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|
%%
%% This is file `grafbase.mf',
%% generated with the docstrip utility.
%%
%% The original source files were:
%%
%% grafbase.dtx (with options: `MF')
%%
%% -------------------------------------------------------------------
%%
%% Copyright 2002--2009, Daniel H. Luecking
%%
%% Mfpic may be distributed and/or modified under the conditions of the
%% LaTeX Project Public License, either version 1.3c of this license or (at
%% your option) any later version. The latest version of this license is in
%% <http://www.latex-project.org/lppl.txt>
%% and version 1.3c or later is part of all distributions of LaTeX version
%% 2008/12/01 or later.
%%
%% Mfpic has maintenance status "author-maintained". The Current Maintainer
%% is Daniel H. Luecking. There are several Base Interpreters associated
%% with mfpic: plain TeX, LaTeX, plain Metafont and plain MetaPost.
%%
%%% File: grafbase.dtx
%%% A part of mfpic 1.00 2009/09/22
%%%
if (known grafbaseversion) or (known grafbase):
message "Grafbase (" & jobname & "): You have loaded grafbase more "
& "than once! Please make sure that it is loaded only once.";
endinput;
fi
boolean grafbase; grafbase := true;
string fileversion, filedate;
fileversion := "1.00"; filedate := "2009/09/22";
message " Loading grafbase macros, version " & fileversion & " " &
filedate & ".";
def GBmsg expr s = message "Grafbase (" & jobname & "): " & s; enddef;
def GBwarn expr s = GBmsg "Warning, " & s; enddef;
def GBerrmsg (expr s) expr t = errhelp t;
errmessage "Grafbase (" & jobname & "): " & s; errhelp "";
enddef;
boolean MFPIC; MFPIC := false;
def checkversions (expr g)=
numeric grafbaseversion; grafbaseversion := g;
if unknown mfpicversion: % no mfpic, or < 0.63
GBmsg "Recent mfpic not detected.";
elseif g = mfpicversion:
MFPIC := true;
else:
message "";
GBwarn "Version mismatch: "
& "mfpic and grafbase versions do not match.";
message "";
fi
enddef;
checkversions (100);
if unknown base_name : input plain;
elseif not string base_name: input plain;
elseif base_name <> "plain": input plain;
fi
boolean METAPOST;
METAPOST := known color Geamparalele din Babadag;
numeric metapostversion;
if METAPOST:
GBerrmsg ("wrong compiler.")
"This file is for Metafont. For Metapost use grafbase.mp.";
fi
metapostversion := 0;
if not boolean debug: boolean debug; debug := false; fi
def GBdebug =
begingroup
save >>; def >> = message enddef;
>> "Grafbase DEBUG";
enddef;
def GBenddebug =
>> "End DEBUG";
endgroup
enddef;
vardef mftitle expr t =
if string t: t; message t; fi
enddef;
if unknown mode:
GBerrmsg ("Metafont mode is unknown.")
"Set mode to a known mode. Perhaps localfont or ljfour. "
& "If you proceed, a generic 600dpi mode will be used.";
if known localfont: mode := localfont;
else:
mode_def GBgeneric =
proofing := 0;
fontmaking := 1;
tracingtitles := 0;
if unknown pixels_per_inch:
pixels_per_inch := 600;
fi
blacker := 0;
fillin := 0;
o_correction := 1;
enddef;
mode := GBgeneric;
fi
fi
mode_setup;
if debug:
GBdebug;
>> "pixels_per_inch = " & decimal pixels_per_inch;
GBenddebug;
fi
font_identifier := "MFpic graphics";
font_coding_scheme := "Arbitrary";
interim designsize := 128pt#;
if unknown aspect_ratio: aspect_ratio := 1; fi
if unknown hppp: hppp := 1 fi;
if unknown currenttransform:
transform currenttransform;
currenttransform := identity yscaled aspect_ratio;
fi
interim warningcheck := 0;
interim turningcheck := 0;
numeric unitlen, xscale, yscale, xneg, xpos, yneg, ypos;
unitlen := 1 bp#;
xscale := 7.2;
yscale := 7.2;
xneg := 0; xpos := 10;
yneg := 0; ypos := 10;
newinternal deg, pi, radian;
deg := 1; pi := 3.14159;
radian := 57.29578;
numeric degree; degree := deg;
newinternal penwd; penwd := 0.5pt;
pen drawpen;
def resizedrawpen (expr s) =
interim penwd := s;
setvariable (pen) (drawpen) pencircle scaled penwd;
save currentpen; pen currentpen; pickup drawpen;
enddef;
numeric hatchwd; hatchwd := 0.5bp;
pen hatchpen; hatchpen := pencircle scaled hatchwd;
boolean clipall; clipall := false;
boolean ClipOn; ClipOn := false;
path ClipPath[]; numeric ClipPath; ClipPath = 0;
boolean truebbox; truebbox := false;
def DoClip (suffix v) =
if ClipOn and (ClipPath > 0): clipsto (v, ClipPath); fi
enddef;
def noclip (text t) =
hide ( setboolean (ClipOn) false; t)
enddef;
boolean showbbox; showbbox := false;
let color = numeric; color black, white;
let rgbcolor = numeric;
let cmykcolor = numeric;
black := 0; white := 1;
def withcolor text t = enddef;
def _wc_ = withcolor enddef;
color currentcolor, drawcolor, fillcolor, hatchcolor,
headcolor, pointcolor, tlabelcolor, background;
currentcolor := fillcolor := drawcolor := hatchcolor :=
headcolor := pointcolor := tlabelcolor := black;
background := white;
vardef snapto expr t =
if numeric t:
if unknown t: 0
elseif t < 0: 0
elseif t > 1: 1
else: t
fi
else:
GBerrmsg ("Improper expression type.")
"The argument to `snapto' must be a numeric.";
fi
enddef;
vardef rgbgray (expr g) = (snapto g) * white enddef;
vardef cmykgray (expr g) = cmyk(0,0,0,1 - snapto g) enddef;
vardef knowncolor expr clr = (known clr) and (iscolor clr) enddef;
vardef grayscalegray (expr g) = snapto g enddef;
vardef gray (expr g) = grayscalegray (g) enddef;
vardef cmyk (expr c, m, y, k) = rgb (1-c-k, 1-m-k, 1-y-k) enddef;
vardef makegray primary clr =
if knowncolor clr: clr else: black fi
enddef;
def makergb = makegray enddef;
def makecmyk = makegray enddef;
vardef iscolor expr clr = color clr enddef;
vardef forceclr (expr c) =
if unknown c :
if numeric c: grayscaleblack
elseif rgbcolor c: rgbblack
elseif cmykcolor c: cmykblack
else: black
fi
elseif numeric c: gray (c)
elseif iscolor c: c
else: black
fi
enddef;
vardef named (suffix c) = forceclr (c) enddef;
vardef togray (expr r, g, b) =
gray (sqrt((2r*r + 4g*g + b*b)/7))
enddef;
vardef rgbtogray (expr r, g, b) =
togray(snapto r, snapto g, snapto b)
enddef;
vardef cmyktogray (expr c, m, y, k) =
rgbtogray (1-c-k,1-m-k,1-y-k)
enddef;
vardef cmyktorgb (expr c,m,y,k) =
rgb(1-c-k,1-m-k,1-y-k)
enddef;
vardef rgbtocmyk (expr r,g,b) =
cmyk(1-r,1-g,1-b,0)
enddef;
vardef rgb (expr r, g, b) =
togray (snapto r, snapto g, snapto b)
enddef;
vardef RGB (expr R, G, B) =
rgb (R/255, G/255, B/255)
enddef;
def list (suffix v) (text lst) =
v := 0; for _itm = lst: v[incr v] := _itm; endfor
if v = 0:
GBerrmsg ("No list to process!")
"An attempt was made to produce an array from a "
& "list of expressions having no valid entries.";
fi
enddef;
def map (text proc) (text lst) =
hide (_map := 0;)
for _a = lst:
if _map = 0: hide (_map := 1;) else: , fi
proc (_a)
endfor
enddef;
vardef knownnumericarray suffix arr =
setboolean (_kna) (known arr) and (numeric arr);
if _kna :
_kna := (arr = floor arr) and (arr >= 1);
for _idx = 1 upto arr :
exitif not _kna;
_kna := (known arr[_idx]) and (numeric arr[_idx]);
endfor
fi
_kna
enddef;
def copyarray (suffix src, dest) =
for _idx = 1 upto src: dest[_idx] := src[_idx]; endfor
dest := src;
enddef;
def maparr (text proc) (suffix p) =
for _idx = 1 upto p: proc (p[_idx]); endfor
enddef;
def textpairs = gsetarray (pair) enddef;
def setuniquepairs (suffix p) (text t) =
save p; pair p[];
setpairs (_up) (t);
if _up > 0:
p := 1; p1 := _up1;
for _i = 2 upto _up:
if _up[_i] <> p[p]: p[incr p] := _up[_i]; fi
endfor
else:
p := 0;
fi
enddef;
vardef chpair (text proc) (expr p) =
(proc (xpart p), proc (ypart p))
enddef;
vardef floorpair (expr p) = (floor (xpart p), floor (ypart p)) enddef;
vardef ceilingpair (expr p) =
(ceiling (xpart p), ceiling (ypart p))
enddef;
def hroundpair (expr p) = (hround (xpart p), hround (ypart p)) enddef;
vardef goodpair (expr p) = hroundpair(p.t_) enddef;
vardef emin (expr a, b) = if a < b: a else: b fi enddef;
vardef emax (expr a, b) = if a > b: a else: b fi enddef;
vardef pairmin (expr z, w) =
( emin (xpart z, xpart w), emin (ypart z, ypart w ) )
enddef;
vardef pairmax (expr z, w) =
( emax (xpart z, xpart w), emax (ypart z, ypart w ) )
enddef;
vardef minpair (suffix p) = setpair (_mp) p1;
for _idx = 2 upto p - 1: _mp := pairmin (_mp, p[_idx]); endfor
pairmin (_mp, p[p])
enddef;
vardef maxpair (suffix p) = setpair (_mp) p1;
for _idx = 2 upto p - 1: _mp := pairmax (_mp, p[_idx]); endfor
pairmax (_mp, p[p])
enddef;
primarydef Z xprod W = (xpart Z * ypart W - xpart W * ypart Z) enddef;
def force_initial (expr p) (suffix f) =
hide( setnumeric (_n) length f;
f := p
if _n = 0:
{0,0}
else:
..controls post0 (f) and pre 1 (f).. subpath (1,_n) of f
fi;)
enddef;
def force_terminal (expr p) (suffix f) =
hide(setpath (_f) reverse f;
force_initial (p) (_f);
f := reverse _f;)
enddef;
def force_equal_ends (suffix f, g) =
hide(save _p; pair _p;
_p := .5[pnt[length f] (f), pnt0(g)];
force_terminal (_p) (f); force_initial (_p) (g);)
enddef;
def replace_ends_of_cycle (expr p) (suffix f) =
hide(
if cycle f:
save _n; _n := length f;
f := p
if _n = 0: &cycle
else: .. controls post0 (f) and pre 1 (f) ..
if _n = 1: cycle
else: subpath (1, _n - 1) of f ..
controls post[_n - 1](f) and pre[_n](f) .. cycle
fi
fi;
fi)
enddef;
pair thetimes;
numeric _Xtime, _Ytime;
tertiarydef a intersects b =
begingroup
thetimes := a intersectiontimes b;
_Xtime := xpart thetimes;
_Ytime := ypart thetimes;
(_Xtime > -1)
endgroup
enddef;
tertiarydef a misses b = ((a intersectiontimes b) < origin) enddef;
vardef makepicture (expr s) =
if picture s: s
elseif path s: picpath (s)
else: nullpicture
fi
enddef;
vardef onepointpath (expr cyclic, q) =
q if cyclic: &cycle else: {0,0} fi
enddef;
vardef fallbackpath (expr cyclic, p) (text t) =
onepointpath (cyclic, p)
enddef;
def even = not odd enddef;
primarydef a divides b =
((b mod a) = 0)
enddef;
vardef image (text t) =
newpicture (currentpicture);
t;
currentpicture
enddef;
def beginimage =
begingroup
newpicture (currentpicture);
enddef;
def endimage =
; currentpicture
endgroup
enddef;
def makeimage (suffix name) (expr refpt) =
setpair (_image_reference_point) zconv(refpt);
setpicture (name) beginimage
enddef;
def concludeimage =
endimage shifted
-goodpair (_image_reference_point)
enddef;
def setvariable (text kind) (suffix name) =
save name; kind name; name :=
enddef;
def gsetvariable (text kind) (suffix name) = kind name; name :=
enddef;
def setnumeric (suffix name) = save name; name := enddef;
def setboolean = setvariable (boolean) enddef;
def setpair = setvariable (pair) enddef;
def setpath = setvariable (path) enddef;
def setpicture = setvariable (picture) enddef;
def setstring = setvariable (string) enddef;
def settransform = setvariable (transform) enddef;
def setpen = setvariable (pen) enddef;
def settension (suffix tn) expr tens =
setnumeric (tn) if tens > 0: tens else: default_tension fi;
enddef;
def fixtension (suffix tn) = if tn < .75: tn := .75; fi enddef;
def newpicture (suffix pic) = setpicture (pic) nullpicture; enddef;
def convertpath (suffix g) expr f = setpath (g) zconv (f); enddef;
def setarray (text kind) (suffix name) =
save name; kind name[]; list (name)
enddef;
def setpairs = setarray (pair) enddef;
def gsetarray (text kind) (suffix name) =
numeric name; kind name[]; list (name)
enddef;
def setbbox (suffix ll, ur) =
save ll, ur; pair ll, ur; getbbox (ll, ur)
enddef;
def setsplit (suffix s) expr ss =
setnumeric (s) emax (1, ceiling ss);
enddef;
def setrgbcolor = setcolor enddef;
def setcmykcolor = setcolor enddef;
def setcolor = setvariable (color) enddef;
def gsetcolor = gsetvariable (color) enddef;
setcolor(rgbblack) rgb(0,0,0);
setcolor(red) rgb(1,0,0);
setcolor(green) rgb(0,1,0);
setcolor(blue) rgb(0,0,1);
setcolor(rgbwhite) rgb(1,1,1);
setcolor(cmykwhite) cmyk(0,0,0,0);
setcolor(cyan) cmyk(1,0,0,0); % Maybe these should
setcolor(magenta) cmyk(0,1,0,0); % be rbg for backward
setcolor(yellow) cmyk(0,0,1,0); % compatibility?
