[pstricks] Ghostscript 9.53 transparency operators
Herbert Voss
Herbert.Voss at fu-berlin.de
Tue Mar 30 18:19:01 CEST 2021
Am 30.03.21 um 16:05 schrieb Alexander Grahn:
> >
> >
> >Error: /undefined in --load--
> >Operand stack:
> > .setfillconstantalpha.bak .setfillconstantalpha
> >
>
> Ok. I did not claim my fix would work with obsolete GS versions, but with the
> new one, 9.53.*, it definitely does. Therefore my request to revise the current
> pstricks.pro.
I had a bug in the current pstricks.pro! Any change to the code must work
with GhostScript before and after 9.3
Try the attached example with the modified pstricks.pro
Herbert
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% $Id: pstricks.pro 1055 2019-05-16 11:59:06Z herbert $
%
%% PostScript prologue for pstricks.tex.
%% Version 1.33, 2020/09/21
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%
%
% Define the follwing gs-functions if not known, eg when using distiller
%
revision 952 gt
{
systemdict /.setopacityalpha known not
{
(\n\n%%%% WARNING: Transparency operations ignored - need to use -dALLOWPSTRANSPARENCY\n\n) print flush
/.setopacityalpha { pop } bind def
/.setshapealpha { pop } bind def
}
{
/.setopacityalpha /.setfillconstantalpha load def
/.setblendmode { pop } def
/.setshapealpha {dup .setfillconstantalpha .setstrokeconstantalpha true .setalphaisshape } def
} ifelse
}
{
systemdict /.setopacityalpha known not
{
(\n\n%%%% WARNING: Transparency operations ignored - need to use -dNOSAFER\n\n) print flush
/.setopacityalpha { pop } bind def
/.setshapealpha { pop } bind def
} if
} ifelse
%%<bool> .setalphaisshape -
%% If true, the values set by setstrokeconstantalpha and setfillconstantalpha are interpreted as shape values. The initial value of the AIS flag is false.
%
/tx at Dict 200 dict def % the main PSTricks dictionary
tx at Dict begin
/ADict 25 dict def % The arrow dictionary
/CM { matrix currentmatrix } bind def
/SLW /setlinewidth load def
/CLW /currentlinewidth load def
/CP /currentpoint load def
/ED { exch def } bind def
/L /lineto load def
/T /translate load def
/TMatrix { } def
/RAngle { 0 } def
/Sqrt { dup 0 lt { pop 0 } { sqrt } ifelse } def % return 0 for negative arguments
/Atan { /atan load stopped { pop pop 0 } if } def % return 0 if atan not known
/ATAN1 {neg -1 atan 180 sub } def % atan(x) (only one parameter)
/Div { dup 0 eq { pop } { div } ifelse } def % control the division
/Log { dup 1e-20 lt { pop -1e30 }{ log } ifelse } def % control the log
/tan { dup cos abs 1.e-10 lt
{ pop 1.e10 } % return 1.e10 as infinit
{ dup sin exch cos div } ifelse % default sin/cos
} def
/Tan { dup sin exch cos Div } def % sin(x)/cos(x) x in degrees
/Acos {dup dup mul neg 1 add dup 0 lt { % arc cos, returns 0 when negative root
pop pop 0 }{ sqrt exch atan} ifelse } def
/Acos2 { 2 dict begin
/x ED /y ED
y abs 1.0e-20 lt { 1.0e30 } if
x y div
dup dup mul neg 1 add dup 0 lt { % arc cos needs two values x,y
pop pop 0 }{ sqrt exch atan} ifelse
y 0 lt { 180 add } if
} def
/Power { % a^b latest ghostscript don't allow -4^-3.1
2 dict begin % hold all local
/b ED
/a ED
a 0 lt % prevent something like (-4)^(-3.1)=> 1/(-4)^3
{ b 0 lt
{ a b cvi exp }
{ a b exp } ifelse
}
{ a 0 eq { 0 }{ a b exp } ifelse
} ifelse
end
} def
%
/NET { neg exch neg exch T } def % change coordinate system to the negative one
/Pyth { dup mul exch dup mul add sqrt } def % Pythagoras, expects 2 parameter
/addCoors {
3 -1 roll % xA xB yB yA
add % xA xB yB+yA
3 1 roll % yB+yA xA xB
add % yB+yA xA+xB
exch % xA+xB yA+yB
} def
/Pyth2 { % Pythagoras, xA yA xB yB
3 -1 roll % xA xB yB yA
sub % xA xB yB-yA
3 1 roll % yB-yA xA xB
sub % yB-yA xA-xB
Pyth } def
/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian (original)
/PtoCrel { pst at angleunit PtoC } def % Polar to Cartesian with \degrees[??]
