1, l2], j)
- * angleToLightness(
- tubeAngleToAbsoulteAngle((
- arccos(pthdir*((offsetPathLength*2)-1)),
- pathAngle,
- tubeAngle)
- ), -2(1/2arclength(currentPath))+sqrt(1 - (2offsetPathLength - 1)**2)*(1/2arclength(currentPath)), point offsetPathTime of currentPath)
+ * normalVectorToLightness(
+ tubeAnglesToNormalVector((
+ arcsin(pthdir*((offsetPathLength*2)-1)),
+ pathAngle,
+ tubeAngle)
+ ), -2(1/2arclength(currentPath))+sqrt(1 - (2offsetPathLength - 1)**2)*(1/2arclength(currentPath)), point offsetPathTime of currentPath)
)
, 0);
endfor;
@@ -604,24 +773,27 @@
%
% This macro converts some measurements of point on tube to absolute angle.
% Since there are three such measurements, macro gets them as as a single
-% argument of "color" type, in case it will eventually appear as a result
+% argument of "color" type, in case it would eventually appear as a result
% of some other macro.
%
+% redpart is the angle on the tube's circumference
+% greenpart is the angle of the tube path
+% bluepart is the angle of the tube's outline
+%
-vardef tubeAngleToAbsoulteAngle (expr p) =
- save a;
- numeric a[];
- a1 := bluepart(p) + 1/2pi;
- a2 := arccos(cos(redpart(p))*sin(a1));
- a3 := greenpart(p) + 1/2pi;
- a4 := arccos((cos(a1) * cos(a3) - cos(a2) * sin(a3))*(99/100));
- a5 := arccos((cos(a1) * sin(a3) + cos(a2) * cos(a3))*(99/100));
- (a5, a4)
+vardef tubeAnglesToNormalVector (expr p) =
+ save normalVector;
+ color normalVector;
+ normalVector := (0, 0, 1);
+ normalVector := rotateXYZaround.y(normalVector, -bluepart(p));
+ normalVector := rotateXYZaround.x(normalVector, redpart(p));
+ normalVector := rotateXYZaround.z(normalVector, -greenpart(p));
+ normalVector
enddef;
%
-% frontends to simplify tube drawing. tubeOutline variable changes on every call
-% of any tube frontend function and can be used afterwards.
+% frontend to simplify tube drawing. tubeOutline variable changes on every call
+% of the function and can be used afterwards.
%
path tubeOutline;
@@ -628,60 +800,42 @@
boolean drawTubeEnds;
drawTubeEnds := true;
-vardef tube.l (expr p)(text offsetFunction)=
- save q;
+vardef tube@#(expr p)(text offsetFunction)=
+ save q, respic;
path q[];
+ picture respic;
q0 := offsetPathSubdivide(p);
q1 := offsetPathTemplate(q0, 0)(offsetFunction);
q2 := offsetPathGenerate (q0, q1, 0);
q3 := offsetPathGenerate (q0, q1 yscaled -1, 0);
tubeOutline := q3--reverse(q2)--cycle;
- image(
- tubeGenerate (q2, q3, q1, 0);
- if (cycle p) or (not drawTubeEnds):
- draw q2 withpen thinpen;
- draw q3 withpen thinpen;
+ if str @# = "e":
+ if not drawTubeEnds:
+ image(
+ draw q2 withpen thinpen;
+ draw q3 withpen thinpen;
+ )
else:
- draw q2--reverse(q3)--cycle withpen thinpen;
- fi;
- )
-enddef;
-
-vardef tube.t (expr p)(text offsetFunction)=
- save q;
- path q[];
- q0 := offsetPathSubdivide(p);
- q1 := offsetPathTemplate(q0, 0)(offsetFunction);
- q2 := offsetPathGenerate (q0, q1, 0);
- q3 := offsetPathGenerate (q0, q1 yscaled -1, 0);
- tubeOutline := q3--reverse(q2)--cycle;
- image(
- tubeGenerateAlt (q2, q3, q1);
- if (cycle p) or (not drawTubeEnds):
- draw q2 withpen thinpen;