setcolor(cmykblack) cmyk(0,0,0,1);
setcolor(grayscaleblack) gray(0);
setcolor(grayscalewhite) gray(1);
def setoutputtemplate text garbage = enddef;
def romannumeral = _romannumeral (true) enddef;
vardef _romannumeral (expr prefix, X) =
save Y, _tmp, U; string U;
Y.m := X div 1000; % thousands digit
_tmp := X - 1000Y.m; % hundreds digits and lower
Y.c := _tmp div 100; % hundreds
_tmp := _tmp - 100Y.c; % tens and units
Y.x := _tmp div 10; % tens
Y.i := _tmp - 10Y.x; % units
strrepeat("m", Y.m) &
romandigit(prefix, "c", "d", "m", Y.c) &
romandigit(prefix, "x", "l", "c", Y.x) &
romandigit(prefix, "i", "v", "x", Y.i)
enddef;
vardef romandigit (expr prefix, bot, mid, top, n) =
if n > 9 : top & strrepeat(bot, n-10) % shouldn't happen
elseif n > 8 :
if prefix: bot & top % "ix"
else: mid & bot & bot & bot & bot % "viiii"
fi
elseif n > 4 : mid & strrepeat (bot, n-5) % "v"--"viii"
elseif n > 3 :
if prefix: bot & mid % "iv"
else: bot & bot & bot & bot % "iiii"
fi
else: strrepeat (bot, n) % ""--"iii" for 0--3
fi
enddef;
vardef strrepeat (expr st, rep) =
setstring (_sr) "";
for i = 1 upto rep: _sr := _sr & st; endfor
_sr
enddef;
transform ztr, vtr;
def setztr =
if debug:
GBdebug;
>> "charwd = " & decimal charwd & "pt#";
>> "charht = " & decimal charht & "pt#";
>> "w_ = " & decimal w_ & " pixels";
>> "h_ = " & decimal h_ & " pixels";
>> "unitlen = " & decimal unitlen & "pt#";
>> "hppp = " & decimal hppp;
>> "xneg = " & decimal xneg;
>> "xpos = " & decimal xpos;
>> "yneg = " & decimal yneg;
>> "ypos = " & decimal ypos;
>> "xscale = " & decimal xscale;
>> "yscale = " & decimal yscale;
GBenddebug;
fi
save ztr, vtr;
transform ztr, vtr;
vtr := identity xscaled xscale yscaled yscale scaled (unitlen*hppp);
ztr := identity shifted (-xneg, -yneg) transformed vtr;
if debug:
GBdebug;
>> "ztr is";
show ztr;
>> "vtr is";
show vtr;
GBenddebug;
fi
enddef;
vardef zconv (expr a) = a transformed ztr enddef;
vardef invzconv (expr a) = a transformed (inverse ztr) enddef;
vardef vconv (expr v) = v transformed vtr enddef;
vardef invvconv (expr v) = v transformed (inverse vtr) enddef;
def active_plane = currentpicture enddef;
def initpic =
setztr;
resizedrawpen (penwd);
if ClipOn: ClipPath := 1;
ClipPath1 := rect (origin, (w_, h_));
fi
if debug:
GBdebug;
>> "Drawing nominal bounding box around picture";
GBenddebug;
noclip ( safedraw rect (origin, (w_, h_)) );
fi
enddef;
def mfpicenv = enddef;
def endmfpicenv = enddef;
def bounds (expr a, b, c, d) =
xneg := a; xpos := b;
yneg := c; ypos := d;
enddef;
string extra_beginmfpic; extra_beginmfpic := "";
string extra_endmfpic; extra_endmfpic := "";
def beginmfpic (expr ch) =
begingroup
gcode := ch;
save w_, h_, d_;
charwd := (xpos-xneg)*xscale*unitlen;
charht := (ypos-yneg)*yscale*unitlen;
chardp := 0;
charcode := if known ch: byte ch else: 0 fi;
w_ := hround (charwd*hppp);
h_ := vround (charht*hppp);
d_ := vround (chardp*hppp);
charic := 0; clearxy; clearit; clearpen;
scantokens extra_beginchar;
initpic;
scantokens extra_beginmfpic;
enddef;
def endmfpic =
scantokens extra_endmfpic;
if debug:
GBdebug;
>> "TFM charwd = " & decimal charwd & "pt#";
>> "TFM charht = " & decimal charht & "pt#";
GBenddebug;
fi
DoClip (active_plane);
if clipall: clipto (active_plane) rect (origin, (w_, h_)); fi
if showbbox: noclip ( safedraw rect (origin, (w_, h_)) ); fi
scantokens extra_endchar;
if proofing > 0: makebox (proofrule); fi
chardx := w_; % desired width of character in pixels
shipit;
if displaying > 0: makebox (screenrule); showit; fi
endgroup
enddef;
pair label_adjust;
label_adjust := origin;
numeric label_sep, labelpath_sep ;
label_sep := 0; labelpath_sep := 0;
def verbatimtex text t = enddef;
vardef newgblabel (expr hf, vf, BL, r) (text s) (text pts) =
enddef;
vardef gblabel (expr a, b, c, d, r) (text s) (text t) =
newgblabel (b, d, (c = 0) and (d = 0), r) (s) (t);
enddef;
vardef ref_shift (expr hf, vf, BL, ll, ur) =
- ( (hf)[xpart ll, xpart ur],
(vf)[if BL: 0 else: (ypart ll) fi, ypart ur] )
enddef;
vardef thegblabel (expr z, r, p) =
((p shifted z) rotated r) shifted label_adjust
enddef;
vardef textrect (expr lbl, rad, loc) =
textrectx (.5, .5, false, 0) (origin, lbl, rad, loc)
enddef;
vardef textoval (expr lbl, mult, loc) =
xellipse (true, .5, .5, false, 0) (origin, lbl, mult, loc)
enddef;
vardef textellipse (expr lbl, rat, loc) =
xellipse (false, .5, .5, false, 0) (origin, lbl, rat, loc)
enddef;
boolean roundends; roundends := true;
vardef textrectx (expr a, b, c, rot, xy, lbl, rad, loc) =
save ll, ur, _r, f, zz;
pair ll, ur, zz; path f;
pathdims (xy, lbl) (ll, ur);
readjustdims (ll, ur) (labelpath_sep)
_r := if numeric rad: rad
elseif not boolean rad: 0
elseif rad: emin (xpart(ur-ll), ypart (ur-ll))/sqrt(2)
else: 0
fi;
if _r = 0:
f := rect (ll, ur);
else:
save p, q;
pair p[]; path q;
p1 := ur - _r*dir(45);
p3 := ll + _r*dir(45);
p2 := (xpart p3, ypart p1);
p4 := (xpart p1, ypart p3);
q := if _r < 0: reverse fi quartercircle scaled 2_r;
f :=
(q shifted p1)--(q rotated 90 shifted p2)
--(q rotated 180 shifted p3)
--(q rotated -90 shifted p4)--cycle;
fi
readjustdims (ll, ur) (label_sep - labelpath_sep);
invvconv (thegblabel (ref_shift(a, b, c, ll, ur), rot, f)) shifted loc
enddef;
def textovalx = xellipse (true) enddef;
def textellipsex = xellipse (false) enddef;
vardef xellipse (expr aspect, a, b, c, r, xy, lbl, mult, loc) =
if mult = 0:
textrectx (a, b, c, r) (xy, lbl, 0, loc)
else:
save ll, ur, cc, ww, hh, f;
pair ll, ur, cc; path f;
pathdims (xy, lbl) (ll, ur);
readjustdims (ll, ur) (labelpath_sep)
cc := .5[ll, ur];
(ww, hh) = ur - cc;
if (ww = 0) or (hh = 0):
f = (ll--ur);
else:
save aa, bb;
aa := ww ++ if aspect: ww else: hh fi *mult;
bb := hh ++ if aspect: hh else: ww fi /mult;
f := ellipse (cc, aa, bb, 0);
fi
readjustdims (ll, ur) (label_sep - labelpath_sep);
invvconv (thegblabel (ref_shift(a, b, c, ll, ur), r, f)) shifted loc
fi
enddef;
def pathdims (expr xy, lbl) (suffix ll, ur) =
if pair lbl:
ll := xy; ur := lbl;
else:
ll := ur := origin;
fi
enddef;
def readjustdims (suffix ll, ur) (expr s) =
ll := ll - s*(1,1);
ur := ur + s*(1,1);
enddef;
newinternal reallysmall; reallysmall := 3epsilon;
newinternal nottoosmall; nottoosmall := eps/2 + 2epsilon;
def signof (expr X) = if X < 0: - fi enddef;
def TruncateWarn expr s =
GBwarn s & " is too large or undefined, so it will be truncated.";
enddef;
vardef secd primary X =
setnumeric (temp) cosd(X);
if abs(temp) < reallysmall:
TruncateWarn "Secant or Tangent";
temp := signof (temp) reallysmall;
fi
1/temp
enddef;
vardef tand primary X = sind(X)*secd(X) enddef;
vardef cscd primary X =
setnumeric (temp) sind(X);
if abs(temp) < reallysmall:
TruncateWarn "Cosecant or Cotangent";
temp := signof(temp) reallysmall;
fi
1/temp
enddef;
vardef cotd primary X = cosd(X)*cscd(X) enddef;
vardef acos primary X =
if abs X > 1:
TruncateWarn "Argument of arccosine";
angle (signof(X) 1, 0)
else:
angle (X, 1 +-+ X)
fi
enddef;
vardef asin primary X =
if abs X > 1:
TruncateWarn "Argument of arcsine";
angle (0, signof(X) 1)
else:
angle (1 +-+ X, X)
fi
enddef;
vardef atan primary X = angle (1, X) enddef;
vardef sin primary X = sind (X*radian) enddef;
vardef cos primary X = cosd (X*radian) enddef;
vardef tan primary X = tand (X*radian) enddef;
vardef cot primary X = cotd (X*radian) enddef;
vardef sec primary X = secd (X*radian) enddef;
vardef csc primary X = cscd (X*radian) enddef;
vardef degrees (expr t) = t*radian enddef;
vardef radians (expr t) = t/radian enddef;
vardef invcos primary X = (acos X)/radian enddef;
vardef invsin primary X = (asin X)/radian enddef;
vardef invtan primary X = (atan X)/radian enddef;
vardef exp primary X = mexp (256 * X) enddef;
vardef ln primary X = (mlog X) / 256 enddef;
def log = ln enddef;
vardef logbase (expr B) primary X = (mlog X)/(mlog B) enddef;
def logtwo = logbase( 2) enddef;
def logten = logbase(10) enddef;
vardef cosh primary X =
setnumeric (temp) 2 exp (-abs(X));
if temp < reallysmall:
TruncateWarn "Cosh";
temp := reallysmall;
fi
1/temp + temp/4
enddef;
vardef sinh primary X =
setnumeric (temp) 2 exp (-abs(X));
if temp < reallysmall:
TruncateWarn "Sinh";
temp := reallysmall;
fi
signof (X) (1/temp - temp/4)
enddef;
vardef sech primary X =
setnumeric (temp) exp(-(abs (X)));
2temp/(1 + temp*temp)
enddef;
vardef tanh primary X =
setnumeric (temp) exp(-2(abs (X)));
signof (X) (1 - temp)/(1 + temp)
enddef;
vardef csch primary X =
save temp, tempa; temp := exp(-(abs (X)));
tempa := (1 - temp*temp)/2;
if tempa < reallysmall:
TruncateWarn "Csch";
tempa := reallysmall;
fi
signof (X) temp / tempa
enddef;
vardef coth primary X =
setnumeric (temp) tanh(X);
if abs(temp) < reallysmall:
TruncateWarn "Coth";
temp := signof (X) reallysmall;
fi
1/temp
enddef;
vardef acosh primary y =
if y < 1:
TruncateWarn "acosh";
0
else:
ln (y + (y +-+ 1))
fi
enddef;
vardef asinh primary y = ln (y + (y ++ 1)) enddef;
vardef atanh primary y =
if abs (y) < 1:
(ln (1 + y) - ln (1 - y))/2
else:
TruncateWarn "atanh";
signof (y) infinity
fi
enddef;
vardef Arg primary Z = (angle Z)/radian enddef;
vardef Log primary Z = (ln (abs Z), Arg Z) enddef;
vardef cis primary T = dir (T*radian) enddef;
vardef zexp primary Z = (exp (xpart Z)) * cis (ypart Z) enddef;
vardef sgn primary Z = if not (Z = origin): unitvector fi Z enddef;
vardef conj primary Z = (xpart Z, -ypart Z) enddef;
vardef Moebius (expr A) primary Z =
save _D; pair _D;
_D := (1, 0) + (Z zscaled (conj A));
(Z + A)/(abs _D) rotated (- angle _D)
enddef;
vardef pshdist (expr Z,W) = abs(Moebius(-W)(Z)) enddef;
vardef polar primary p = (xpart p) * dir (ypart p) enddef;
def id (expr x) = x enddef;
primarydef x**y =
if y=2: x*x
elseif (x = floor x) and (abs y = floor y):
1 for n=1 upto y: *x endfor
else: takepower y of x
fi
enddef;
let ^ = **;
transform T_stack[];
numeric T_stack; T_stack := 0;
def T_push (expr T) = T_stack[incr T_stack] := T; enddef;
def T_pop (suffix $) =
if T_stack > 0:
$ := T_stack[T_stack];
T_stack := T_stack - 1;
fi
enddef;
def bcoords = hide ( T_push (ztr) ) enddef;
def ecoords = hide ( T_pop (ztr); vtr := vectorpart ztr ) enddef;
vardef vectorpart primary T = T shifted -(origin transformed T) enddef;
def apply_t (text Transformer) =
ztr := identity Transformer transformed ztr;
vtr := vectorpart ztr;
enddef;
def xslant = slanted enddef; % (x+sy, y).
def yslant primary s = % (x, y+sx).
transformed
begingroup
save T; transform T;
origin transformed T = origin;
(1, 0) transformed T = (1, s);
(0, 1) transformed T = (0, 1);
T
endgroup
enddef;
def zslant primary p = % (xu+yv, xv+yu), where p = (u, v).