/PtoCab { dup cos 4 -1 roll mul 3 1 roll sin mul } def % Polar to Cartesian (Ellipse) a b phi-> x y
/AnytoDeg { pst at angleunit } def
/DegtoAny { 1 pst at angleunit div} def
/AnytoRad { AnytoDeg DegtoRad } def
/RadtoAny { RadtoDeg DegtoAny } def
%
%/Rand { rand 4294967295 div } def % a real random number
/Rand { rand 2147483447 div } def % a real random number between 0 and 1
%----------------- hv added 20050516 ---------------
/PiDiv2 1.57079632680 def
/Pi 3.14159265359 def
/TwoPi 6.28318530718 def
/Euler 2.71828182846 def
%/e Euler bind def
%
/RadtoDeg { 180 mul Pi div } bind def % convert from radian to degrees
/DegtoRad { Pi mul 180 div } bind def % viceversa
%
/startGlobal { true setglobal globaldict begin } bind def
/endGlobal { end false setglobal } bind def
/pssetRGBcolor /setrgbcolor load def
/pssetCMYKcolor /setcmykcolor load def
/pssetGraycolor /setgray load def
%
%----------------- hv end---------------------------
/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def
%
/PathLength {
flattenpath /z 0 def
{ /y1 ED /x1 ED /y2 y1 def /x2 x1 def }
{ /y ED /x ED PathLength@ }
{}
{ /y y2 def /x x2 def PathLength@ }
/pathforall load stopped { pop pop pop pop } if
z
} def
%
/STP { .996264 dup scale } def % BP/PT scaling
/STV { SDict begin normalscale end STP } def %
%
/DashLine {
dup 0 gt
{ /a .5 def PathLength exch div }
{ pop /a 1 def PathLength } ifelse
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dup /X ED % pattern array
0 get /y ED % length of first black segment
/z 0 X {add} forall def % length of the full pattern
%% Computation of the scaling factor as described by van Zandt:
b a .5 sub 2 mul y mul sub z Div round
z mul a .5 sub 2 mul y mul add b exch Div
%%%% scaling factor on stack.
/z ED %% now, z is the scaling factor
false % for the length test below
X { z mul } forall X astore %% modification TN 04-08-07
%%% Checking whether at least one dash in X has positive length:
{0 gt or} forall
{ X 1 a sub y mul }
{ [ 1 0 ] 0 }
ifelse
setdash stroke
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%
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/b PathLength def
/a ED /z ED /y CLW def
/z y z add def
a 0 gt {
/b b a div def
}{
a 0 eq {
/b b y sub def
}{ a -3 eq {
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} ifelse
[ 0 b b z Div round Div dup 0 le { pop 1 } if ]
a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse
setdash 1 setlinecap stroke
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%
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2 div cvi /n ED % n pairs
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n 1 sub {
/YB ED /XB ED
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/YLength YB YA sub def
/PAngle YLength XLength Atan def
/XYLength XLength YLength Pyth def
%% for negative SymStep we calculate the distance
SymStep 0 lt
{ %XYLength SymStep div abs cvi
/nSym SymStep abs cvi def }
{ /nSym XYLength SymStep div cvi def }
ifelse
0.5 setflat
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/deltaY YLength nSym div def
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{ XA YA moveto }
{ XA Shift sub YA Shift sub moveto }
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gsave
curveticks
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{
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Symbol show
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{ XA Shift sub YA Shift sub moveto }
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SymbolLinewidth setlinewidth stroke
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{
rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if
Symbol show
}
ifelse
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pop % delete the mark symbol
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%
/LineFill { % hv ------------ patch 7 -------------
gsave
abs /hatchWidthInc ED
abs /hatchSepInc ED
abs CLW add /a ED
a 0 dtransform round exch round exch
2 copy idtransform
exch Atan rotate
idtransform pop /a ED