- draw q3 withpen thinpen;
- else:
- draw q2--reverse(q3)--cycle withpen thinpen;
- fi;
- )
-enddef;
-
-vardef tube.e (expr p)(text offsetFunction)=
- save q;
- path q[];
- q0 := offsetPathSubdivide(p);
- q1 := offsetPathTemplate(q0, 0)(offsetFunction);
- q2 := offsetPathGenerate (q0, q1, 0);
- q3 := offsetPathGenerate (q0, q1 yscaled -1, 0);
- tubeOutline := q3--reverse(q2)--cycle;
- if not drawTubeEnds:
+ tubeOutline
+ fi
+ else:
image(
- draw q2 withpen thinpen;
- draw q3 withpen thinpen;
- )
- else:
- tubeOutline := q3--reverse(q2)--cycle;
- tubeOutline
+ if str @# = "l":
+ respic := image(tubeGenerate (q2, q3, q1, 0););
+ elseif str @# = "s":
+ respic := image(tubeGenerate.stipples(q2, q3, q1, 0);)
+ elseif str @# = "t":
+ respic := image(tubeGenerateAlt (q2, q3, q1););
+ fi;
+ if (cycle p) or (not drawTubeEnds):
+ draw q2 withpen thinpen;
+ draw q3 withpen thinpen;
+ else:
+ draw q2--reverse(q3)--cycle withpen thinpen;
+ fi;
+ clip respic to (q2--reverse(q3)--cycle);
+ draw respic;
+ )
fi
enddef;
@@ -689,36 +843,66 @@
% Sphere can be used as a cap for a tube, so it has same 2**n lines.
%
-vardef sphere.c (expr d) =
- save currentCircle, origCircle, currentRadius, currentDepth, order, circleThickness;
+vardef sphere@#(expr d) =
+ save currentCircle, origCircle, currentRadius, currentDepth, order, circleThickness, lineDensity, shadingPicture;
path currentCircle, origCircle;
numeric currentRadius, currentDepth, order;
+ picture shadingPicture;
+ if (str @# = "") or (str @# = "c"):
+ lineDensity := shadingDensity;
+ elseif (str @# = "s"):
+ lineDensity := stippleShadingDensity;
+ fi;
origCircle := fullcircle;
- order := 2**ceiling(log((1/2d)/shadingDensity, 2));
+ order := 2**ceiling(log((1/2d)/lineDensity, 2));
image(
draw fullcircle scaled d withpen thinpen;
- for i := 1 upto order:
- currentRadius := i/order;
- currentCircle := origCircle scaled (currentRadius*d) rotated uniformdeviate (1/4pi);
- if odd(i):
- circleThickness := maxShadingStrokeWidth * ((abs(d - (shadingDensity*order)))/order);
- else:
- circleThickness := maxShadingStrokeWidth;
- fi;
- currentDepth:= -(1-sqrt(1-currentRadius**2))*(1/2d);
- if shadowsEnabled:
- currentCircle := shadowCut(currentCircle, currentDepth);
- fi;
- brushGenerate (currentCircle,
- offsetPathTemplate (currentCircle, 0) (
- circleThickness
- * angleToLightness(
- sphereAngleToAbsoulteAngle(
- (angleRad(direction offsetPathTime of currentCircle), currentRadius)
- ), currentDepth, point offsetPathTime of currentCircle
- )
- ), 0);
- endfor;
+ shadingPicture := image(
+ for i := 1 upto order:
+ currentRadius := i/order;
+ currentCircle := origCircle scaled (currentRadius*d) rotated uniformdeviate (1/4pi);
+ if odd(i):
+ circleThickness := maxShadingStrokeWidth * ((abs(d - (lineDensity*order)))/order);
+ else:
+ circleThickness := maxShadingStrokeWidth;
+ fi;
+ currentDepth:= -(1-sqrt(1-currentRadius**2))*(1/2d);
+ if shadowsEnabled:
+ currentCircle := shadowCut(currentCircle, currentDepth);
+ fi;
+ if (str @# = "") or (str @# = "c"):
+ brushGenerate (currentCircle,
+ offsetPathTemplate (currentCircle, 0) (