transformed
begingroup
save T; transform T;
xpart T = ypart T = 0;
xxpart T = yypart T = xpart p;
xypart T = yxpart T = ypart p;
T
endgroup
enddef;
def xyswap = zslant (0, 1) enddef;
def boost primary X = zslant (cosh X, sinh X) enddef;
vardef transformedpath (text Transformer) expr f = f Transformer
enddef;
def rotatedpath (expr p, th) =
transformedpath (
transformed vtr
rotatedaround (p transformed vtr, th)
transformed (inverse vtr)
)
enddef;
def reflectedpath (expr p, q) =
transformedpath (
transformed vtr
reflectedabout (p transformed vtr, q transformed vtr)
transformed (inverse vtr)
)
enddef;
def scaledpath (expr p, s) =
transformedpath (shifted -p scaled s shifted p)
enddef;
def xscaledpath (expr a, s) =
transformedpath (shifted (-a, 0) xscaled s shifted (a, 0))
enddef;
def yscaledpath (expr b, s) =
transformedpath (shifted (0, -b) yscaled s shifted (0, b))
enddef;
def slantedpath = xslantedpath enddef;
def xslantedpath (expr b, s) =
transformedpath (shifted (0, -b) slanted s shifted (0, b))
enddef;
def yslantedpath (expr a, s) =
transformedpath (shifted (-a, 0) yslant s shifted (0, a))
enddef;
def shiftedpath (expr v) = transformedpath (shifted v) enddef;
def xyswappedpath = transformedpath (xyswap) enddef;
vardef partialpath (expr a, b) expr f =
save flag, flo, fhi, lo, hi, n;
boolean flag; flag = true;
convertpath (g) f;
n := length f;
flo := snapto emin(a,b);
if flo = 0:
lo := 0;
elseif flo < 1:
setuplengtharray (cum, tot, idx) g;
flag := false;
lo := gettime (cum, idx) (flo*tot);
else:
lo := n;
fi
fhi := snapto emax (a,b);
if flo = fhi:
hi := lo;
elseif fhi < 1:
if flag: setuplengtharray (cum, tot, idx) g; fi
hi := gettime (cum, idx) (fhi*tot);
else:
hi := n;
fi
if a > b: reverse fi subpath (lo, hi) of f
enddef;
vardef gsubpath (expr a, b) expr f = subpath (a, b) of f enddef;
def setuplengtharray (suffix cum, tot, idx) =
save cum, tot, idx; idx := 0; tot := makelengtharray (cum)
enddef;
vardef pathtime@# (suffix p) =
if @# <= 0: 0
elseif @# >= 1: length p
else:
setuplengtharray (cum, tot, idx) p;
gettime (cum, idx) (@#*tot)
fi
enddef;
vardef pathpoint (expr frac) (suffix p) =
convertpath (_pp) p; pnt[pathtime[frac] (_pp)] (p)
enddef;
def mono (suffix u) = cull u keeping (1, infinity); enddef;
def andto (suffix u) (expr v) =
mono (u); addto u also v; cull u keeping (2, 2);
enddef;
primarydef u picand v =
begingroup setpicture (t) u; andto (t, v); t endgroup
enddef;
def orto (suffix u) (expr v) =
mono (u); addto u also v; cull u keeping (1, infinity);
enddef;
primarydef u picor v =
begingroup setpicture (t) u; orto (t, v); t endgroup
enddef;
def xorto (suffix u) (expr v) =
mono (u); addto u also v; cull u keeping (1, 1);
enddef;
primarydef u picxor v =
begingroup setpicture (t) u; xorto (t, v); t endgroup
enddef;
def subto (suffix u) (expr v) =
mono (u); addto u also -v; cull u keeping (1, infinity);
enddef;
primarydef u picsub v =
begingroup setpicture (t) u; mono (t); subto (t, v); t endgroup
enddef;
def coloraddto (expr clr) (suffix u) (expr v) =
if clr < white:
orto (u, v);
else:
subto (u, v);
fi;
enddef;
def coloraddon (expr clr) (suffix v) =
if clr < white:
_orto (active_plane, v);
else:
_subto (active_plane, v);
fi;
enddef;
def _orto (suffix u, v) =
mono (u); mono (v);
addto u also v;
cull u keeping (1, 2);
enddef;
def _subto (suffix u, v) =
mono (u); mono (v); addto u also -v; cull u keeping (1, 1);
enddef;
vardef interior expr c =
newpicture (v);
addto v contour (c.t_);
cull v dropping (0,0);
v
enddef;
vardef interiors suffix cc =
newpicture (_ints);
for _idx = 1 upto cc:
addto _ints also interior cc[_idx]);
endfor
mono (_ints);
_ints
enddef;
def clipto (suffix vt) expr c =
if path c:
andto (vt, interior c);
fi
enddef;
def clipsto (suffix vt, cc) =
andto (vt, interiors cc);
enddef;
vardef Clipped (suffix vt) expr c =
setpicture (_Cl) vt; clipto (_Cl) c; _Cl
enddef;
def clip = Clipped enddef;
vardef picneg (suffix vt) expr c =
setpicture (_pn) interior c;
_subto (_pn, vt);
_pn
enddef;
def shpath (suffix v) (expr q, f) =
addto v doublepath (f.t_) withpen (q.t_);
enddef;
numeric minpenwd;
minpenwd := 1; % 1 pixel
vardef picpath expr d =
newpicture (v);
if penwd >= minpenwd:
shpath (v, drawpen) (d);
mono (v);
fi
v
enddef;
def picdot (suffix v) (expr w, p) =
addto v also
(w shifted goodpair (p));
enddef;
vardef setdot (expr apath, sc) =
if cycle apath: interior
else: picpath
fi
(apath scaled emax (ceiling (sc), minpenwd))
enddef;
numeric shadepicsize; shadepicsize := 0.8bp;
vardef shadepic (suffix dims) (expr grparam) =
pair dims;
setnumeric (_frac) 2*emin (grparam, 1 - grparam);
save _hp, _vp, _dotwd, _dotht;
if aspect_ratio < 1:
_vp := emax (2, hround (shadepicsize.o_));
_hp := hround (_vp._o_);
_dotwd := hround (_hp*sqrt _frac);
_dotht := if _dotwd = 0: 0
else: hround (_hp*_vp*_frac/_dotwd)
fi;
else:
_hp := emax (2, hround (shadepicsize));
_vp := hround (_hp.o_);
_dotht := hround (_vp*sqrt _frac);
_dotwd := if _dotht = 0: 0
else: hround (_hp*_vp*_frac/_dotht)
fi;
fi
dims := ( _hp, _vp._o_ );
newpicture (_shp);
addto _shp contour rect (origin, (_dotwd, _dotht));
picdot (_shp, _shp, dims);
dims := 2dims; mono (_shp);
if grparam >= .5: _shp
else: (interior (rect (origin, dims))) picsub _shp
fi
enddef;
vardef shaded (expr clr) expr c =
if cycle c:
if (clr <= black) or (clr >= white):
interior c
else:
save shdims, shpic;
picture shpic; pair shdims;
shpic := shadepic (shdims) (clr);
setbbox (ll, ur) c;
newpicture (vsh);
fillwith (vsh) (shpic, shdims, ll, ur);
clipto (vsh) c; vsh
fi
else: picpath c % should we? or just make it null?
fi
enddef;
vardef fillwith (suffix v) (expr pic, dims, ll, ur) =
newpicture (b);
save fwdims, _ll, _ur; pair fwdims, _ll, _ur;
fwdims := goodpair (dims);
_ll := floorpair (ll.t_);
_ur := ur.t_;
for s = xpart _ll step xpart fwdims until xpart _ur:
addto b also pic shifted (s, 0);
endfor
for s = ypart _ll step ypart fwdims until ypart _ur:
addto v also b shifted (0, s);
endfor
mono (v);
enddef;
def thatchf (suffix v) (expr CT, sp, a, b) =
begingroup
setnumeric (_sp) signof (ypart b - ypart a) abs(sp);
for _y = _sp*( ceiling ((ypart a)/_sp) ) step _sp until ypart b:
shpath (v, hatchpen)
( ( (xpart a, _y)--(xpart b, _y) ) transformed CT );
endfor
mono (v);
endgroup
enddef;
def tile (suffix atile) (expr unit, width, height, clipit) =
picture atile.pic; atile.pic := nullpicture;
pair atile.dims;
atile.dims := round ((width, height)*unit);
begingroup
save active_plane;
def active_plane = atile.pic enddef;
save ztr, vtr; transform ztr, vtr;
ztr := identity scaled unit; vtr := ztr;
save xneg, xpos, yneg, ypos;
xneg := 0; xpos := width; yneg := 0; ypos := height;
save ClipOn; boolean ClipOn;
if clipit:
ClipOn := true;
setarray (path) (ClipPath) (rect(origin, atile.dims));
else:
ClipOn := false;
fi
enddef;
def endtile =
DoClip (active_plane);
endgroup
enddef;
vardef is_tile (suffix atile) =
(known atile.pic ) and (picture atile.pic) and
(known atile.dims) and (pair atile.dims )
enddef;
vardef pnt@# (expr p) = point @# of p enddef;
vardef pre@# (expr p) = precontrol @# of p enddef;
vardef post@# (expr p) = postcontrol @# of p enddef;
def getbbox (suffix ll, ur) expr g =
setsplit (_s) bbox_split;
ur := ll := pnt 0 (g);
for _j = 1 upto length g:
ll := pairmin (ll, pnt[_j] (g)); ur := pairmax (ur, pnt[_j] (g));
endfor
for _j = 1 upto _s*(length g):
ctrlsbbox (subpath ((_j-1)/_s, _j/_s) of g) (ll, ur);
endfor
if showbbox: noclip ( safedraw rect (ll, ur) ); fi
enddef;
numeric bbox_split; bbox_split := 2;
def ctrlsbbox (expr p) (suffix ll, ur) =
ll := pairmin ( pairmin (ll, post0 (p)), pre 1 (p) );
ur := pairmax ( pairmax (ur, post0 (p)), pre 1 (p) );
enddef;
def safedraw = colorsafedraw (drawcolor) enddef;
def colorsafedraw (expr clr) expr d =
begingroup
setpicture (v) picpath d;
DoClip (v); coloraddon (clr, v);
endgroup
enddef;
def NoCycle (expr s) expr p =
GBwarn s & " cannot be applied to an open path."
& " The path will be drawn instead.";
safedraw p;
enddef;
vardef isgray (expr X) = (X > black) and (X < white) enddef;
def safefill = colorsafefill (fillcolor) enddef;
vardef colorsafefill (expr clr) expr c =
if cycle c:
setpicture (v) interior c;
DoClip (v);
if isgray (clr):
_subto (active_plane) (v);
v := nullpicture;
v := shaded (clr) c;
fi
coloraddon (clr, v);
else: NoCycle("fill") c;
fi
enddef;
def safeunfill expr c =
if cycle c: noclip (colorsafefill (background) c);
else: NoCycle("unfill") c;
fi
enddef;
def safeclip expr c =
if cycle c: clipto (active_plane) c;
else: NoCycle("clip") c;
fi
enddef;
def store (suffix fs) expr f =
hide (
if (not path f) and (not pair f):
GBerrmsg ("Improper expression type.")
"The second argument to `store' must be a path or pair.";
fi
if not path fs: path fs; fi
fs := f
)
enddef;
vardef stored (suffix fs) expr f = store (fs) f; f enddef;
def drawn = colordrawn (drawcolor) enddef;
vardef colordrawn (expr clr) expr f =
colorsafedraw (clr) (zconv (f)); f
enddef;
def zigzag = colorzigzag (drawcolor) enddef;
def colorzigzag (expr clr) = colorwiggle (false, clr, 0) enddef;
def sinewave = colorsinewave (drawcolor) enddef;
def colorsinewave = colorwiggle (true) enddef;
vardef colorwiggle (expr smth, clr, tens, blen, elen, len, wid) expr f =
convertpath (g) f;
setuplengtharray (cumlen, totlen, ct) g;
save B;
if cycle f:
B := 0;
else:
B := abs(blen)/_rescale_factor;
totlen := totlen - B - abs(elen)/_rescale_factor;
fi
setnumeric (n) 2*round (totlen/len*_rescale_factor);
if n < 2:
colorsafedraw (clr) g;
else:
save T, U, X, Y, Z, p;
pair U, X, Y, Z; path p;
T := if cycle f: 0 else: gettime (cumlen, ct) (B) fi;
Z := pnt[T] (g);
p :=if not cycle f: (subpath (0,T) of g)
if smth: {curl 0} ..tension tens.. else: -- fi
fi
for i = 1 upto n:
hide(
T := gettime (cumlen, ct) (B+(i/n)*totlen);
X := Z; Z := pnt[T] (g);
Y := .5[X,Z]; U := sgn (Z-X);
)
(Y + (U zscaled (0, if even i: - fi wid)))
if smth: {U}..tension tens.. else: -- fi
endfor
if cycle f: cycle
else: if smth: {curl 0} fi (subpath (T, length g) of g)
fi;
newpicture (v);
if smth:
save n, k;
n := length p; k = n div 50;
for i = 0 step 50 until 50*(k-1):
shpath (v, drawpen) (subpath (i,i+50) of p);
endfor
shpath (v, drawpen) (subpath (50k,n) of p);
else: shpath (v, drawpen) (p);
fi
DoClip(v); coloraddon (clr, v);
fi
f
enddef;
def corkscrew = colorcorkscrew (drawcolor) enddef;
vardef colorcorkscrew (expr clr, tens, blen, elen, len, wid) expr f =
convertpath (g) f;
setuplengtharray (cumlen, totlen, ct) g;
save B;
if cycle f:
B := 0;
else:
B := abs(blen)/_rescale_factor;
totlen := totlen - B - abs(elen)/_rescale_factor;
fi
setnumeric (n) round (totlen/len*_rescale_factor);
if n < 2:
colorsafedraw (clr) g;
else:
save T, U, X, Y, Z, p;
pair U, X, Y, Z; path p;
T := if cycle f: 0 else: gettime (cumlen, ct) (B) fi;
Z := pnt[T] (g);
p :=if (not cycle f) and (B > 0): (subpath (0,T) of g)-- fi
for i = 1 upto n:
hide(
T := gettime (cumlen, ct) (B+(i/n)*totlen);
X := Z; Z := pnt[T] (g);
Y := .5[X,Z]; U := sgn (Z-X);
)
(X + (U zscaled (0,-wid))){ U}..tension tens..
(Y + (U zscaled (0, wid))){-U}..tension tens..
endfor
if cycle f: cycle
else:
{U}(Z + (U zscaled (0,-wid)))
if elen <> 0: --(subpath(T, length g) of g) fi
fi;
newpicture (v);
save n, k;
n := length p; k = n div 50;
for i = 0 step 50 until 50*(k-1):
shpath (v, drawpen) (subpath (i,i+50) of p);
endfor
shpath (v, drawpen) (subpath (50k,n) of p);
DoClip(v); coloraddon (clr, v);
fi
f
enddef;
def filled = colorfilled (fillcolor) enddef;
vardef colorfilled (expr clr) expr c =
colorsafefill (clr) zconv (c); c
enddef;
vardef unfilled expr c = safeunfill zconv (c); c enddef;
vardef Clip expr c = safeclip zconv (c); c enddef;
numeric shadewd; shadewd := 0.5bp;
path shadedotpath;
shadedotpath := fullcircle;
vardef shade (expr sp) expr f =
convertpath (g) f;
setnumeric (gr) 1 - (.88*abs(shadewd)/sp)**2;
if not cycle g: NoCycle("shade") g;
elseif gr <= 0: safefill g;
else:
setbbox (ll, ur) g;
ll := floorpair (ll);
% setpair (dv) ceiling (sp/(sqrt 2))*(1,1);
% test hex spacing:
setpair (dv) ( ceiling(.5sp), ceiling(.5sp*sqrt 3) );
setpicture (sh) setdot (shadedotpath, abs(shadewd));
newpicture (v);
fillwith (v) (sh, 2dv, ll, ur);
newpicture (w);
addto w also v shifted goodpair (dv);
DoClip (v); DoClip (w);
clipto (v) (g); clipto (w) (g);
_orto (active_plane, v);
v := nullpicture;
_orto (active_plane, w);
fi
f
enddef;
polkadotwd := 5bp;
mindotspace := 1bp;
path polkadotpath; polkadotpath := fullcircle;
vardef polkadot (expr sp) expr f =
convertpath (g) f;
if not cycle g: NoCycle("polkadot") g;
elseif sp <= emax (2*polkadotwd/3, mindotspace):
safefill g;
else:
setbbox (ll, ur) g;
save dx, dy, dshift; pair dshift;
dx := sp/2; dy := dx*sqrt 3;
dshift := (xpart(ur - ll) mod dx, ypart (ur - ll) mod dy)/2;
save p, dims; pair p, dims;
p := ll + dshift;
dims := 2(dx, dy);
setpicture (thepolkadot) setdot (polkadotpath, polkadotwd);
newpicture (v);
fillwith (v) (thepolkadot, dims, p, ur);
fillwith (v) (thepolkadot, dims, p + (dx, dy), ur);
DoClip (v); clipto (v) g;
if isgray (fillcolor):
_subto (active_plane) (v);
v := nullpicture;
thepolkadot :=
shaded (fillcolor) polkadotpath scaled ceiling (polkadotwd);
fillwith (v) (thepolkadot, dims, p, ur);
fillwith (v) (thepolkadot, dims, p + (dx, dy), ur);
DoClip (v); clipto (v) g;
fi
coloraddon (fillcolor, v);
fi
f
enddef;
def thatch = colorthatch (hatchcolor) enddef;
vardef colorthatch (expr clr) (expr sp, theta) expr f =
convertpath (g) f;
if not cycle g: NoCycle("hatch") g;
elseif sp <= abs(hatchwd): colorsafefill (clr) g;
else:
newpicture (v);
setbbox (ll, ur) g rotated -theta;
thatchf (v, identity rotated theta, sp, ll, ur);
DoClip (v); clipto (v) (g);
coloraddon (clr, v);
fi
f
enddef;
def hhatch (expr sp) = thatch (sp, 0) enddef;
def vhatch (expr sp) = thatch (sp, 90) enddef;
def lhatch (expr sp) = thatch (sp, -45) enddef;
def rhatch (expr sp) = thatch (sp, 45) enddef;
def xhatch = colorxhatch (hatchcolor) enddef;
def colorxhatch (expr clr, sp) =
colorthatch (clr) (sp, 45) colorthatch (clr) (sp, -45)
enddef;
vardef NoTile (suffix atile) expr g =
GBwarn str atile & " is not a valid tile for tess()."