.25 .25 itransform pathbbox
/y2 ED
a Div ceiling cvi /x2 ED /y1 ED
a Div cvi /x1 ED /y2 y2 y1 sub def
clipType % must be defined in pstricks.tex: clip -- eoclip
newpath
2 setlinecap
systemdict
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x1 a mul y1 moveto 0 y2 rlineto stroke
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a 0 dtransform round exch round exch
2 copy idtransform
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.25 .25 itransform
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/y2 ED /x2 ED /y1 ED /x1 ED
y2 y1 sub a div 2 add cvi /Ny ED
x2 x1 sub a div 2 add cvi /Nx ED
clipType % must be defined in pstricks.tex: clip -- eoclip
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/xA0 x1 dotRadius add CLW add def
Ny {
/xA xA0 def
Nx {
newpath
xA yA dotRadius 0 360 arc
SolidDot { gsave fill grestore } if
stroke
xA a add /xA ED
} repeat
yA a add /yA ED
} repeat
grestore
} def
%
/PenroseFill {% on stack: scaling factor
/Scale ED
% 1 exch div round /penroseFactor ED
% a 0 dtransform round exch round exch
% 2 copy idtransform
% exch Atan rotate
% idtransform pop /a ED
% .25 .25 itransform pathbbox
% /y2 ED
% a Div ceiling cvi /x2 ED /y1 ED
% a Div cvi /x1 ED /y2 y2 y1 sub def
clip
newpath
gsave
220 150 translate
Scale dup scale
systemdict /setstrokeadjust known { true setstrokeadjust } if
/I/S/L/W/G/+/Z/F/E/D[/def/exch/for{E D}/add{s E get mul}
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grestore
% pop pop
} def
%
/PenroseFillA {% on stack: scaling factor, border color, kite color, dart color
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Scale dup scale
/border_colour ED
/kite_colour ED
/dart_colour ED
clip
newpath
gsave
100 100 translate
6
Scale 1 lt { 1 Scale dup add div mul cvi } if %%%% Number of iterations
10 %%%% Long side length in millimeters
/border_width { L 0.06 mul }def %%%% Choose the scalefactor for the borders
/L exch 25.4 div 72 mul def %%%% Conversion: mm -> inches -> points
/f{-1 5 sqrt add 2 div}bind def %%%% The reciprocal of the golden ratio
/l{L f mul}bind def %%%% Short side length l = L*f
/Ll{L l add}bind def %%%% Ll = L + l
/c{36 cos L mul}bind def %%%% c = L*cos(36)
/s{36 sin L mul}bind def %%%% s = L*sin(36)
/draw_tile { 0 0 moveto c s lineto 0 lineto gsave closepath gsave fill grestore
0 setlinewidth stroke grestore border_colour stroke } bind def
/half_kite { dup dup 0 gt{ 1 sub gsave f f neg scale -36 rotate half_dart
Ll 0 translate 144 rotate kite grestore }
{ kite_colour L draw_tile }ifelse
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{ dart_colour l draw_tile }ifelse
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border_width setlinewidth 1 setlinejoin 1 setlinecap
% 450 0 translate
dup f exch neg exp dup scale
5 {kite 72 rotate } repeat stroke
grestore
} def
%
%
/TruchetFill { % on stack: scaling factor
10 dict begin
dup dup scale
1 exch div round /penroseFactor ED
a 0 dtransform round exch round exch
2 copy idtransform
exch Atan rotate
idtransform pop /a ED
.25 .25 itransform pathbbox
/y2 ED
a Div ceiling cvi /x2 ED /y1 ED
a Div cvi /x1 ED /y2 y2 y1 sub def
clip
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systemdict
/setstrokeadjust known { true setstrokeadjust } if
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/ha a 2 div def
/mha ha neg def
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rand dup 2 idiv 2 mul eq { 90 rotate } if
mha mha moveto ha mha lineto
ha ha lineto mha ha lineto
% closepath .1 setlinewidth stroke
contents
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0 ha moveto ha 0 lineto
0 mha moveto mha 0 lineto
% 1 setlinewidth stroke
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/dotiling {
f ma mul a f a mul {
/i exch def
f ma mul a f a mul {
/j exch def
gsave i j translate
tile stroke grestore
} for
} for
} def
%
/f 3 def
5 srand dotiling
end % local user dict
} def
%
/BeginArrow {
ADict begin % hold it local, for end see EndArrow
/@mtrx CM def
gsave
2 copy T
2 index sub neg exch
3 index sub exch Atan