+ circleThickness
+ * normalVectorToLightness(
+ sphereAnglesToNormalVector(
+ (angleRad(point offsetPathTime of currentCircle), arcsin(currentRadius))
+ ), currentDepth, point offsetPathTime of currentCircle
+ )
+ ), 0);
+ elseif (str @# = "s"):
+ begingroup
+ save stippleShadingDensity;
+ if order > 0:
+ stippleShadingDensity := d/order; % When the distance between the lines changes, wtipples should spread further ap
+ else:
+ stippleShadingDensity := 1/2d;
+ fi;
+ thinBrushGenerate.stipples(currentCircle,
+ offsetPathTemplate (currentCircle, 0) (
+ circleThickness
+ * normalVectorToLightness(
+ sphereAnglesToNormalVector(
+ (angleRad(point offsetPathTime of currentCircle), arcsin(currentRadius))
+ ), currentDepth, point offsetPathTime of currentCircle
+ )
+ ), 0);
+ endgroup
+ fi;
+ endfor;
+ );
+ clip shadingPicture to (fullcircle scaled d);
+ draw shadingPicture;
)
enddef;
@@ -729,7 +913,7 @@
% so all we need to do is to fade lines correspondingly
%
-vardef sphere.l (expr d, lat) =
+vardef sphereLat (expr d, lat) =
save p, a, x, y, sphlat, latrad, n, c, currentPath, nline, tlat;
path p[], currentPath, currentArc;
sphlat := 0;
@@ -779,8 +963,8 @@
)**abs(sind(lat))
)**2)
, nline)
- * angleToLightness(
- sphereAngleToAbsoulteAngle((
+ * normalVectorToLightness(
+ sphereAnglesToNormalVector((
(
if (abs(point offsetPathTime of currentPath) > 0):
angleRad(point offsetPathTime of currentPath)
@@ -787,7 +971,7 @@
else:
0
fi
- + 1/2pi), 2abs(point offsetPathTime of currentPath)/(d+1))
+ ), arcsin(2abs(point offsetPathTime of currentPath)/(d+1)))
), 0, point offsetPathTime of currentPath)
), 0);
fi;
@@ -815,17 +999,16 @@
enddef;
%
-% This one converts point location on sphere to absolute angle
+% This one converts point location on sphere to normal vector
%
-vardef sphereAngleToAbsoulteAngle (expr p) =
- save a;
- numeric a[];
- a1 := xpart(p) - 1/2pi;
- a2 := arcsin(ypart(p));
- a3 := arccos(sin(a2)*cos(a1));
- a4 := pi - arccos(sin(a2)*sin(a1));
- (a3, a4)
+vardef sphereAnglesToNormalVector (expr p) =
+ save normalVector;
+ color normalVector;
+ normalVector := (0, 0, 1);
+ normalVector := rotateXYZaround.y(normalVector, ypart(p));
+ normalVector := rotateXYZaround.z(normalVector, -xpart(p));
+ normalVector
enddef;
%
@@ -832,12 +1015,14 @@
% Once we get two angles at some point of some surface, we can compute light intensity there.
%
-vardef angleToLightness (expr p, d, q) =
+vardef normalVectorToLightness (expr normalVector, d, q) =
save returnValue, shiftedShadowPath;
path shiftedShadowPath;
if shadowsEnabled:
for i := 0 step 1 until numberOfShadows:
- shiftedShadowPath := shadowPath[i] shifted (lightDirectionVector scaled (d-shadowDepth[i]));
+ shiftedShadowPath := shadowPath[i] shifted
+ ((redpart(lightDirectionVectorXYZ), greenpart(lightDirectionVectorXYZ))
+ scaled ((d-shadowDepth[i])*bluepart(lightDirectionVectorXYZ)));
if q isInside shiftedShadowPath:
returnValue := 1;
fi;
@@ -844,8 +1029,8 @@
endfor;
fi;
if not known returnValue:
- returnValue := (cos(xpart(p) + xpart(lightDirection))++cos(ypart(p) - ypart(lightDirection)));