& " The path will be drawn instead.";
safedraw g;
enddef;
vardef tess (suffix atile) expr c =
convertpath (_g) c;
if not cycle _g: NoCycle("tess") _g;
elseif not is_tile (atile): NoTile (atile) _g;
else:
setbbox (_ll, _ur) _g;
newpicture (_ts);
fillwith (_ts) (atile.pic, atile.dims, _ll, _ur);
DoClip (_ts); clipto (_ts) _g;
_orto (active_plane, _ts);
fi
c
enddef;
if unknown segment_split: segment_split := 8; fi
if unknown dashsize: dashsize := 3bp; fi
if unknown dashgap: dashgap := dashsize + 2penwd; fi
if unknown dash_finish: dash_finish := .5; fi
if unknown dash_start: dash_start := .5; fi
if unknown _rescale_factor: _rescale_factor := 0.1in; fi
numeric last_dot_size; last_dot_size := 0;
vardef gendashed (suffix pat) expr f =
convertpath (_g) f;
save _dpat;
if not mkdasharrays (pat) (_dpat):
GBwarn "Dash pattern " & str pat
& " undefined. Path will be drawn instead.";
safedraw _g;
elseif _dpat.rep < 2:
safedraw _g;
else:
save _dl;
forsuffixes _s = start, rep, finish:
_dl._s := 0;
for i = 1 upto _dpat._s:
_dpat._s[i] := _dpat._s[i]/_rescale_factor;
_dl._s := _dl._s + _dpat._s[i];
endfor
endfor
if _dl.rep = 0:
GBwarn "Dash pattern " & str pat & " has length 0. "
& "Path will be drawn instead.";
safedraw _g;
else:
setuplengtharray (_cumlen, _totlen, _ct) _g;
save _n, _sf, _no_dots;
boolean _no_dots; _no_dots := true;
_sf := scale_adjust (_n, _dl) (_totlen);
if _n < 0: safedraw _g;
else:
forsuffixes _s = start, rep, finish:
for _i = 1 upto _dpat._s:
if (_dpat._s[_i] = 0) and _no_dots: _no_dots := false;
else: _dpat._s[_i] := _dpat._s[_i]*_sf;
fi
endfor
_dl._s := _dl._s*_sf;
endfor
if _no_dots:
else:
if unknown plot_pic:
save plot_pic; path plot_pic;
plot_pic := dotpath;
fi;
last_dot_size :=
if known plot_pic.size: plot_pic.size else: penwd fi;
setpicture (dashingdot) makesymbol (plot_pic, last_dot_size);
fi
save _t, _d, _v;
picture _v; _v := nullpicture;
_d0 := 0; _t0 := 0;
dashit (_dpat.start) (_v);
if _n > 0:
save _m; _m := ceiling sqrt(_n);
for _j = 0 step _m until _n - 1:
for _i = 0 upto _m - 1:
exitif (_i + _j) > _n - 1;
_d0 := _dl.start + (_j + _i)*_dl.rep;
_t0 := gettime (_cumlen, _ct) (_d0);
dashit (_dpat.rep) (_v);
endfor
DoClip (_v);
coloraddon (drawcolor, _v);
_v := nullpicture;
endfor
fi
_d0 := _totlen - _dl.finish;
_t0 := gettime (_cumlen, _ct) (_d0);
dashit (_dpat.finish) (_v);
DoClip (_v);
coloraddon (drawcolor, _v);
fi
fi
fi
f
enddef;
vardef makelengtharray (suffix clen) suffix p =
setsplit (_s) segment_split;
numeric clen[];
clen := _s * length p; clen0 := 0;
for _i = 1 upto clen:
clen[_i] := clen[_i-1] + abs (pnt[_i/_s] (p) - pnt[(_i-1)/_s] (p)) /
_rescale_factor;
endfor
clen[clen]
enddef;
vardef scale_adjust (suffix n, pl) (expr lngth) =
n := (lngth - pl.start - pl.finish)/pl.rep;
n := if n < 0: -1 else: round(n) fi;
lngth/(pl.start + emax (n, 0)*pl.rep + pl.finish)
enddef;
vardef gettime (suffix arr, ct) (expr lngth) =
setnumeric (_gtl) emax (arr[ct], emin (arr[arr], lngth));
setsplit (_s) segment_split;
forever: exitif ( (arr[ct] <= _gtl) and (_gtl <= arr[ct+1]) );
next ct;
endfor
if arr[ct] = arr[ct+1]: ct
else: ( ct + (_gtl - arr[ct]) / (arr[ct+1] - arr[ct]) )
fi /_s
enddef;
def next suffix X = X := X + 1; enddef;
def dashit (suffix pos) (suffix pic) =
for _k = 1 upto pos:
if odd _k:
if pos[_k] = 0:
_d1 := _d0; _t1 := _t0;
picdot (pic, dashingdot, pnt [_t0] (_g));
else:
_d1 := _d0 + pos[_k];
_t1 := gettime (_cumlen, _ct) (_d1);
shpath (pic, drawpen) (subpath (_t0, _t1) of _g);
fi
else:
_d0 := _d1 + pos[_k];
_t0 := gettime (_cumlen, _ct) (_d0);
fi
endfor
enddef;
def dashpat (suffix pat) (text t) =
list (pat) (t);
if (pat = 0) or (odd (pat) and (pat > 1)):
pat[incr pat] := 0;
fi
enddef;
vardef mkdasharrays (suffix src, dest) =
save _bad; boolean _bad; _bad := false;
forsuffixes _s = start, rep, finish:
numeric dest._s, dest._s[];
boolean _bad._s;
if knownnumericarray src._s:
copyarray (src._s) (dest._s);
_bad._s := false;
else:
_bad := _bad._s := true;
fi
endfor
% _bad = one of the three arrays not copied.
if _bad:
if knownnumericarray src: _bad := false;
if _bad.rep: % make dest.rep = src
copyarray (src) (dest.rep);
fi
if _bad.start: % shrink first dash to get dest.start
copyarray (src) (dest.start);
dest.start1 := dash_start*src1;
fi
if _bad.finish: % use partial first dash for dest.finish
dest.finish := 1;
dest.finish1 := dash_finish*src1;
fi
fi
fi
not _bad
enddef;
vardef Dashed (expr dlen, dgap) expr f =
save dashes; dashpat (dashes) (dlen, dgap);
gendashed (dashes) f
enddef;
def DASHED = Dashed enddef;
def dashed = Dashed enddef;
vardef doplot (expr spath, sc, dgap) expr f =
save dots; dashpat (dots) (0, dgap);
setpicture (plot_pic) makesymbol (spath, sc);
plot_pic.size := sc;
gendashed (dots) f
enddef;
path dotpath; dotpath := fullcircle;
def dotted = doplot (dotpath) enddef;
vardef plotnodes (expr symbol, size) expr f =
if size > 0:
save pln; pair pln[];
pln := 0;
for _a = 0 upto (length f) if cycle f: - 1 fi:
pln[incr pln] := pnt[_a] (f);
endfor
dosymbols (drawcolor, symbol, size) (pln);
fi
f
enddef;
def showcontrols = colorshowcontrols (pointcolor) enddef;
vardef colorshowcontrols (expr clr, syma, symb, size) expr f =
save shpre, shpost;
pair shpre[], shpost[];
shpre := 0; shpost := 0;
for a = 0 upto (length f) if cycle f: - 1 fi:
shpre [incr shpre] := pre [a] (f);
shpost[incr shpost] := post[a] (f);
colorsafedraw (clr)
(zconv (shpre[shpre]--pnt[a](f)--shpost[shpost]));
endfor
if size > 0:
if not numeric syma: dosymbols (clr, syma, size) (shpre) ; fi
if not numeric symb: dosymbols (clr, symb, size) (shpost); fi
fi
f
enddef;
def doubledraw = colordoubledraw (drawcolor) enddef;
vardef colordoubledraw (expr clr, sep) expr f =
convertpath (g) f;
colorsafedraw (clr) (parapath ( sep/2) g);
colorsafedraw (clr) (parapath (-sep/2) g);
f
enddef;
vardef makesymbol (expr spath, sc) =
if picture spath :
setpicture (v) spath; mono (v); v
elseif path spath: setdot (spath, sc)
else:
GBwarn "Undefined symbol for plotting, "
& "dotpath will be used instead.";
setdot (dotpath, sc)
fi
enddef;
vardef bpoint (expr ptwd, b) =
fullcircle scaled ptwd shifted b
enddef;
def pointd (expr ptwd, filled) (text t) =
if filled:
plotsymbol (SolidCircle, ptwd) (t);
else:
begingroup;
setboolean (clearsymbols) true;
plotsymbol (Circle, ptwd) (t);
endgroup
fi
enddef;
boolean clearsymbols; clearsymbols := false;
vardef clearable (expr pth) =
if path pth:
( pnt0 (pth) = pnt[length pth] (pth) ) and (not cycle pth)
and (length pth > 0)
else: false
fi
enddef;
def clearopenpath expr f =
if clearable (f): safeunfill f & cycle; fi
enddef;
def plotsymbol = colorplotsymbol (pointcolor) enddef;
def colorplotsymbol (expr clr, spath, sc) (text t) =
if sc > 0:
begingroup
setpairs (_cpls) (t);
if _cpls > 0: dosymbols (clr, spath, sc) (_cpls); fi
endgroup
fi
enddef;
def dosymbols (expr clr, spath, sc) (suffix arr) =
if clearsymbols and clearable (spath):
addsymbols (background, makesymbol (spath&cycle, sc)) (arr);
fi
addsymbols (clr, makesymbol (spath, sc)) (arr);
enddef;
def addsymbols (expr clr, symb) (suffix arr) =
newpicture (_pls);
for _idx = 1 upto arr:
picdot (_pls, symb, zconv (arr[_idx]));
endfor
DoClip (_pls); coloraddon (clr, _pls);
enddef;
def putimage (suffix pic) (text t) =
newpicture (_pti);
for _itm = t:
addto _pti also
(pic shifted goodpair (zconv (_itm)));
DoClip (_pti); addto active_plane also _pti;
_pti := nullpicture;
endfor
mono active_plane
enddef;
def arrowdraw (expr hlen) (expr f) =
store (curpath) headpath (hlen, 0, 0) drawn f;
enddef;
def xaxis (expr hlen) = arrowdraw (hlen) ((xneg, 0)--(xpos, 0));
enddef;
def yaxis (expr hlen) = arrowdraw (hlen) ((0, yneg)--(0, ypos));
enddef;
def axes (expr hlen) = xaxis (hlen); yaxis (hlen); enddef;
laxis := baxis := raxis := taxis := 0;
vardef axisline.x = (xneg + laxis, 0)--(xpos - raxis, 0) enddef;
vardef axisline.y = (0, yneg + baxis)--(0, ypos - taxis) enddef;
vardef axisline.l = axisline.y shifted (xneg + laxis, 0) enddef;
vardef axisline.b = axisline.x shifted (0, yneg + baxis) enddef;
vardef axisline.r = axisline.y shifted (xpos - raxis, 0) enddef;
vardef axisline.t = axisline.x shifted (0, ypos - taxis) enddef;
vardef axis@# (expr len) = headpath (len, 0, 0) axisline@# enddef;
vardef borderrect =
rect((xneg+laxis,yneg+baxis),(xpos-raxis,ypos-taxis))
enddef;
numeric inside, outside, centered, onleft, onright, ontop, onbottom;
inside := -2;
outside := -1;
onright := 1;
onleft := 2;
centered := .5[onright, onleft];
onbottom := onright;
ontop := onleft;
ltick := rtick := ttick := btick := inside;
xtick := ytick := centered;
vardef axismarks (expr inang, tp, loc, pdir) (expr len) (text t) =
save _tp, _U, _P, _tic, _ticang;
pair _U, _P; path _tic;
_ticang := if tp < 0: inang else: 90 fi;
_tp := abs(tp) - 1;
_U := unitvector (vconv (pdir)) rotated _ticang;
_tic := (-_U--(0,0)) shifted (_tp*_U) scaled len;
for _a = t:
safedraw (_tic shifted zconv (loc + _a*pdir));
endfor
enddef;
def xmarks = axismarks ( 90, xtick, origin, right) enddef;
def ymarks = axismarks (-90, ytick, origin, up) enddef;
def lmarks = axismarks (-90, ltick, (xneg + laxis, 0), up) enddef;
def bmarks = axismarks ( 90, btick, (0, yneg + baxis), right) enddef;
def rmarks = axismarks ( 90, rtick, (xpos - raxis, 0), up) enddef;
def tmarks = axismarks (-90, ttick, (0, ypos - taxis), right) enddef;
path griddotpath; griddotpath := fullcircle;
def grid = vargrid (0.5bp) enddef;
vardef vargrid (expr dsize, xsp, ysp) =
save gdot, gridpic; picture gdot, gridpic;
gdot := setdot (griddotpath, dsize);
gridpic := nullpicture;
for n = ceiling ((xneg + laxis)/xsp) upto floor ((xpos - raxis)/xsp):
for m = ceiling ((yneg + baxis)/ysp) upto floor ((ypos - taxis)/ysp):
picdot (gridpic, gdot, zconv ((n*xsp, m*ysp)));
endfor
endfor
coloraddon (pointcolor, gridpic);
enddef;
def vgrid = vargrid enddef;
def hgridlines (expr ysp) =
for n = ceiling ((yneg + baxis)/ysp) upto floor ((ypos - taxis)/ysp):
safedraw zconv ((xneg + laxis, n*ysp)--(xpos - raxis, n*ysp));
endfor
enddef;
def vgridlines (expr xsp) =
for n = ceiling ((xneg + laxis)/xsp) upto floor ((xpos - raxis)/xsp):
safedraw zconv ((n*xsp, yneg + baxis)--(n*xsp, ypos - taxis));
endfor
enddef;
def gridlines (expr xsp, ysp) =
vgridlines (xsp); hgridlines (ysp);
enddef;
def vectorfield (expr len, xsp, ysp) (text fcn) (text cond) =
save _vf, _is_OK;
vardef _vf (expr x,y) = ((0,0)--(fcn)) shifted (x,y) enddef;
vardef _is_OK (expr x,y) = cond enddef;