rotate newpath
} def
%
/EndArrow { @mtrx setmatrix CP grestore end } def % end the ADict
%
/Arrow {
CLW mul add dup
2 div /w ED
mul dup /h ED
mul /a ED
{ 0 h T 1 -1 scale } if
w neg h moveto
0 0 L w h L w neg a neg rlineto
gsave fill grestore
} def
%
/ArrowD { % the sides are drawn as curves (hv 20071211)
CLW mul add dup
2 div /w ED
mul dup /h ED
mul /Inset ED
{ 0 h T 1 -1 scale } if % changes the direction
% we use y=w/h^2 * x^2 as equation for the control points
% for the coordinates the arrow is seen from top to bottom
% the bottom (tip) is (0;0)
w neg h moveto % lower left of >
w 9 div 4 mul neg h 3 div 2 mul
w 9 div neg h 3 div
0 0 curveto % tip of >
w 9 div h 3 div
w 9 div 4 mul h 3 div 2 mul
w h curveto % upper left of >
w neg Inset neg rlineto % move to x=0 and inset
gsave fill grestore
} def
%
/Tbar {
CLW mul add /z ED
z -2 div CLW 2 div moveto
z 0 rlineto stroke
0 CLW moveto
} def
%
/Bracket {
CLW mul add dup CLW sub 2 div
/x ED mul CLW add /y ED /z CLW 2 div def
x neg y moveto
x neg CLW 2 div L x CLW 2 div L x y L stroke
0 CLW moveto
} def
%
/RoundBracket {
CLW mul add dup 2 div
/x ED mul /y ED /mtrx CM def
0 CLW 2 div T x y mul 0 ne { x y scale } if
1 1 moveto
.85 .5 .35 0 0 0 curveto
-.35 0 -.85 .5 -1 1 curveto
mtrx setmatrix stroke 0 CLW moveto
} def
%
/SD { 0 360 arc fill } def
%
/EndDot { % DS is the dot size
{ /z DS def } { /z 0 def } ifelse % outer or inner dimen
/b ED % the color definition
0 z DS SD
b { 0 z DS CLW sub SD } if
0 DS z add CLW 4 div sub
moveto
} def
%
/Shadow { [ { /moveto load } { /lineto load } { /curveto load } {
/closepath load } /pathforall load stopped { pop pop pop pop CP /moveto
load } if ] cvx newpath 3 1 roll T exec } def
%
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counttomark 2 div dup cvi /n ED % n 2 div on stack
n eq not { exch pop } if % even numbers of points? delete one
] aload /Points ED
showpoints not { Points aload pop } if
% { ] aload /Points ED }
% { n 2 mul 1 add -1 roll pop } ifelse % delete the mark symbol
} def
%
/Line {
NArray n 0 eq not
{ n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def
n { Lineto } repeat
CP 4 2 roll ArrowB L pop pop
} if
} def
%
/LineToYAxis {
/Ox ED % Save the x origin value
NArray % all x-y pairs on stack
n { 2 copy moveto % go to current point
Ox exch Lineto % line to y-axis
pop % delete old x-value
} repeat
} def
%
/LineToXAxis{
/Oy ED % Save the y origin value
NArray % all x-y pairs on stack
n 0 eq not
{ n 1 eq { 0 0 /n 2 def } if
ArrowA
/n n 2 sub def
CP 2 copy moveto pop Oy Lineto
n { 2 copy moveto pop Oy Lineto } repeat
CP
4 2 roll
ArrowB
2 copy moveto pop Oy
L
pop pop } if
} def
%
/Arcto {
/a [ 6 -2 roll ] cvx def
a r
/arcto load stopped { 5 } { 4 } ifelse { pop } repeat
a
} def
%
/CheckClosed {
dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq
and { pop pop /n n 1 sub def } if
} def
%
/Polygon {
NArray n 2 eq { 0 0 /n 3 def } if
n 3 lt
{ n { pop pop } repeat }
{ n 3 gt { CheckClosed } if
n 2 mul -2 roll
/y0 ED /x0 ED /y1 ED /x1 ED
x1 y1
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x1 y1 moveto
/n n 2 sub def
n { Lineto } repeat
x1 y1 x0 y0 6 4 roll Lineto
Lineto pop pop closepath } ifelse
} def
%
/SymbolPolygon { % on stack [ x y x y ...
counttomark % number of elements
2 add /m ED
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m 2 div cvi /n ED % n pairs
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n 1 sub {
/YB ED /XB ED
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/YLength YB YA sub def
/PAngle YLength XLength Atan def
/XYLength XLength YLength Pyth def
/nSym XYLength SymStep Div cvi def
/Shift Symbol stringwidth pop 2 Div def
/deltaX XLength nSym Div def
/deltaY YLength nSym Div def
XA Shift sub YA Shift sub moveto
nSym {
gsave rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if
Symbol show
grestore
deltaX deltaY rmoveto
} repeat
% XB Shift sub YB Shift sub moveto Symbol show
/YA YB def /XA XB def
} repeat
pop % delete the mark symbol
} def
%
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/mtrx CM def