- returnValue := angleToLightnessPP(returnValue);
+ returnValue := 1 - (normalVector dotprodXYZ lightDirectionVectorXYZ);
+ returnValue := lightnessPP(returnValue);
fi;
if returnValue > 1:
1
@@ -854,8 +1039,8 @@
fi
enddef;
-vardef angleToLightnessPP (expr v) =
- v**3
+vardef lightnessPP (expr v) =
+ v
enddef;
% Shadows are global
@@ -874,7 +1059,9 @@
numeric pathShadowCut;
currentPath := pathToCut;
for j := 0 step 1 until numberOfShadows:
- shiftedShadowPath := shadowPath[j] shifted (lightDirectionVector scaled (currentDepth - shadowDepth[j]));
+ shiftedShadowPath := shadowPath[j] shifted
+ ((redpart(lightDirectionVectorXYZ), greenpart(lightDirectionVectorXYZ))
+ scaled ((currentDepth - shadowDepth[j])*bluepart(lightDirectionVectorXYZ)));
forever:
pathShadowIntersection := shiftedShadowPath firstIntersectionTimes currentPath;
pathShadowCut := ypart(pathShadowIntersection);
@@ -1256,19 +1443,19 @@
picture p[];
path lm;
begingroup
- save angleToLightnessPP;
- vardef angleToLightnessPP (expr v) =
- 1/2(v**3)
+ save lightnessPP;
+ vardef lightnessPP (expr v) =
+ 1/2v
enddef;
- p1 := image(draw sphere.l(2s, lat));
- vardef angleToLightnessPP (expr v) =
+ p1 := image(draw sphereLat(2s, lat));
+ vardef lightnessPP (expr v) =
if (abs(cos(sphlat)) > 7/8 + uniformdeviate (1/20)):
- 1/4(v**2)
+ 1/4v
else:
- 1/3(v**2) + 2/3
+ 1/3v + 2/3
fi
enddef;
- p2 := image(draw sphere.l(2s, lat));
+ p2 := image(draw sphereLat(2s, lat));
endgroup;
image(
draw fullcircle scaled 2s withpen thinpen;
@@ -1280,9 +1467,9 @@
thinBrushGenerate (lm,
offsetPathTemplate (lm, 0) (
2/3minStrokeWidth + 1/3minStrokeWidth
- * angleToLightness(
- sphereAngleToAbsoulteAngle(
- (angleRad(point offsetPathTime of lm) + 1/4pi, abs(point offsetPathTime of lm)/2s)
+ * normalVectorToLightness(
+ sphereAnglesToNormalVector(
+ (angleRad(point offsetPathTime of lm), arcsin(abs(point offsetPathTime of lm)/2s))
), 0, point offsetPathTime of lm
)
), 0);
@@ -1375,7 +1562,7 @@
enddef;
vardef solid (expr p, a, t) =
- save stripes, stripeskind, d, i, j, c;
+ save stripes, stripeskind, d, i, j, c, strokeVariation;
picture stripes, stripeskind;
pair c;
stripes := image(
@@ -1385,18 +1572,19 @@
c := 1/2[ulcorner(p rotated (90 - a)), lrcorner(p rotated (90 - a))] rotated (a - 90);
for i:= 0 step (3/2shadingDensity)/d1 until 1:
if (t = 1):
+ strokeVariation := uniformdeviate(1)-1/2;
j := round(i*d1/(3/2shadingDensity));
if (j mod 4) = 0:
- stripeskind := dashpattern (on 8shadingDensity off 4shadingDensity);
+ stripeskind := dashpattern (on (8-strokeVariation)*shadingDensity off (4+strokeVariation)*shadingDensity);
fi;
if ((j mod 4) = 1) or ((j mod 4) = 3):
- stripeskind := dashpattern (off 1shadingDensity on 6shadingDensity off 5shadingDensity);
+ stripeskind := dashpattern (off 1shadingDensity on (6-strokeVariation)*shadingDensity off (5+strokeVariation)*shadingDensity);
fi;
if (j mod 4) = 2:
stripeskind := dashpattern (on 0 off 12shadingDensity);
fi;
fi;
- draw ((dir(a) scaled 1/2d2) -- (dir(a + 180) scaled 1/2d2)) shifted c shifted i[dir(a + 90) scaled 1/2d1, dir(a -90) scaled 1/2d1] withpen thinpen