mkvectorfield (len, xsp, ysp) (_vf, _is_OK);
enddef;
vardef mkvectorfield (expr len, xsp, ysp) (suffix vf, isOK) =
for n = ceiling ((xneg + laxis)/xsp) upto floor ((xpos - raxis)/xsp):
for m = ceiling ((yneg + baxis)/ysp) upto floor ((ypos - taxis)/ysp):
if isOK (n*xsp,m*ysp): arrowdraw (len) (vf(n*xsp,m*ysp)); fi
endfor
endfor
enddef;
def plrvectorfield (expr len, rsp, tsp) (text fcn) (text cond) =
save _vf, _is_OK, _A, _B, _C, _D;
_A := xneg + laxis; _B := xpos + raxis;
_C := yneg + baxis; _D := ypos + taxis;
vardef _vf (expr r,t) = ((0,0)--(fcn)) shifted (r*dir t) enddef;
vardef _is_OK (expr r,t) =
save _X, _Y; _X := r*cosd t; _Y := r*sind t;
(cond) and (_A < _X) and (_X < _B) and (_C < _Y) and (_Y < _D)
enddef;
mkplrvectorfield (len, rsp, tsp) (_vf, _is_OK);
enddef;
vardef mkplrvectorfield (expr len, rsp, tsp) (suffix vf, isOK) =
save rmin, rmax, tmin, tmax;
getpolarbounds;
if rmin = 0:
if isOK (0,tmin): arrowdraw (len) (vf (0,tmin)); fi
rmin := rsp;
fi
for n = ceiling (rmin/rsp) upto floor (rmax/rsp):
for m = ceiling (tmin/tsp) upto floor (tmax/tsp):
if isOK (n*rsp,m*tsp): arrowdraw (len) (vf (n*rsp,m*tsp)); fi
endfor
endfor
enddef;
def patcharcs (suffix X) (expr rstart, rstop, rstep, tstart, tstop) =
for rad = (if rstart = 0: rstep else: rstart fi)
step rstep until rstop:
orto (X, picpath zconv (arcplr (origin, tstart, tstop, rad)) );
endfor
enddef;
def patchrays (suffix X) (expr tstart, tstop, tstep, rstart, rstop) =
for _ang = tstart step tstep until tstop:
orto (X) (picpath zconv ((rstart*dir _ang)--(rstop*dir _ang)));
endfor
enddef;
def plrpatch (expr rstart, rstop, rstep, tstart, tstop, tstep) =
begingroup
newpicture (v);
patcharcs (v) (rstart, rstop, rstep, tstart, tstop);
coloraddon (drawcolor, v);
v := nullpicture;
patchrays (v) (tstart, tstop, tstep, rstart, rstop);
coloraddon (drawcolor, v);
endgroup
enddef;
def gridarcs (expr rstep) =
beginpolargrid;
if rmin = 0:
picdot (gridpic, setdot (griddotpath, penwd), zconv (origin));
fi
rmin := rstep * floor (rmin/rstep + 1);
rmax := rstep * ceiling (rmax/rstep - 1);
patcharcs (gridpic) (rmin, rmax, rstep, tmin, tmax);
endpolargrid (drawcolor, .5penwd);
enddef;
def gridrays (expr tstep) =
beginpolargrid;
tmin := tstep * ceiling (tmin/tstep);
tmax := tstep * floor (tmax/tstep);
patchrays (gridpic) (tmin, tmax, tstep, rmin, rmax);
endpolargrid (drawcolor, .5penwd);
enddef;
def polargrid (expr rstep, tstep) =
gridarcs (rstep); gridrays (tstep);
enddef;
def polargridpoints (expr dsize, rstep, tstep) =
beginpolargrid;
setpicture (gdot) setdot (griddotpath, dsize);
if rmin = 0:
picdot (gridpic, gdot, zconv (origin));
rmin := rstep;
fi
for n = ceiling (rmin/rstep) upto floor (rmax/rstep):
for m = ceiling (tmin/tstep) upto floor (tmax/tstep):
picdot ( gridpic, gdot, zconv ( polar ((n*rstep, m*tstep)) ) );
endfor
endfor
endpolargrid (pointcolor, .5dsize);
enddef;
def beginpolargrid =
begingroup;
save rmax, rmin, tmax, tmin;
getpolarbounds;
newpicture (gridpic);
enddef;
def getpolarbounds =
save p, r, t;
pair p[];
p0 := (xneg, yneg); p1 := (xneg, ypos);
p2 := (xpos, ypos); p3 := (xpos, yneg);
r0 := abs(p0); rmax := r0;
for j = 1 upto 3:
r[j] := abs(p[j]);
if rmax < r[j]: rmax := r[j]; fi
endfor
rmin := 0;
if (xneg < 0) and (xpos > 0) and (yneg < 0) and (ypos > 0):
tmin := 0; tmax := 360;
elseif (p0 = origin): tmin := 0; tmax := 90;
elseif (p1 = origin): tmin := -90; tmax := 0;
elseif (p2 = origin): tmin := -180; tmax := -90;
elseif (p3 = origin): tmin := 90; tmax := 180;
else:
tmax := tmin := t0 := angle p0;
for j = 1 upto 3:
t := t0 + anglefromto (p0, p[j]);
if tmax < t: tmax := t; fi
if tmin > t: tmin := t; fi
endfor
if (xneg < 0) and (0 < xpos):
rmin := emin (abs(yneg), abs(ypos));
elseif (yneg < 0) and (0 < ypos):
rmin := emin (abs(xneg), abs(xpos));
else:
rmin := min (r0, r1, r2, r3);
fi
fi
enddef;
def endpolargrid (expr clr, size)=
clipto (gridpic) rect ( zconv ((xneg, yneg)) - size*(1,1),
zconv ((xpos, ypos)) + size*(1,1) );
coloraddon (clr, gridpic);
endgroup
enddef;
vardef polarpatch (expr rstart, rstop, rstep, tstart, tstop, tstep) =
plrpatch (rstart, rstop, rstep, tstart, tstop, tstep);
safedraw zconv ( arcplr (origin, tstart, tstop, rstop) );
safedraw zconv ( ((rstart, 0)--(rstop, 0)) rotated tstop );
enddef;
vardef rect (expr ll, ur) =
ll--(xpart ur, ypart ll)--ur--(xpart ll, ypart ur)--cycle
enddef;
vardef triangle (expr A, B, C) = A--B--C--cycle enddef;
vardef regularpolygon (expr n) (suffix Bob) (text eqns) =
pair Bob[]; Bob := emax (round (abs (n)), 2);
eqns;
for _uncle = 1 upto Bob - 1:
(Bob1 - Bob0) rotated (360/Bob*_uncle) = Bob[_uncle+1] - Bob0;
endfor
mkpoly (true) (Bob)
enddef;
vardef altitudept expr n of t =
save A, B, C, zz; pair A, B, C, zz;
B := pnt[n + 1] (t);
C := pnt[n + 2] (t);
zz = whatever[B,C];
zz = pnt[n](t) + whatever*((C-B) rotated 90);
zz
enddef;
vardef altitude expr n of t =
(pnt[n](t))--(altitudept n of t)
enddef;
vardef medianpt expr n of t =
0.5[pnt[n + 1] (t), pnt[n + 2] (t)]
enddef;
vardef median expr n of t =
(pnt[n](t))--(medianpt n of t)
enddef;
vardef anglebisectorpt expr n of t =
save A, B, C; pair A, B, C;
A := pnt[n ] (t);
B := pnt[n + 1] (t);
C := pnt[n + 2] (t);
save zz; pair zz;
zz = whatever[B,C];
zz = A + whatever*((B-A) rotated (.5*cornerangle (A,B,C)));
zz
enddef;
vardef anglebisector expr n of t =
(pnt[n](t))--(anglebisectorpt n of t)
enddef;
vardef anglefromto (expr u, v) =
if (u = origin) or (v = origin): 0
else: angle (v rotated (-angle u))
fi
enddef;
vardef cornerangle (expr A, B, C) =
if (A = B) and (B = C) : 60
elseif (A=B) or (A=C) : 90
else: anglefromto (B - A, C - A)
fi
enddef;
vardef mkpath (expr smooth, tens, cyclic) (suffix pts) =
if smooth: mksmooth (tens)
else: mkpoly
fi (cyclic, pts)
enddef;
vardef mkpoly (expr cyclic) (suffix pts) =
for _i = 1 upto pts-1: pts[_i]-- endfor
pts[pts] if cyclic: -- cycle else: {0,0} fi
enddef;
vardef polyline (expr cyclic) (text t) =
setpairs (_pl) (t);
if _pl=0: NoPoints ("polyline", _pl); fi
mkpoly (cyclic, _pl)
enddef;
def NoPoints (expr s) (suffix pts) =
GBwarn s & " attempted with empty list."; pts[incr pts] := origin;
enddef;
vardef turtle (text t) =
setnumeric (_tu) 0;
setpair (_tmp) origin;
pair _tu[];
for _a = t:
_tmp := _tmp + _a;
_tu[incr _tu] := _tmp;
endfor
if _tu = 0: NoPoints("turtle", _tu); fi
mkpoly (false, _tu)
enddef;
vardef brownianpath (expr start, num, sc) =
setnumeric (_brp) 1;
setpair (_tmp) start;
pair _brp[]; _brp1 := _tmp;
for _idx := 1 upto num:
_tmp := _tmp + sc/(sqrt 2)*(normaldeviate,normaldeviate);
_brp[incr _brp] := _tmp;
endfor
mkpoly (false, _brp)
enddef;
vardef mksmooth (expr tens, cyclic) (suffix pts) =
if pts = 1: onepointpath (cyclic, pts1)
else:
settension (_tn) tens; fixtension (_tn);
pts1 if cyclic: {pts[2]-pts[pts]} fi
for _i = 2 upto pts-1:
..tension _tn..pts[_i]{pts[_i+1]-pts[_i-1]}
endfor
..tension _tn..pts[pts]
if cyclic: {pts[1]-pts[pts-1]}..tension _tn..cycle fi
fi
enddef;
vardef mktenser (expr tens, cyclic) (suffix pts) =
if pts = 1: onepointpath (cyclic, pts1)
else:
settension (_tn) tens; fixtension (_tn);
pts1 if cyclic: {pts[2]-pts[pts]} fi
for _i = 2 upto pts-1:
..tension atleast _tn..pts[_i]{pts[_i+1]-pts[_i-1]}
endfor
..tension atleast _tn..pts[pts]
if cyclic: {pts[1]-pts[pts-1]}..tension atleast _tn..cycle fi
fi
enddef;
vardef mkconvex (expr tens, cyclic) (suffix pts) =
save _B, _d, _tmp; pair _d[];
settension (_tn) tens; fixtension (_tn);
if pts < 4: mktenser (_tn, cyclic) (pts)
else:
for _j = 2 upto pts - 1:
_B[_j] := sqrt(abs((pts[_j]-pts[_j-1])xprod(pts[_j+1]-pts[_j])));
endfor
if cyclic:
_B1 := sqrt(abs((pts1 - pts[pts])xprod(pts2 - pts1)));
_B[pts] := sqrt(abs((pts[pts]-pts[pts-1])xprod(pts1 - pts[pts])));
else:
_B1 := _B2;
_B[pts] := _B[pts-1];
fi
for _j = 2 upto pts - 1:
_tmp := _B[_j-1] + _B[_j+1];
_d[_j] :=
if _tmp = 0: origin % signal to use curl1
else:
( _B[_j+1]*(pts[_j] - pts[_j-1]) +
_B[_j-1]*(pts[_j+1] - pts[_j]) )/_tmp
fi;
endfor
if cyclic:
_tmp := _B[pts] + _B2;
_d1 :=
if _tmp = 0: origin
else:
(_B2*(pts1 - pts[pts]) + _B[pts]*(pts2 - pts1))/_tmp
fi;
_tmp := _B[pts-1] + _B1;
_d[pts] :=
if _tmp = 0: origin
else:
( _B1*(pts[pts] - pts[pts-1]) +
_B[pts-1]*(pts1 - pts[pts]) )/_tmp
fi;
else:
_d1 := origin; _d[pts] := origin;
fi
pts1
for _j = 1 upto pts-1:
{if _d[_j] = origin: curl1 else: _d[_j] fi}
..tension atleast _tn..pts[_j+1]
endfor
{if _d[pts] = origin: curl1 else: _d[pts] fi}
if cyclic: ..tension atleast _tn..cycle fi
fi
enddef;
numeric default_tension; default_tension := 1;
def curve = tcurve (default_tension) enddef;
vardef tcurve (expr tens, cyclic) (text t) =
setpairs (_tc) (t); mksmooth (tens, cyclic, _tc)
enddef;
def ccurve = tccurve (default_tension) enddef;
vardef tccurve (expr tens, cyclic) (text t) =
setuniquepairs (_tcc) (t); mkconvex (tens, cyclic, _tcc)
enddef;
vardef mkbezier (expr tens, cyclic) (suffix pts) =
settension (_tn) tens; fixtension (_tn);
pts1
for _i = 2 upto pts: ..tension _tn..pts[_i] endfor
if cyclic: ..tension _tn..cycle else: {0,0} fi
enddef;
def bezier = tbezier (default_tension) enddef;
vardef tbezier (expr tens, cyclic) (text t) =
setpairs (_tbs) (t);
if _tbs=0: NoPoints ("bezier", _tbs); fi
mkbezier (tens, cyclic) (_tbs)
enddef;
vardef mkqbezier (expr cyclic) (suffix pts) =
pts1
if pts=1: {0,0}
else:
for _i = 2 step 2 until pts - 1:
..controls 1/3[pts[_i], pts[_i-1] ] and 1/3[pts[_i], pts[_i+1] ]..
pts[_i+1]
endfor
if cyclic:
..controls 1/3[ pts[pts], pts[pts - 1] ]
and 1/3[ pts[pts], pts1 ]..cycle
fi
fi
enddef;
vardef qbezier (expr cyclic) (text t) =
setpairs (_qbz) (t);
if _qbz=0: NoPoints ("qbezier", _qbz);
else:
if (cyclic and odd _qbz) or (not cyclic and even _qbz):
_qbz[incr _qbz] := _qbz[_qbz-1];
fi
mkqbezier (cyclic) (_qbz)
fi
enddef;
vardef mkcbezier (expr cyclic) (suffix pts) =
pts1
if pts=1: {0,0}
else:
for _i = 1 step 3 until pts - 3:
..controls pts[_i+1] and pts[_i+2] .. pts[_i+3]
endfor
if cyclic:
..controls pts[pts - 1] and pts[pts]..cycle
fi
fi
enddef;
vardef cbezier (expr cyclic) (text t) =
setpairs (_cbz) (t);
if _cbz=0: NoPoints ("qbezier", _cbz);
else:
% Need 0 mod 3 for cyclic, otherwise 1 mod 3
setnumeric (_mdt) _cbz mod 3;
if cyclic:
if _mdt <> 0: _cbz[incr _cbz] := _cbz[_cbz-1]; fi
if _mdt = 1 : _cbz[incr _cbz] := _cbz1; fi
else: % need 1 more, duplicate next to last
if _mdt = 0:
_cbz := _cbz + 1;
_cbz[_cbz] := _cbz[_cbz-1];
_cbz[_cbz-1] := _cbz[_cbz-2];
fi
if _mdt = 2: % need 2 more, duplicate last 2.