T rotate
/h ED
/w ED
dup 0 eq { pop } { CLW mul neg
/d ED
/a w h Atan def
/h d a sin Div h add def
/w d a cos Div w add def } ifelse
mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div
/ArrowA { moveto } def
/ArrowB { } def
false Line
closepath mtrx setmatrix } def
%
/Triangle {
/mtrx CM def
translate
rotate /h ED 2 div /w ED
dup CLW mul /d ED
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/w w d h w Atan 2 div dup cos exch sin Div mul sub def
mark
0 d w neg d 0 h w d 0 d
/ArrowA { moveto } def
/ArrowB { } def
false
Line
closepath
mtrx
% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis)
% setmatrix } def
setmatrix pop
} def
% DG/SR modification end
%
/CCA {
/y ED /x ED
2 copy y sub /dy1 ED
x sub /dx1 ED
/l1 dx1 dy1 Pyth def
} def
%
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/l0 l1 def
/x1 x dx sub def
/y1 y dy sub def
/dx0 dx1 def
/dy0 dy1 def
CCA
/dx dx0 l1 c exp mul dx1 l0 c exp mul add def
/dy dy0 l1 c exp mul dy1 l0 c exp mul add def
/m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos abs b exp a mul dx dy Pyth Div 2 div def
/x2 x l0 dx mul m mul sub def
/y2 y l0 dy mul m mul sub def
/dx l1 dx mul m mul neg def
/dy l1 dy mul m mul neg def
} def
%
/IC {
/c c 1 add def
c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } ifelse
/a a 2 mul 3 div 45 cos b exp div def
CCA
/dx 0 def
/dy 0 def
} def
%
/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def
/NC { CC x1 y1 x2 y2 x y curveto } def
/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def
/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def
/NAC { x2 y2 x y curveto CC x1 y1 } def
/EAC { x2 y2 x y ArrowB curveto pop pop } def
%
/OpenCurve {
NArray n 3 lt
{ n { pop pop } repeat }
{ BOC /n n 3 sub def n { NC } repeat EOC } ifelse
} def
%
/CurvePath {
%% for negative SymStep we calculate the distance
SymStep 0 lt { gsave PathLength SymStep div abs /SymStep ED grestore } if
0.5 setflat
flattenpath /z 0 def /z0 0 def
{ /y1 ED /x1 ED /y2 y1 def /x2 x1 def
x1 Shift sub y1 Shift sub moveto
gsave
curveticks
{ x1 y1 translate startAngle rotate
0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
SymbolLinewidth setlinewidth stroke
}
{ startAngle rotate Symbol show }
ifelse
grestore /z0 z def }
{ /y ED /x ED PathLength@ z z0 sub SymStep ge {
x Shift sub y Shift sub moveto
gsave
curveticks
{ y yOld sub x xOld sub Atan 180 sub CorrAngle sub /rotAngle ED
x y translate rotAngle rotate
0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
SymbolLinewidth setlinewidth stroke
}
{
rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
Symbol show
}
ifelse
grestore /z0 z def } if
/yOld y def /xOld x def }
{} %% the lineto part
{ /y y2 def /x x2 def PathLength@
x Shift sub y Shift sub moveto
gsave
curveticks
{ y yOld sub x xOld sub Atan 180 sub /rotAngle ED
x y translate rotAngle rotate
0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
SymbolLinewidth setlinewidth stroke
}
{
x Shift sub y Shift sub moveto
rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
Symbol show
}
ifelse
grestore
}
pathforall
% curveticks
% { gsave
% x y translate rotAngle rotate
% 0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
% SymbolLinewidth setlinewidth stroke grestore
% } if
z
} def
%
/OpenSymbolCurve {
OpenCurve
0.1 setflat
/Shift Symbol stringwidth pop 2 div def
CurvePath
} def
%
/AltCurve {
{ false NArray n 2 mul 2 roll
[ n 2 mul 3 sub 1 roll ] aload
/Points ED
n 2 mul -2 roll }
{ false NArray } ifelse
n 4 lt { n { pop pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse
} def
%
/AltOpenSymbolCurve {
AltCurve
0.1 setflat
/Shift Symbol stringwidth pop 2 div def
CurvePath
} def
%
/ClosedCurve {
NArray n 3 lt
{ n { pop pop } repeat }
{ n 3 gt { CheckClosed } if
6 copy n 2 mul 6 add 6 roll
IC CC x y moveto n { NC } repeat
closepath pop pop
} ifelse
} def
%
/ClosedSymbolCurve {
ClosedCurve
0.1 setflat
/Shift Symbol stringwidth pop 2 div def
CurvePath
} def
%
/CalcBezierSpline {% Christoph Bersch
10 dict begin
/getX { Points exch 2 mul get } def