+ draw ((dir(a) scaled 1/2(d2-uniformdeviate(3shadingDensity))) -- (dir(a + 180) scaled 1/2d2)) shifted c shifted i[dir(a + 90) scaled 1/2d1, dir(a -90) scaled 1/2d1] withpen thinpen
dashed stripeskind;
endfor;
);
@@ -1537,14 +1725,6 @@
) maskedWith (q3 -- reverse(q2) -- (q2 yscaled 0 shifted (0, -h)) -- (reverse(q3) yscaled 0 shifted (0, -h)) -- cycle)
maskedWith q6;
draw shadedEdge(q6);
- thinBrushGenerate (q5,
- offsetPathTemplate (q5, 0) (
- minDashStrokeWidth + minStrokeWidth
- * angleToLightness(
- (arccos(1 - offsetPathLength*2), 1/2pi)
- , 0, point offsetPathTime of q5
- )
- ), 0);
)
enddef;
@@ -1658,9 +1838,9 @@
thinBrushGenerate (fullcircle scaled i,
offsetPathTemplate (fullcircle scaled i, 0) (
2/3minStrokeWidth + minStrokeWidth
- * angleToLightness(
- sphereAngleToAbsoulteAngle(
- (angleRad(direction offsetPathTime of fullcircle), i/4d)
+ * normalVectorToLightness(
+ sphereAnglesToNormalVector(
+ (angleRad(point offsetPathTime of fullcircle), arcsin(i/4d))
), 0, point offsetPathTime of fullcircle scaled i
)
), 0);
@@ -1668,9 +1848,9 @@
thinBrushGenerate (fullcircle scaled i,
offsetPathTemplate (fullcircle scaled i, 0) (
1/4minStrokeWidth + minStrokeWidth
- * angleToLightness(
- sphereAngleToAbsoulteAngle(
- (angleRad(direction offsetPathTime of fullcircle) + pi, 1/2)
+ * normalVectorToLightness(
+ sphereAnglesToNormalVector(
+ (angleRad(point offsetPathTime of fullcircle) + pi, arcsin(1/2))
), 0, point offsetPathTime of fullcircle scaled i
)
), 0);
@@ -1709,9 +1889,9 @@
thinBrushGenerate (fullcircle scaled i,
offsetPathTemplate (fullcircle scaled i, 0) (
2/3minStrokeWidth + minStrokeWidth
- * angleToLightness(
- sphereAngleToAbsoulteAngle(
- (angleRad(direction offsetPathTime of fullcircle) + pi, i/4d)
+ * normalVectorToLightness(
+ sphereAnglesToNormalVector(
+ (angleRad(point offsetPathTime of fullcircle) + pi, arcsin(i/4d))
), 0, point offsetPathTime of fullcircle scaled i
)
), 0);
@@ -1740,7 +1920,110 @@
)
enddef;
+
%
+% This one roughly finds the center of mass for a closed shape
+%
+
+vardef shapeCenterOfMass (expr p) =
+ save i, a, aTotal, q;
+ numeric i, a, aTotal;
+ pair rv, q[];
+ q0 := point 0 of p;
+ aTotal := 0;
+ rv := (0, 0);
+ for i := 1 step 1 until (length(p)-2):
+ q1 := point i of p;
+ q2 := point (i+1) of p;
+ if (xpart(q1-q0) = 0):
+ a := (abs(ypart(q1-q0)/cm)*abs(xpart(q2-q0)/cm))/2;
+ elseif (ypart(q1-q0) = 0):
+ a := (abs(xpart(q1-q0)/cm)*abs(ypart(q2-q0)/cm))/2;
+ elseif (abs(xpart(q1-q0)) > abs(ypart(q1-q0))):
+ begingroup
+ save qA;
+ pair qA;
+ qA = whatever[q0, q0 + (0,1)];
+ qA = whatever[q2, q2 + (q1-q0)];
+ a := (abs(ypart(qA-q0)/cm)*abs(xpart(q1-q0)/cm))/2;
+ endgroup
+ else:
+ begingroup
+ save qA;
+ pair qA;
+ qA = whatever[q0, q0 + (1,0)];
+ qA = whatever[q2, q2 + (q1-q0)];
+ a := (abs(xpart(qA-q0)/cm)*abs(ypart(q1-q0)/cm))/2;
+ endgroup
+ fi;
+ %a := 2;
+ aTotal := aTotal + a;
+ rv := rv + ((q0 + q1 + q2) scaled (a/3));
+ endfor;
+ if (aTotal > 0):
+ rv := rv scaled (1/aTotal);
+ else:
+ rv := (0, 0);
+ fi;
+ rv
+enddef;
+
+%
+% This macro is for drawing shaded flat surfaces
+%
+