_cbz := _cbz + 2; % add 2 slots
_cbz[_cbz] := _cbz[_cbz-2]; % fill them
_cbz[_cbz-1] := _cbz[_cbz-2]; % with last node
_cbz[_cbz-2] := _cbz[_cbz-3]; % orig last slot = orig previous.
fi
fi
mkcbezier (cyclic) (_cbz)
fi
enddef;
vardef fcncontrol (expr ftens, X, Y, Z) =
Y if (xpart(Z-Y) <> 0) and (xpart(Y-X) <> 0):
+ xpart(Z-Y)/3/xpart(Z-X)*(Z - X)/ftens fi
enddef;
vardef mkfcnpath (expr ftens) (suffix q) =
settension (_tn) ftens;
if _tn <= 0: _tn := 1; fi
for _i = 1 upto q - 1:
q[_i]..controls fcncontrol (_tn) (q[_i-1], q[_i], q[_i+1])
and fcncontrol (_tn) (q[_i+2], q[_i+1], q[_i])..
endfor
q[q]{0,0}
enddef;
def fcncurve = functioncurve (default_tension) enddef;
def tfcncurve = functioncurve enddef;
vardef functioncurve (expr ftens) (text t) =
settension (_ftens) ftens; if _ftens < 1/3: _ftens := 1/3; fi
setuniquepairs (_fc) (t);
if _fc > 1: _fc0 := _fc1; _fc[_fc+1] := _fc[_fc]; fi
mkfcnpath (_ftens) (_fc)
enddef;
def openqbs = qspline (false) enddef;
def closedqbs = qspline (true) enddef;
vardef mkqbs (suffix b) =
0.5[ b1, b2]
if b<3: {0,0}
else:
for _i = 2 upto b-1:
..controls 1/6[ b[_i], b[_i-1] ] and 1/6[ b[_i], b[_i+1] ]..
0.5[ b[_i], b[_i+1] ]
endfor
fi
enddef;
vardef qspline (expr cyclic) (text t) =
setpairs (_qs) (t);
if _qs=0: NoPoints ("qspline", _qs); fi
if _qs=1: _qs[incr _qs] := _qs1; fi
if cyclic:
_qs[incr _qs] := _qs1; _qs[incr _qs] := _qs2;
fi
mkqbs (_qs) if cyclic: & cycle fi
enddef;
vardef mkcbs (suffix b) =
(b[1]+4b[2]+b[3])/6
if b < 4: {0,0}
else:
for _i = 3 upto b-1:
..controls 1/3[ b[_i-1], b[_i] ] and 1/3[ b[_i], b[_i-1] ]
.. (b[_i-1] + 4b[_i] + b[_i+1])/6
endfor
fi
enddef;
def mkopencbs = mkcbs enddef;
vardef mkclosedcbs (suffix b) =
mkcbs (b) & opencbs (b[b-2],b[b-1],b[b], b1, b2, b3) & cycle
enddef;
def opencbs = cspline (false) enddef;
def closedcbs = cspline (true) enddef;
vardef cspline (expr cyclic) (text t) =
setpairs (_cs) (t);
if _cs=0: NoPoints ("cspline", _cs); fi
for _idx = _cs upto 2: _cs[incr _cs] := _cs[_idx]; endfor
if cyclic:
for _idx = 1 upto 3: _cs[incr _cs] := _cs[_idx]; endfor
fi
mkcbs (_cs) if cyclic: & cycle fi
enddef;
def init_spline_eqns (suffix pts) =
save _spl_pre, _spl_post;
pair _spl_pre[], _spl_post[];
for j= 2 upto pts - 1:
_spl_post[j] + _spl_pre[j] = 2pts[j];
_spl_pre[j+1]+2_spl_pre[j] = 2_spl_post[j]+_spl_post[j-1];
endfor
enddef;
def closed_spline_eqns (suffix pts) =
_spl_post1 + _spl_pre1 = 2pts1;
_spl_post[pts] + _spl_pre[pts] = 2pts[pts];
_spl_pre2 + 2_spl_pre1 = 2_spl_post1 + _spl_post[pts];
_spl_pre1+2_spl_pre[pts] = 2_spl_post[pts]+_spl_post[pts-1];
enddef;
def relaxed_spline_eqns (suffix pts) =
_spl_pre2 + pts1 = 2_spl_post1;
pts[pts] + _spl_post[pts-1] = 2_spl_pre[pts];
enddef;
vardef mksplinepath (expr closed) (suffix pts) =
pts1..controls _spl_post1 and
for j = 2 upto pts if not closed: -1 fi:
_spl_pre[j]..pts[j]..controls _spl_post[j] and
endfor
if closed: _spl_pre1..cycle else: _spl_pre[pts]..pts[pts] fi
enddef;
def mkspline (expr closed) (suffix pts) =
init_spline_eqns (pts);
if closed: closed_spline_eqns (pts);
else: relaxed_spline_eqns (pts);
fi
mksplinepath (closed) (pts)
enddef;
vardef dospline (expr closed) (text the_list) =
setpairs (_sp) (the_list);
if _sp=0: NoPoints ("dospline", _sp); fi
if _sp=1: _sp[incr _sp] := _sp1; fi
mkspline (closed) (_sp)
enddef;
def init_fcnspl_eqns (suffix pts) =
save _dx, _sl; numeric _dx[], _sl[];
_dx1 := xpart (pts2 - pts1);
for j = 2 upto pts - 1:
_dx[j] := xpart (pts[j+1] - pts[j]);
_sl[j + 1]*_dx[j] + _sl[j-1]*_dx[j-1] + 2_sl[j]*(_dx[j] + _dx[j-1])
= 3*ypart(pts[j+1] - pts[j-1]);
endfor
enddef;
def periodic_fcnspl_eqns (suffix pts) =
_sl1 = _sl[pts];
_sl2*_dx1 + 2_sl1*_dx1 + 2_sl[pts]*_dx[pts-1] + _sl[pts-1]*_dx[pts-1]
= 3 * ypart (pts[2] - pts[pts-1]);
enddef;
def relaxed_fcnspl_eqns (suffix pts) =
_sl2*_dx1 + 2_sl1*_dx1 = 3 * ypart(pts2 - pts1);
_sl[pts-1]*_dx[pts-1] + 2_sl[pts]*_dx[pts-1]
= 3 * ypart(pts[pts] - pts[pts-1]);
enddef;
vardef mkfcnsplpath (suffix pts) =
pts1..controls (pts1 + (1, _sl1)/3*_dx1) and
for j = 2 upto pts - 1:
(pts[j] - (1, _sl[j])/3*_dx[j-1]) ..pts[j]..
controls (pts[j] + (1,_sl[j])/3*_dx[j]) and
endfor
(pts[pts] - (1,_sl[pts])*_dx[pts-1]/3)..pts[pts]
enddef;
vardef mkfcnspline (expr periodic) (suffix pts) =
init_fcnspl_eqns (pts);
if periodic: periodic_fcnspl_eqns (pts);
else: relaxed_fcnspl_eqns (pts);
fi
mkfcnsplpath (pts)
enddef;
vardef fcnspline (expr periodic) (text the_list) =
setpairs (_fs) (the_list);
if _fs<2:
if _fs=0: NoPoints ("fcnspline", _fs); fi
onepointpath (false, _fs1)
else:
mkfcnspline (periodic) (_fs)
fi
enddef;
vardef mkarc (expr center, begpt, endpt, sweep) =
if (sweep = 0): begpt--endpt
else:
setnumeric (n) ceiling (abs(sweep)/45);
setpair (d) (begpt - center) rotated (signof (sweep) 90);
begpt{d}
for j = 1 upto n-1:
..(begpt rotatedabout (center, j/n*sweep)){d rotated (j/n*sweep)}
endfor ..endpt{d rotated sweep}
fi
enddef;
vardef arc (expr center, begpt, sweep) =
if (center = begpt) or (sweep = 0): begpt--begpt
else:
mkarc (center, begpt, begpt rotatedabout (center, sweep), sweep)
fi
enddef;
def arccps = arc enddef;
vardef arcpps (expr begpt, endpt, sweep) =
if begpt = endpt: begpt--endpt
else:
setpair (cd) unitvector (endpt-begpt);
if abs(sweep) <= 45:
begpt{cd rotated (-sweep/2)}..endpt{cd rotated (sweep/2)}
elseif abs(sweep) <= 90:
save m; pair m;
m = begpt + whatever*( cd rotated (-sweep/4));
m = 0.5[begpt, endpt] + whatever*(cd rotated 90);
begpt{cd rotated (-sweep/2)}..m{cd}..endpt{cd rotated (sweep/2)}
else:
setnumeric (ang) 90 - ((sweep/2) mod 180);
if abs(ang) = 90:
GBwarn "undefined arc. A line segment will be used instead.";
begpt--endpt
else:
save c; pair c;
c = begpt + whatever*(cd rotated ang);
c = if abs(ang) < 30:
(0.5)[begpt, endpt] + whatever*(cd rotated 90)
else:
endpt + whatever*(-cd rotated -ang)
fi;
mkarc (c, begpt, endpt, sweep)
fi
fi
fi
enddef;
vardef arcpp (expr small, begpt, endpt, rad) =
save full, diam, chord, ang;
full := signof (rad) 360;
diam := 2rad;
chord := abs(endpt-begpt);
if chord < abs(diam):
ang := if not small: full - fi 2*asin (chord/diam);
else: ang := signof (rad) 180;
fi
arcpps (begpt, endpt, ang)
enddef;
def arcppr (expr begpt, endpt, rad, small) =
arcpp (small, begpt, endpt, rad)
enddef;
vardef arcplr (expr center, frtheta, totheta, rad) =
if rad = 0: center--center
else:
mkarc (center, center + rad*dir frtheta,
center + rad*dir totheta, totheta - frtheta)
fi
enddef;
vardef arcalt (expr center, radius, frtheta, totheta) =
arcplr (center, frtheta, totheta, radius)
enddef;
vardef arcppp (expr first, second, third) =
arcpps (first, second, 2*cornerangle (third, first, second)) &
arcpps (second, third, 2*cornerangle (first, second, third))
enddef;
vardef ellipse (expr center, radx, rady, angle) =
fullcircle xscaled (2*radx) yscaled (2*rady) rotated angle
shifted center
enddef;
vardef circle (expr center, rad) =
fullcircle scaled (2*rad) shifted center
enddef;
vardef circlecp (expr center, point) =
mkarc (center, point, point, 360) & cycle
enddef;
vardef circleppp (expr one, two, three) =
arcpps (one, two, 2*cornerangle (three, one, two))
& arcpps (two, three, 2*cornerangle (one, two, three))
& arcpps (three, one, 2*cornerangle (two, three, one))
& cycle
enddef;
vardef circlepps (expr one, two, sweep) =
save ang, full;
full := signof (sweep) 360;
ang := sweep mod full;
arcpps (one, two, ang) & arcpps (two, one, full - ang) & cycle
enddef;
vardef circlepp (expr small, one, two, rad) =
arcpp (small, one, two, rad) & arcpp (not small, two, one, rad) & cycle
enddef;
def circleppr (expr one, two, rad, small) =
circleppr (one, two, rad, small)
enddef;
vardef pathcenter expr p =
save a, cntr, n; pair cntr, a[];
n := length p;
a1 = pnt 0 (p);
a3 = pnt [n/2] (p);
if cycle p:
a2 = pnt [n/4] (p);
a4 = pnt [3n/4] (p);
else:
a2 := a3;
a4 := pnt[n] (p);
fi
cntr = .5[a1, a3] + whatever*((a3 - a1) rotated 90);
cntr = .5[a2, a4] + whatever*((a4 - a2) rotated 90);
cntr
enddef;
vardef circumcircle expr t =
circleppp (pnt0 (t), pnt1 (t), pnt2 (t))
enddef;
vardef incircle expr t =
save A, B, C; pair A, B, C;
A := pnt0 (t);
B := pnt1 (t);
C := pnt2 (t);
save a, b, c, D, E, F;
D := abs (B-A) = a + b;
E := abs (C-B) = b + c;
F := abs (A-C) = a + c;
circleppp ((a/D)[A,B], (b/E)[B,C], (c/F)[C,A])
enddef;
vardef excircle expr n of t =
save A, B, C; pair A, B, C;
A := pnt[n] (t);
B := pnt[n + 1] (t);
C := pnt[n + 2] (t);
save a, b, c, D, E, F;
D := abs (B-A) = a - b;
E := abs (C-B) = b + c;
F := abs (C-A) = a - c;
circleppp ((a/D)[A,B], (b/E)[B,C], (c/F)[A,C])
enddef;
vardef ninepointcircle expr t =
circleppp (medianpt 0 of t, medianpt 1 of t, medianpt 2 of t)
enddef;
vardef pshcircle (expr disk, ctr, rad) =
if disk:
if rad >= 1 :
if rad > 1:
GBerrmsg ("Impossible pseudohyperbolic circle.")
"The radius of a pseudohyperbolic circle can be at most 1.";
fi
circle ((0,0),1)
elseif abs(ctr) >= 1 :
if abs(ctr) > 1:
GBerrmsg ("Impossible pseudohyperbolic circle.")
"The center of a pseudohyperbolic circle must be in"
& "the unit disk.";
fi
onepointpath (true,ctr)
else:
% compute Euclidean center and radius (and a denominator used twice
% in calculations).
save _r, _dnm;
_r := abs(ctr);
_dnm := 1 - _r*_r*rad*rad;
circle ( (1 - rad*rad)/_dnm*ctr, rad*(1 - _r*_r)/_dnm)
fi
else:
if rad >= 1 :
GBerrmsg ("Impossible pseudohyperbolic circle.")
"The radius of a pseudohyperbolic circle must be less than 1.";
onepointpath (true,ctr)
elseif ypart ctr <= 0:
if ypart ctr < 0:
GBerrmsg ("Impossible pseudohyperbolic circle.")
"The center of a pseudohyperbolic circle must be in"
& "the upper half-plane.";
fi
onepointpath (true,ctr)
else:
% compute Euclidean center and radius (and a denominator used twice
% in calculations).