/getY { Points exch 2 mul 1 add get } def
/n Points length 1 sub 2 idiv def
/GetFirstControlPoints {
/x n array def
/tmp n array def
/b 2 def
x 0 rhs 0 get b div put
1 1 n 1 sub {
/i exch def
tmp i 1 b div dup 4 1 roll put
i n 1 sub lt { 4 }{ 3.5 } ifelse exch sub /b exch def
x i rhs i get x i 1 sub get sub b div put
} for
1 1 n 1 sub {
n exch sub
dup dup x exch 1 sub 2 copy 6 2 roll
get 3 1 roll tmp exch get
exch x exch get mul sub
put
} for
x
} def
%
n 1 eq {
0 getX 2 mul 1 getX add 3 div
0 getY 2 mul 1 getY add 3 div
exch dup 3 1 roll 2 mul 0 getX sub
exch dup 3 1 roll 2 mul 0 getY sub
[ 0 getX 0 getY 7 3 roll 1 getX 1 getY ] /outPoints exch def
} {
/outPoints 6 n mul 2 add array def
0 1 n {
dup dup 6 mul dup 1 add
outPoints exch 5 -1 roll getY put
outPoints exch 3 -1 roll getX put
} for
/rhs n array def
1 1 n 2 sub {
rhs exch dup dup getX 4 mul exch 1 add getX 2 mul add put
} for
rhs 0 0 getX 1 getX 2 mul add put
rhs n 1 sub dup getX 8 mul n getX add 2 div put
GetFirstControlPoints
1 1 n 2 sub {
rhs exch dup dup getY 4 mul exch 1 add getY 2 mul add put
} for
rhs 0 0 getY 1 getY 2 mul add put
rhs n 1 sub dup getY 8 mul n getY add 2 div put
GetFirstControlPoints
0 1 n 1 sub {
/i exch def
2 copy
i get outPoints 6 i mul 3 add 3 -1 roll put
i get outPoints 6 i mul 2 add 3 -1 roll put
2 copy
i n 1 sub lt {
i 1 add get i 1 add getY 2 mul exch sub outPoints 6 i mul 5 add 3 -1 roll put
i 1 add get i 1 add getX 2 mul exch sub outPoints 6 i mul 4 add 3 -1 roll put
}{
n 1 sub get n getY add 2 div outPoints 6 n 1 sub mul 5 add 3 -1 roll put
n 1 sub get n getX add 2 div outPoints 6 n 1 sub mul 4 add 3 -1 roll put
} ifelse
} for
pop pop
} ifelse
outPoints
end
} def
/Spline {
/showpoints ED
counttomark 2 div dup cvi /n ED
n eq not { exch pop } if
] /Points ED
n 1 gt {
CalcBezierSpline
mark exch aload pop
ArrowA
n 2 sub {
6 2 roll 4 2 roll curveto
} repeat
6 2 roll 4 2 roll ArrowB curveto
} if
} def
/OpenSymbolSpline {
Spline
0.1 setflat
/Shift Symbol stringwidth pop 2 div def
CurvePath
} def
%
/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def
/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def
/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } def
%
/FontDot {
DS 2 mul dup
matrix scale matrix concatmatrix exch matrix
rotate matrix concatmatrix exch
findfont exch makefont setfont
} def
%
/Rect {
x1 y1 y2 add 2 div moveto
% x1 y2 lineto
% x2 y2 lineto
% x2 y1 lineto
% x1 y1 lineto
x1 y1 lineto % counter clockwise path
x2 y1 lineto
x2 y2 lineto
x1 y2 lineto
closepath
} def
%
/OvalFrame {
x1 x2 eq y1 y2 eq or
{ pop pop x1 y1 moveto x2 y2 L }
{ y1 y2 sub abs x1 x2 sub abs 2 copy gt
{ exch pop } { pop } ifelse
2 div exch { dup 3 1 roll mul exch } if
2 copy lt { pop } { exch pop } ifelse
/b ED
x1 y1 y2 add 2 div moveto
x1 y2 x2 y2 b arcto
x2 y2 x2 y1 b arcto
x2 y1 x1 y1 b arcto
x1 y1 x1 y2 b arcto
16 { pop } repeat
closepath
} ifelse
} def
%
/Frame {
CLW mul /a ED
3 -1 roll
2 copy gt { exch } if
a sub /y2 ED
a add /y1 ED
2 copy gt { exch } if
a sub /x2 ED
a add /x1 ED
1 index 0 eq { pop pop Rect } { OvalFrame } ifelse
} def
%
/BezierNArray {
/f ED
counttomark 2 div dup cvi /n ED
n eq not { exch pop } if
n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat
f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse
} def
%
/OpenBezier {
BezierNArray
n 1 eq
{ pop pop }
{ ArrowA n 4 sub 3 idiv
{ 6 2 roll 4 2 roll curveto } repeat
6 2 roll 4 2 roll ArrowB curveto } ifelse
} def
%
/OpenSymbolBezier {
OpenBezier
0.1 setflat
/Shift Symbol stringwidth pop 2 div def
CurvePath
} def
%
/ClosedBezier {
BezierNArray
n 1 eq
{ pop pop }
{ moveto n 1 sub 3 idiv
{ 6 2 roll 4 2 roll curveto } repeat
closepath } ifelse
} def
%
/ClosedSymbolBezier {
/f ED % save showpoints value
2 copy /yEnd ED /xEnd ED
counttomark -2 roll 2 copy /yStart ED /xStart ED
counttomark 2 roll
f
ClosedBezier
0.1 setflat
/Shift Symbol stringwidth pop 2 div def
CurvePath
[ xEnd yEnd xStart yStart SymbolLine
} def
%
/BezierShowPoints {
gsave
Points aload length 2 div cvi /n ED