+vardef flatSurface@#(expr surfPath, normalVector, hatchAngle) =
+ save p, aHatch, hatchImage, surfLight, totalHeight, totalWidth, lineDensity, distFromEdge, hatchLength;
+ path p, aHatch;
+ picture hatchImage;
+ numeric distFromEdge, hatchLength;
+ surfLight := normalVectorToLightness(normalVector, 0, (0, 0));
+ p := surfPath rotated -hatchAngle;
+ if (str @# = "") or (str @# = "hatches"):
+ lineDensity := shadingDensity;
+ elseif (str @# = "stipples"):
+ lineDensity := stippleShadingDensity;
+ fi;
+ hatchImage := image(
+ totalHeight := abs(ypart(llcorner(p)) - ypart(urcorner(p)));
+ totalWidth := abs(xpart(llcorner(p)) - xpart(urcorner(p)));
+ %fill surfPath withcolor (surfLight, surfLight, surfLight);
+ for i := ypart(llcorner(p)) step (totalHeight/round(totalHeight/lineDensity)) until ypart(urcorner(p)):
+ distFromEdge := abs((i - ypart(llcorner(p)))/(ypart(urcorner(p))-ypart(llcorner(p))));
+ aHatch := (xpart(llcorner(p)),i) -- (xpart(lrcorner(p)), i);
+ aHatch := (point xpart(aHatch firstIntersectionTimes p) of aHatch) --
+ (point xpart(reverse(aHatch) firstIntersectionTimes p) of reverse(aHatch));
+ hatchLength := arclength(aHatch);
+ if arclength(aHatch) > 0:
+ aHatch := aHatch rotated hatchAngle;
+ aHatch := pathSubdivide(aHatch,3+round(uniformdeviate(2)));
+ if (str @# = "") or (str @# = "hatches"):
+ draw brush(aHatch)(
+ (2minStrokeWidth*(1/15+surfLight))*
+ (1-6/7sqrt(
+ sin(offsetPathLength*pi)*(hatchLength/totalWidth)*
+ sin(distFromEdge*pi)
+ ))
+ );
+ elseif (str @# = "stipples"):
+ draw thinBrush.stipples(aHatch)(
+ (stippleSize*(1/15+surfLight))*
+ (1-5/6sqrt(
+ sin(offsetPathLength*pi)*(hatchLength/totalWidth)*
+ sin(distFromEdge*pi)
+ ))
+ );
+ fi;
+ fi;
+ endfor;
+ );
+ clip hatchImage to surfPath;
+ image(
+ draw hatchImage;
+ )
+enddef;
+
+%
% These macros are for drawing wood texture. A bunch of wood-related global
% variables are also here.
%
@@ -1871,7 +2154,6 @@
save v, valueExists;
string v;
boolean valueExists;
- valueExists := false;
if str @# = "":
if not string listName:
string listName;
@@ -1884,12 +2166,9 @@
if unknown listName@#:
listName@# := "";
fi;
+ valueExists := false;
if omitDuplicates:
- for i=scantokens(listName@#):
- if (i = valueToAdd):
- valueExists := true;
- fi;
- endfor;
+ valueExists := isInList@#(valueToAdd, listName)
fi;
if not valueExists:
if string valueToAdd:
@@ -1909,6 +2188,38 @@
fi;
enddef;
+vardef isInList@#(expr valueToLookFor)(suffix listName) =
+ save rv, i;
+ boolean rv;
+ rv := false;
+ if str @# = "":
+ if not string listName:
+ string listName;
+ fi;
+ else:
+ if not string listName0:
+ string listName[];
+ fi;
+ fi;
+ if unknown listName@#:
+ listName@# := "";
+ fi;
+ if string valueToLookFor:
+ forsuffixes i=scantokens(listName@#):
+ if (str i = valueToLookFor):
+ rv := true;
+ fi;
+ endfor;
+ else:
+ for i=scantokens(listName@#):
+ if (i = valueToLookFor):
+ rv := true;
+ fi;
+ endfor;
+ fi;
+ rv
+enddef;
+
vardef sortList (expr listToSort, ascending) =
save nPre, nPost, pivot, isSorted, lastValue, preList, postList, rv;
numeric nPre, nPost, pivot;
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