% Euclidean center at xpart ctr + (1 + R^2)/(1 - R^2)*ypart ctr
% Euclidean radius 4R/(1 - R^2)*ypart ctr
save _y, _dnm;
_y := ypart ctr;
_dnm := 1 - rad*rad;
circle ( (xpart ctr, (1 + rad*rad)/_dnm * _y), 2rad/_dnm*_y)
fi
fi
enddef;
vardef barycenter expr t =
save m; m := length t if not cycle t: + 1 fi;
pnt0(t)/m for k = 1 upto m - 1: + pnt[k](t)/m endfor
enddef;
vardef sector (expr center, rad, frtheta, totheta) =
center -- arcalt (center, rad, frtheta, totheta) -- cycle
enddef;
vardef mkfcn (expr sm, tens) (expr bmin, bmax, bst) (text pf) =
save _p; pair _p[]; _p := 0;
save _dx, _n, _r; numeric _dx, _n, _r;
if bmax = bmin: _n := 1;
else:
_r := bmax - bmin;
_dx := max (abs(bst), nottoosmall*abs(_r), epsilon);
_n := emax (round(abs(_r)/_dx), 1);
fi
for _i = 0 upto _n: _p[incr _p] := pf(bmin + _i/_n*_r); endfor
mkpath (sm, tens, false, _p)
enddef;
def tfcn (expr sm) = mkfcn (sm, default_tension) enddef;
def parafcn (expr sm) = tparafcn (sm, default_tension) enddef;
vardef tparafcn (expr sm, tn) (expr bmin, bmax, bst) (text pf) =
save _fp; vardef _fp (expr t) = pf enddef;
mkfcn (sm, tn) (bmin, bmax, bst) (_fp)
enddef;
vardef xfcn (expr sm) (expr xmin, xmax, st) (text _fx) =
save _fp; vardef _fp (expr _x) = (_x, _fx(_x)) enddef;
mkfcn (sm, default_tension) (xmin, xmax, st) (_fp)
enddef;
def function (expr sm) = tfunction (sm, default_tension) enddef;
vardef tfunction (expr sm, tens, xmin, xmax, st) (text _fx) =
save _fp; vardef _fp (expr x) = (x, _fx) enddef;
mkfcn (sm, tens) (xmin, xmax, st) (_fp)
enddef;
def btwnfcn (expr sm) = tbtwnfcn (sm, default_tension) enddef;
vardef tbtwnfcn (expr sm, tn, xlo, xhi, st)(text _fx)(text _gx) =
tfunction (sm, tn) (xlo, xhi, st) (_fx) --
( reverse tfunction (sm, tn) (xlo, xhi, st) (_gx) ) -- cycle
enddef;
def belowfcn (expr sm) = tbelowfcn (sm, default_tension) enddef;
vardef tbelowfcn (expr sm, tn, xlo, xhi, st)(text _fx) =
(xlo,0)--(xhi,0)--
(reverse tfunction (sm, tn, xlo, xhi, st)(_fx))--cycle
enddef;
vardef rfcn (expr sm, tmin, tmax, st) (text ft) =
save _fq; vardef _fq (expr t) = (ft(t)) * (dir t) enddef;
mkfcn (sm, default_tension) (tmin, tmax, st) (_fq)
enddef;
def plrfcn (expr sm) = tplrfcn (sm, default_tension) enddef;
vardef tplrfcn (expr sm, tens, tmin, tmax, st) (text ft) =
save _fq; vardef _fq (expr t) = (ft) * (dir t) enddef;
mkfcn (sm, tens) (tmin, tmax, st) (_fq)
enddef;
def btwnplrfcn (expr sm) = tbtwnplrfcn (sm, default_tension) enddef;
vardef tbtwnplrfcn (expr sm, tn, tlo, thi, st)(text _ft)(text _gt)=
tplrfcn (sm, tn, tlo, thi, st) (_ft) --
( reverse tplrfcn (sm, tn, tlo, thi, st) (_gt) ) -- cycle
enddef;
def plrregion (expr sm) = tplrregion (sm, default_tension) enddef;
vardef tplrregion (expr sm, tn, tlo, thi, st) (text _ft) =
(0,0)--tplrfcn (sm, tn, tlo, thi, st ) (_ft)--cycle
enddef;
numeric tolerancefactor;
tolerancefactor := .02;
vardef mklevelset (expr sm, tens, X, Y, t, a, b, c, d) =
save _inside_;
vardef _inside_ (expr U, V) =
inside_levelset (U, V) and (a < U) and (U < b)
and (c < V) and (V < d)
enddef;
if not _inside_ (X, Y):
GBwarn "Invalid seed point for levelset.";
pairmax((a,c), pairmin((X,Y), (b,d)))&cycle
else:
save ls, W, A, B, prev, curr, seed;
pair ls[], prev, curr, seed;
seed := (X,Y);
ls := 0; W := 0;
save _first_, _next_, get_next;
vardef _first_ (expr U) = _inside_ (U, Y) enddef;
vardef _next_ (expr ang) =
_inside_ (X_curr + t * cosd ang, Y_curr + t * sind ang)
enddef;
def get_next (expr angA, angB) =
X_curr := xpart curr; Y_curr := ypart curr;
ls[incr ls] := curr + t * dir (solve _next_ (angA, angB));
prev := curr; curr := ls[ls];
W := W + anglefromto (prev - seed, curr - seed);
enddef;
interim tolerance := t*tolerancefactor;
ls[incr ls] := (solve _first_ (X, b), Y);
curr := ls[ls];
interim tolerance := radian*tolerancefactor;
get_next (180, 0);
for n = 3 upto max_points:
A := angle (curr - prev);
get_next (A + 120, A - 120);
exitif ((abs(W) > 180) or (ls > 10))
and (abs(ls[ls] - ls1) < 1.2t);
endfor
mkpath (sm, tens, true) (ls)
fi
enddef;
numeric max_points;
max_points := 2000;
def levelset (expr s) = tlevelset (s, default_tension) enddef;
vardef tlevelset (expr smth, tens, seed, seg) (text cond) =
save inside_levelset, _t;
vardef inside_levelset (expr x, y) = cond enddef;
_t := if seg <= 0: emax (xpos-xneg, ypos-yneg)/max_points * 20
else: seg fi;
mklevelset (smth, tens, xpart seed, ypart seed, _t)
(xneg, xpos, yneg, ypos)
enddef;
vardef lclosed expr f =
f
if not cycle f:
if pnt0(f) = pnt[infinity](f): & else: -- fi cycle
fi
enddef;
def sclosed = sclosedt (default_tension) enddef;
vardef sclosedt (expr t) expr f =
if cycle f: f
else: save n; n := length f;
if n = 0: f&cycle
elseif n = 1: pnt0(f)..tension t..pnt1(f)..tension t..cycle
else:
(pnt0 (f)) { (pnt1(f)) - (pnt[n] (f)) }..tension t
..(subpath (1, n-1) of f)..tension t
..(pnt[n](f)) { pnt0(f) - pnt[n-1](f) }
..tension t..cycle
fi
fi
enddef;
def bclosed = bclosedt (default_tension) enddef;
vardef bclosedt (expr t) expr f =
f
if not cycle f:
if pnt0(f) = pnt[infinity](f): & else: ..tension t.. fi cycle
fi
enddef;
def uclosed = bclosed enddef;
def uclosedt = bclosedt enddef;
def cbcontrols (suffix b, t) =
b1 := 2[t3, t2];
b2 := 2[t2, t1];
b3 := 2[b1, b2];
b4 := 2[b2, b3];
enddef;
vardef cbclosed expr f =
save n; n := length f;
if cycle f: f
elseif n = 0: f&cycle
else:
save p, q, t; pair p[], q[], t[];
t1 := pnt0(f); t2 := post0(f); t3 := pre1(f);
cbcontrols (p, t); % defines p1 to p4
t1 := pnt[n](f); t2 := pre[n](f); t3 := post[n-1](f);
cbcontrols (q, t); % defines q1 to q4
f..controls q2 and q3..opencbs (q1,q4,p4,p1)
..controls p3 and p2..cycle
fi
enddef;
vardef qbclosed expr f =
if cycle f: f
else: save n; n := length f;
if n = 0: f&cycle
else:
save p; pair p[]; p := 4;
p1 := (3/2)[pnt[n](f), pre[n](f)];
p2 := 2[p1, pnt[n](f)];
p4 := (3/2)[pnt 0 (f), post0 (f)];
p3 := 2[p4, pnt 0 (f)];
f & mkqbs (p) & cycle
fi
fi
enddef;
vardef makesector expr p = (pathcenter p)--p--cycle enddef;
vardef arccomplement expr p =
if cycle p: onepointpath (false, pnt0(p))
else:
setnumeric (nn) length p;
setpairs (pp) (pnt0(p), pnt[.5nn](p), pnt[nn](p));
arcpps (pp3,pp1,2*cornerangle(pp2,pp3,pp1))
fi
enddef;
path cuttings;
vardef cutoffbefore (expr b) expr f =
save t, n; n := length f;
if n > 0:
for k = 1 upto n:
exitif (subpath (0,k) of f) intersects b;
endfor
if _Xtime < 0:
cuttings := pnt0 (f){0,0};
f
else:
cuttings := subpath (0,_Xtime) of f;
subpath (_Xtime, n) of f
fi
else: f
fi
enddef;
vardef cutoffafter (expr b) expr f =
setpath (g) cutoffbefore (b) reverse f;
cuttings := reverse cuttings;
reverse g
enddef;
vardef trimmedpath (expr btrim, etrim) expr f =
save g, h; path g, h;
g := invvconv (fullcircle scaled 2btrim) shifted pnt0(f);
h := invvconv (fullcircle scaled 2etrim) shifted pnt[length f] (f);
cutoffafter (h) cutoffbefore (g) f
enddef;
vardef predirection@# (expr p) =
- postdirection[length p - @#] (reverse p)
enddef;
vardef postdirection@# (expr p) =
save _n; _n := length (p);
setpair (v) __dir (subpath (@#, @# + _n) of p);
if v = origin:
v := - __dir (subpath (@#, @# - _n) of p);
fi
v
enddef;
vardef __dir (expr p) =
save v, w; pair v, w; w := pnt0 (p);
v := origin;
for n = 1 upto length (p):
v := post[n-1] (p) - w; exitif v <> origin;
v := pre [ n ] (p) - w; exitif v <> origin;
v := pnt [ n ] (p) - w; exitif v <> origin;
endfor
sgn v
enddef;
vardef trivial expr p = (__dir (p) = origin) enddef;
newinternal hdwdr, hdten;
boolean hfilled;
def headshape (expr wr, tens, fil) =
interim hdwdr := wr;
interim hdten := if tens>0: tens else: default_tension fi;
if hdten < .75: hdten := .75; fi
setboolean (hfilled) fil;
mkheadpaths;
enddef;
def mkheadpaths =
save Arrowhead, Leftharpoon, Rightharpoon;
path Arrowhead, Leftharpoon, Rightharpoon,
Arrowhead.clear, Leftharpoon.clear, Rightharpoon.clear;
Rightharpoon := (0,0){down}..tension hdten..(.5hdwdr,-1);
Rightharpoon.clear := Rightharpoon--(.5hdwdr,0)--cycle;
Leftharpoon := (reverse Rightharpoon) xscaled -1;
Leftharpoon.clear := (reverse Rightharpoon.clear) xscaled -1;
Arrowhead := Leftharpoon & Rightharpoon;
Arrowhead.clear := Leftharpoon.clear & Rightharpoon.clear & cycle;
if hfilled:
Arrowhead := Arrowhead--cycle;
Rightharpoon := Rightharpoon--(0,-1)--cycle;
Leftharpoon := Leftharpoon--(0,-1)--cycle;
fi
enddef;
headshape (1,1,false);
def head = ahead (headcolor) enddef;
vardef ahead (expr clr, front, back, hwr, tens, filled) =
settension (_tn) tens; fixtension (_tn);
if front <> back:
setpair (side) (hwr/2) * ((front-back) rotated 90);
setpath (f) (back + side)..tension _tn..