moveto
n 1 sub { lineto } repeat
CLW 2 div SLW [ 4 4 ] 0 setdash stroke
grestore
} def
%
/Parab {
/y0 ED /x0 ED /y1 ED /x1 ED
/dx x0 x1 sub 3 div def
/dy y0 y1 sub 3 div def
x0 dx sub y0 dy add x1 y1 ArrowA
x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB
curveto
/Points [ x1 y1 x0 y0 x0 2 mul x1 sub y1 ] def
} def
%
/Parab1 { % 1 end | 0 SP
/ySP ED /xSP ED /y1 ED /x1 ED
/dx xSP x1 sub 3 div def
/dy ySP y1 sub 3 div def
newpath x1 y1 moveto xSP y1 lineto xSP ySP lineto
x1 ySP lineto closepath clip
currentpoint
newpath moveto
xSP dx sub ySP dy add x1 y1 ArrowA
xSP dx add ySP dy add xSP 2 mul x1 sub y1 ArrowB
curveto
/Points [ x1 y1 xSP ySP xSP 2 mul x1 sub y1 ] def
} def
%
/Grid {
newpath
/a 4 string def
/b ED % psk at gridlabels in pt
/c ED % { \pst at usecolor\psgridlabelcolor }
/n ED % psk at griddots
cvi dup 1 lt { pop 1 } if
/s ED % \psk at subgriddiv
s div dup 0 eq { pop 1 } if
/dy ED s div dup 0 eq { pop 1 } if % \pst at number\psyunit abs
/dx ED dy div round dy mul % \pst at number\psxunit abs
/y0 ED dx div round dx mul
/x0 ED dy div round cvi
/y2 ED dx div round cvi
/x2 ED dy div round cvi
/y1 ED dx div round cvi
/x1 ED
/h y2 y1 sub 0 gt { 1 } { -1 } ifelse def
/w x2 x1 sub 0 gt { 1 } { -1 } ifelse def
b 0 gt {
/z1 b 4 div CLW 2 div add def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Helvetica findfont b scalefont setfont
% is set in pstricks.tex
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% /NimbusSanL-Regu findfont b scalefont setfont
/b b .95 mul CLW 2 div add def } if
systemdict /setstrokeadjust known
{ true setstrokeadjust /t { } def }
{ /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add
exch itransform } bind def } ifelse
gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse
/i x1 def
/f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def
/g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def
x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if
dup % run loop two times: lines and labels
{ i dx mul dup xGridOffset add y0 moveto % draw the lines
dup t f moveto
g t L stroke
/i i w add def
} repeat
/i x1 def
GridDX div ceiling cvi
{ i dx mul GridDX mul dup xGridOffset add y0 moveto % plot the labels
b 0 gt
{ gsave c i GridDX mul a cvs dup stringwidth pop /z2 ED
w 0 gt {z1} {z1 z2 add neg} ifelse
h 0 gt {b neg}{z1} ifelse exch GridDX div z2 2 div sub exch
rmoveto show grestore } if
/i i w add def
} repeat
grestore
gsave
n 0 gt
{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
{ 2 setlinecap } ifelse
/i y1 def
/f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def
/g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def
y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if
dup % run loop two times: lines and labels
{ newpath i dy mul dup yGridOffset add x0 exch moveto
dup f exch t moveto
g exch t L stroke
/i i h add def
} repeat
/i y1 def
GridDY div ceiling cvi
{ newpath i dy mul GridDY mul dup yGridOffset add x0 exch moveto
b 0 gt { gsave c i GridDY mul a cvs dup stringwidth pop
/z2 ED
w 0 gt {z1 z2 add neg} {z1} ifelse
h 0 gt {z1} {b neg} ifelse GridDY div b 2 div sub
rmoveto show grestore } if
/i i h add def
} repeat
grestore
} def
%
/ArcArrow {
/d ED /b ED /a ED
gsave
newpath 0 -1000 moveto clip
newpath
0 1 0 0 b
grestore
c mul
/e ED
pop pop pop r a e d PtoC y add exch x add
exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
mul neg d
} def
%
%
/isbool { type (booleantype) cvn eq } def
%
/Ellipse {
dup isbool { /MoveToStart ED }{ /MoveToStart false def }ifelse % false or true
/rotAngle ED
/mtrx CM def
T
rotAngle rotate
scale
MoveToStart { 0 0 moveto 1 0 rmoveto } if % move to the start position
0 0 1 5 3 roll arc
mtrx setmatrix
} def
%
/ArcAdjust { %%%% Vincent Guirardel
% given a target length (targetLength) and an initial angle (angle0) [in the stack],
% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
% This computes an angle t such that (x0,y0) is at distance
% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
% contrary to TvZ's code.
% To achieve, this, one iterates the following process: start with some angle t,
% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
%
% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
% the value of d = add/sub is used to know on which side we have to move.
% It is only used in the initialisation of the angle before the iteration.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Input stack: 1: target length 2: initial angle
% variables used : rx, ry, d (=add/sub)
%
/targetLength ED /angle0 ED
/x0 rx angle0 cos mul def
/y0 ry angle0 sin mul def
% we are looking for an angle t such that (x0,y0) is at distance targetLength
% from the point M(t)=(rx*cos(t),ry*sin(t)))
%initialisation of angle (using 1st order approx = TvZ's code)
targetLength 57.2958 mul
angle0 sin rx mul dup mul
angle0 cos ry mul dup mul
add sqrt div
% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
% (if the ellipse is very curved at the point where we draw the arrow, %
% the value can be much more than 360 degrees !)
% this should avoid going on the wrong side (more than 180 degrees) or go near
% a bad attractive point (at 180 degrees)
dup 90 ge { pop 90 } if
angle0 exch d % add or sub
% maximum number of times to iterate the iterative procedure:
% iterative procedure: takes an angle t on top of stack, computes a
% better angle (and put it on top of stack)
30 { dup
% compute distance D between (x0,y0) and M(t)
dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
% if D almost equals targetLength, we stop
dup targetLength sub abs 1e-5 le { pop exit } if
% stack now contains D t
% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
exch dup cos rx mul x0 sub exch sin ry mul y0 sub
% stack contains: y(t)-y0, x(t)-x0, d
2 index Div targetLength mul y0 add ry Div exch
2 index Div targetLength mul x0 add rx Div
% stack contains x(t')/rx , y(t')/ry , d
% now compute t', and remove D from stack
atan exch pop
} repeat
% we don't look at what happened... in particular, if targetLength is greater
% than the diameter of the ellipse...
% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
% to give back the result as a an angle relative to angle0 we could add the following line:
% angle0 sub 0 exch d
%
% begin bug fix 2006-01-11
% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180
%(we don't want to make the ellipse turn more or less than it should)...
dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
% end bug fix
} def
%
/EllipticArcArrow {
/d ED % is add or sub
/b ED % arrow procedure
/a1 ED % angle
gsave
newpath
0 -1000 moveto
clip % Set clippath far from arrow.
newpath
0 1 0 0 b % Draw arrow to determine length.
grestore
% Length of arrow is on top of stack. Next 3 numbers are junk.
%
a1 exch ArcAdjust % Angular position of base of arrow.
/a2 ED
pop pop pop
a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig
a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig
a1 cos rx mul xOrig add %
a1 sin ry mul yOrig add %
% Now arrow tip coor and base coor are on stack.
b pop pop pop pop % Draw arrow, and discard coordinates.
a2 CLW 8 div
% change value of d (test it by looking if `` 1 1 d '' gives 2 or not )
1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
ArcAdjust
% resets original value of d
1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap.
} def
%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
%
/Rot { CP CP translate 3 -1 roll neg rotate NET } def
%
/RotBegin {
tx at Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if
/TMatrix [ TMatrix CM ] cvx def
/a ED
a Rot /RAngle [ RAngle dup a add ] cvx def
} def
%
/RotEnd {
/TMatrix [ TMatrix setmatrix ] cvx def
/RAngle [ RAngle pop ] cvx def
} def
%
/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
%
/Uput {
/a ED
add 2 div /h ED 2
div /w ED
/s a sin def
/c a cos def
/b s abs c abs 2 copy gt dup
/q ED
{ pop } { exch pop } ifelse def
/w1 c b div w mul def
/h1 s b div h mul def
q { w1 abs w sub dup c mul abs }{ h1 abs h sub dup s mul abs } ifelse
} def
%
/UUput {
5 dict begin
/z ED
abs /y ED
/x ED
q { x s div c mul abs y gt }{ x c div s mul abs y gt } ifelse
{ x x mul y y mul sub z z mul add sqrt z add }
{ q { x s div } { x c div } ifelse abs
} ifelse
a PtoC
h1 add exch
w1 add exch
end
} def
%
end
%-----------------------------------------------------------------------------%
%
% END pstricks.pro
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