{front-back}front{back-front}..tension _tn..(back - side);
if clearhead:
safeunfill (back - side)--(front-side)--(front+side)--
(back+side) & f & cycle;
colorsafedraw (background) (back - side)--(front-side)--
(front+side)--(back+side) & f & cycle;
fi
if filled:
f := f--cycle;
colorsafefill (clr) f;
fi
colorsafedraw (clr) f;
fi
enddef;
def headpath = Gheadpath (false) (Arrowhead) enddef;
def headpathx = Gheadpath (true) (Arrowhead) enddef;
def colorheadpath = colorGheadpath (false) (Arrowhead) enddef;
def colorheadpathx = colorGheadpath (true) (Arrowhead) enddef;
def Gheadpath (expr trim) (suffix ah) =
colorGheadpath (trim) (ah) (headcolor)
enddef;
vardef colorGheadpath
(expr trim) (suffix ah) (expr clr, sc, rot, pos) expr f =
if (sc <> 0) and (known ah) and (path ah):
convertpath (_g) f;
setpair (_P) predirection[length _g] (_g);
if _P <> origin:
_P := _P rotated rot;
setnumeric (_ang) anglefromto (up, _P);
_P := pnt[length _g] (_g) - pos * _P;
setpair (_tip) if known ah.tip: ah.tip else: origin fi;
if trim:
if known ah.clear:
safeunfill (ah.clear shifted - _tip)
scaled sc
rotated _ang
shifted _P;
fi
setnumeric (_ys) max(bp, penwd, last_dot_size);
safeunfill cut_path
xscaled ceiling sc yscaled ceiling _ys
rotated _ang shifted _P;
fi
if cycle ah: colorsafefill else: colorsafedraw fi (clr)
(ah shifted -_tip)
scaled sc
rotated _ang
shifted _P;
fi
fi
f
enddef;
path cut_path; cut_path := (.5,0)--(.5,.71)--(-.5,.71)--(-.5,0)--cycle;
def tailpath (suffix sh) = colortailpath (sh) (headcolor) enddef;
vardef colortailpath (suffix sh) (expr clr, sc, rot, pos) expr f =
if (sc <> 0) and (known sh) and (path sh):
convertpath (_g) f;
setpair(_P) postdirection0 (_g);
if _P <> origin:
_P := _P rotated rot;
if cycle sh: colorsafefill else: colorsafedraw fi (clr)
(sh if known sh.tip: shifted -sh.tip fi)
scaled sc
rotated anglefromto (up, _P)
shifted (pnt0 (_g) + pos * _P);
fi
fi
f
enddef;
def midpath (suffix sh) = colormidpath (sh) (headcolor) enddef;
vardef colormidpath (suffix sh) (expr clr, sc, rot, pos) expr f =
if (sc <> 0) and (known sh) and (path sh):
convertpath (_g) f;
setnumeric (_t) pathtime[pos] (_g);
setpair (_P) postdirection[_t] (_g);
if _P <> origin:
_P := _P rotated rot;
if cycle sh: colorsafefill else: colorsafedraw fi (clr)
sh scaled sc
rotated anglefromto (up, _P)
shifted (pnt[_t] (_g));
fi
fi
f
enddef;
vardef signeddeviate primary X =
(uniformdeviate 1)[-X,X]
enddef;
vardef scaledeviate (expr W, A) =
2 ** (signeddeviate W) * dir A
enddef;
vardef polardeviate primary R =
(uniformdeviate abs(R)) * dir uniformdeviate 360
enddef;
vardef xydeviate primary Z =
(signeddeviate (xpart Z), signeddeviate (ypart Z))
enddef;
vardef randompair (expr maxshift) =
if numeric maxshift: polardeviate (maxshift)
elseif pair maxshift: xydeviate (maxshift)
else: (0,0)
fi
enddef;
vardef detrivialized expr f =
save g; path p, g[]; g := 0;
for k = 1 upto length f:
p := subpath (k-1,k) of f;
if not trivial p: g[incr g] := p; fi
endfor
if g = 0: onepointpath (cycle f, pnt0(f))
else: g1 for k = 2 upto g: &g[k] endfor if cycle f: &cycle fi
fi
enddef;
vardef randompath (expr maxshift, weirdness) expr f =
save g, n; path g;
g := detrivialized f;
n := length g;
if n = 0:
f shifted randompair (maxshift)
else:
save X, U, V;
pair X[], U[], V[];
if cycle g: n := n - 1; fi
for k = 0 upto n:
X[k] := pnt[k](g);
U[k] := X[k] - pre[k](g);
V[k] := post[k](g) - X[k];
endfor
save A, B;
for k := 0 upto n:
X[k] := X[k] shifted randompair (maxshift);
A := anglefromto (U[k],V[k]);
B := signeddeviate (30weirdness);
U[k] := X[k] - (U[k] zscaled scaledeviate (weirdness,B));
B := B - A + A * (2 ** signeddeviate weirdness);
V[k] := X[k] + (V[k] zscaled scaledeviate (weirdness,B));
endfor
X0 for k = 1 upto n:
.. controls V[k-1] and U[k] .. X[k]
endfor
if cycle g:
.. controls V[n] and U0 .. cycle
fi
fi
enddef;
vardef randomlines (expr maxshift) expr f =
save g, n; path g;
g := detrivialized f;
n := length g;
if n = 0:
f shifted randompair (maxshift)
else:
if cycle g: n := n - 1; fi
(pnt0(g) shifted randompair (maxshift))
for k = 1 upto n:
-- (pnt[k](g) shifted randompair (maxshift))
endfor
if cycle g:
-- cycle
fi
fi
enddef;
vardef parasegment (expr d, segs, f) =
if d = 0: f
else:
save u, v, t; pair u[], v[];
for n = 0 upto segs:
t := n/segs;
u[n] := postdirection [t] (f);
v[n] := pnt[t] (f) + (u[n] zscaled (0,d));
endfor
v0{u0}
for n = 1 upto segs: ...v[n]{u[n]} endfor
fi
enddef;
vardef parapath (expr d) expr f =
if d = 0:
f
else:
save a, g, h, p, q, s, t, u, v, w;
path g[], h, p[], q[];
numeric a, s, t;
pair u, v, w, w[];
s := emax (3, emin (segment_split, ceiling (max_points/5/length f)));
p := 0;
for i = 1 upto length f:
h := subpath (i-1, i) of f;
if not trivial h:
q[incr p] := h;
p[p] := parasegment (d, s, h);
fi
endfor
if p = 0:
f
else:
a := if d>0: - fi 180;
h := p1;
for i = 1 upto p-1:
u := predirection 1 (q[i]);
v := postdirection 0 (q[i+1]);
w1 := pnt 1 (q[i]) - (u zscaled (0,d));
w2 := pnt 0 (q[i+1]) - (v zscaled (0,d));
w3 := pnt [infinity] (h);
w4 := pnt 0 (p[i+1]);
g0 := arcpps(w3, w1, a);
g1 := h & g0;
g2 := arcpps(w2, w4, a) & p[i+1];
if (p[i] & g0) intersects reverse g2:
s := length g2 - _Ytime;
t := length h - length p[i] + _Xtime;
g1 := subpath (0, t) of g1;
g2 := subpath (s, length g2) of g2;
force_equal_ends (g1, g2);
h := g1 & g2;
else:
h := h .. p[i+1];
fi
endfor
if cycle f:
u := predirection 1 (q[p]);
v := postdirection 0 (q[1]);
w1 := pnt 1 (q[p]) - (u zscaled (0,d));
w2 := pnt 0 (q[1]) - (v zscaled (0,d));
w3 := pnt [infinity] (h);
w4 := pnt 0 (p[1]);
g3 := arcpps(w3, w1, a);
g0 := arcpps(w2, w4, a);
g1 := g0 & h & g3;
g2 := g0 & p[1];
if (p[p] & g3) intersects reverse g2:
s := length g2 - _Ytime;
t := length g0 + length h - length p[p] + _Xtime;
g1 := subpath (s, t) of g1;
force_equal_ends (g1, g1);
h := g1 & cycle;
else:
h := h..cycle;
fi
fi
h
fi
fi
enddef;
vardef turnangle@# (expr f) =
anglefromto(predirection@# (f), postdirection@#(f))
enddef;
def setdatadashes (text lst) =
save __type; __type := 0;
forsuffixes _itm = lst:
if knownnumericarray _itm :
copyarray (_itm) (__type[__type]);
next __type;
else: GBwarn "Improper dash pattern in setdatadashes.";
fi
endfor
if __type > 1:
save dashtype; dashtype := __type;
for _j = 0 upto dashtype - 1:
copyarray (__type[_j]) (dashtype[_j]);
endfor
else:
SetdataWarn "dashes";
fi
enddef;
def getdashpat expr n = dashtype[n mod dashtype] enddef;
def SetdataWarn expr s =
GBwarn "command setdata"& s &"() failed. Previous values retained.";
enddef;
numeric Solid, Simpledash, Simpledot, Dotdash, Dotdashdot, Dotdashdash;
dashpat (Solid) (0);
dashpat (Simple_dash) (3bp, 4bp);
dashpat (Simple_dot) (0, 4bp);
dashpat (Dot_dash) (0, 4bp, 3bp, 4bp);
dashpat (Dot_dash_dot) (0, 4bp, 3bp, 4bp, 0, 4bp);
dashpat (Dot_dash_dash) (0, 4bp, 3bp, 4bp, 3bp, 4bp);
numeric dashtype, dashtype[], dashtype[][];
def defaultdashes =
setdatadashes (Solid, Simple_dash, Simple_dot,
Dot_dash, Dot_dash_dot, Dot_dash_dash);
enddef;
defaultdashes;
def setdatasymbols (text lst) =
save __type; path __type[];
__type := 0;
for _itm = lst:
if (known _itm) and (path _itm):
__type[__type] := _itm;
next __type;
else:
GBwarn "Improper symbol in setdatasymbols().";
fi
endfor
if __type > 1:
save pointtype; pointtype := __type;
path pointtype[];
for _j = 0 upto pointtype - 1:
pointtype[_j] := __type[_j];
endfor
else:
SetdataWarn "symbols";
fi
enddef;
def getsymbol expr n := pointtype[n mod pointtype] enddef;
def DeclareGBSymbols (text S) =
forsuffixes _itm = S:
path _itm;
path _itm.clear;
pair _itm.tip;
endfor
enddef;
DeclareGBSymbols(
Triangle, Square, Circle, Diamond, Star, Plus, Cross,
Asterisk, Crossbar, Leftbar, Rightbar, Righthook,
Lefthook, SolidTriangle, SolidSquare, SolidCircle,
SolidDiamond, SolidStar
);
vardef undo_cycle expr f = subpath (0, length f) of f enddef;
SolidTriangle := (up--(dir 210)--(dir -30)--cycle) scaled .78;
Triangle := undo_cycle SolidTriangle;
Triangle.clear := SolidTriangle.clear :=
((dir -30)--(cosd 30,1)--(cosd 210,1)--(dir 210)--up--cycle)
scaled .78;
SolidSquare := (up--(-1,1)--(-1,-1)--(1,-1)--(1,1)--cycle) scaled .443;
Square := undo_cycle SolidSquare;
SolidCircle := fullcircle rotated 90;
Circle := undo_cycle SolidCircle;
Circle.clear := SolidCircle.clear :=
halfcircle--(-.5,.5)--(.5,.5)--cycle;
SolidDiamond := (up--left--down--right--cycle)
scaled .522 yscaled 1.44;
Diamond := undo_cycle SolidDiamond;
Diamond.clear := SolidDiamond.clear :=
(right--(1,1)--(-1,1)--left--up--cycle) scaled .522 yscaled 1.44;
Plus := ((0,0)--up--down--(0,0)--left--right) scaled .65;
Plus.clear := (right--(1,1)--(-1,1)--(left)--cycle) scaled .65;
Cross := ((0,0)--(dir 45)--(dir -135)--(0,0)--(dir -45)--(dir 135))
scaled .65;
Cross.clear := ((0,0)--(dir -45)--dir(45)--(dir 135)--(dir -135)--cycle)
scaled .65;
Asterisk := ((0,0)--up--down--(0,0)--(dir 30)--(dir -150)
--(0,0)--(dir -30)--(dir 150)) scaled .6;
Asterisk.clear := ((0,0)--(dir -30)--(cosd 30,1)--(cosd 150,1)
--(dir -150)--cycle) scaled .6;
Crossbar := ((0,0)--left--right) scaled .65;
Crossbar.clear := rect (right,(-1,.5)) scaled .65;
Leftbar := ((0,0)--left);
Rightbar := ((0,0)--right);
Leftbar.clear := rect((0,0),(-1,.5));
Rightbar.clear := rect((0,0),(1,.5));
Righthook := arcpps((0,0),(1,0),180);
Lefthook := Righthook xscaled -1;
Righthook.clear := Righthook--cycle;
Lefthook.clear := Lefthook--cycle;
vardef mkstar (expr n, m) (suffix A) =
save ang; ang := 360/n;
A1 := up; A3 := up rotated ang;
A2 = (whatever)[A1, A1 rotated ( ang*m)];
A2 = (whatever)[A3, A3 rotated (-ang*m)];
for i = 4 upto 2n:
A[i] := A[i-2] rotated ang;
endfor
A := 2n;
mkpoly (true, A)
enddef;
save _A; pair _A[];
SolidStar := mkstar (5, 2, _A) scaled .84;
Star := undo_cycle SolidStar;
Star.clear := polyline (true)
(_A9, _A10, _A1, _A2, _A3, (xpart _A3, 1), (xpart _A9, 1)) scaled .84;
SolidStar.clear := Star.clear;
forsuffixes S =
Triangle, Square, Circle, Diamond, Star, Plus, Cross,
Asterisk, Crossbar, Leftbar, Rightbar, Righthook,
Lefthook, SolidTriangle, SolidSquare, SolidCircle,
SolidDiamond, SolidStar :
S.tip := point 0 of S;
endfor
vardef gcd (expr n, m) =
save a, b, r;
a := emax (abs(m), abs(n));
b := emin (abs(m), abs(n));
if b > 0:
forever:
r := a mod b;
exitif r < 1;
a := b; b := r;
endfor
b
else:
a
fi
enddef;
vardef lcm (expr n, m) =
n/gcd(n, m)*m
enddef;
numeric pointtype; path pointtype[];
def defaultsymbols =
setdatasymbols( Circle, Cross, SolidDiamond, Square, Plus,
Triangle, SolidCircle, Star, SolidTriangle);
enddef;
defaultsymbols;
def computepie (suffix dat) (expr sign, ang, cent, rad) (text data) =
begingroup
save _tot, _max, _toobig;
_max := 0; dat := 0;
for _val = data:
dat[incr dat] := _val;
_max := emax (_max, _val);
endfor
if dat=0: GBwarn "piechart attempted with empty list.";
_toobig := 1;
else:
_toobig := infinity/dat;
fi
if _max > _toobig:
for _idx = 1 upto dat:
dat[_idx] := dat[_idx]/_toobig;
endfor
fi
for _idx = 2 upto dat:
dat[_idx] := dat[_idx - 1] + dat[_idx];
endfor
_tot := dat[dat];
for _idx = dat downto 2:
dat[_idx] := ang + sign*dat[_idx-1]/_tot*360;
endfor
dat1 := ang; dat[dat + 1] := ang + 360sign;
endgroup
enddef;
def piechart (expr sign, ang, cent, rad) (text data) =
save _dat;
computepie (_dat) (sign, ang, cent, rad) (data);
mkpiewedges (_dat, cent, rad);
enddef;
def mkpiewedges (suffix dat) (expr cent, rad) =
numeric piewedge, piedirection, pieangle, pieangle[];
pair piecenter, piedirection[];
path piewedge[];
piecenter := cent;
piedirection := pieangle := piewedge := dat;
for _idx = 1 upto dat:
pieangle[_idx] := dat[_idx];
piewedge[_idx] := sector (piecenter, rad, dat[_idx], dat[_idx+1]);
piedirection[_idx] := dir(0.5[ dat[_idx], dat[_idx+1] ]);
endfor
enddef;
def namedpiechart (suffix nm) (expr sign, ang, cent, rad) (text data) =
save _dat;
computepie (_dat) (sign, ang, cent, rad) (data);
setnumeric (nm) _dat;
pair nm.center, nm.direction[];
path nm.wedge[];
nm.center := cent;
for _idx = 1 upto _dat:
nm.wedge[_idx] := sector (cent, rad, _dat[_idx], _dat[_idx+1]);
nm.direction[_idx] := dir(0.5[ _dat[_idx], _dat[_idx+1] ]);
endfor
enddef;
def barchart (expr firstbar, sep, r, vert)(text data) =
numeric barbegin, barbegin[],
barend, barend[],
barlength, barlength[],
barstart, barstart[],
chartbar, barwd;
path chartbar[];
chartbar := 0; barwd := r*sep;
for _itm = data:
barend[incr chartbar] := if pair _itm: ypart _itm else: _itm fi;
barbegin[chartbar] := if pair _itm: xpart _itm else: 0 fi;
endfor
barbegin := barend := barlength := barstart := chartbar;
for _nn = 1 upto chartbar:
barstart[_nn] := firstbar + sep*(_nn-1);
barlength[_nn] := barend[_nn];
chartbar[_nn] := rect ((barbegin[_nn], 0), ( barend[_nn], barwd))
shifted (0, barstart[_nn]) if vert: xyswap fi;
endfor
enddef;
def namedbarchart (suffix nm) (expr first, sep, r, vert) (text data) =
save nm;
begingroup
save _bb, _ee, _ww;
path nm.bar[];
nm := 0; _ww := r*sep;
for _itm = data:
_ee := if pair _itm: ypart _itm else: _itm fi;
_bb := if pair _itm: xpart _itm else: 0 fi;
nm.bar[incr nm] := rect ((_bb, 0), ( _ee, _ww) )
shifted (0, first + sep*(nm-1)) if vert: xyswap fi;
endfor
endgroup
enddef;
picture totalpicture;
boolean totalnull, currentnull;
def clearit =
currentpicture := totalpicture := nullpicture;
currentnull := totalnull := true;
enddef;
def keepit =
addto totalpicture also currentpicture;
mono (totalpicture);
currentpicture := nullpicture;
totalnull := totalnull or currentnull;
currentnull := true;
enddef;
def addto_currentpicture =
currentnull := false;
addto currentpicture
enddef;
def mergeit (text do) =
if totalnull:
do currentpicture
elseif currentnull:
do totalpicture
else:
begingroup
save _v_; picture _v_;
_v_ := currentpicture;
addto _v_ also totalpicture;
do _v_
endgroup
fi
enddef;
boolean noship; noship := false;
def shipit = if noship: else: mergeit (shipout) fi enddef;
def showit_ = mergeit (show_) enddef;
def show_ suffix v = display v inwindow currentwindow enddef;
numeric gcode; gcode := 0;
% end grafbase.mf
endinput.
%%
%% End of file `grafbase.mf'.
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