% $Id: pstricks.pro 90 2009-01-30 10:58:51Z herbert $
%
%% PostScript prologue for pstricks.tex.
%% Version 1.06, 2009/01/30
%%
%% 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
%
systemdict /.setopacityalpha known not {/.setopacityalpha { pop } def } if
systemdict /.setblendmode known not {/.setblendmode { pop } def } if
systemdict /.setshapealpha known not {/.setshapealpha { pop } def } if
%
/tx@Dict 200 dict def 				% the main PSTricks dictionary
tx@Dict begin
/ADict 25 dict def				% The arrow dictionaray
/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
/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
/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
/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
/Rand { rand 4294967295 div } def		% a real random number
%----------------- 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
%----------------- 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	% 
%
%%-------------- DG begin patch 15 ---------------%%
%/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def
%PathLength } ifelse /b ED /x ED /y ED /z y x add def 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 dup y mul
%/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ]
%0 } ifelse setdash stroke } def
/DashLine {
  dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse
  /b ED /x1 ED /y1 ED /x ED /y ED 
  /z y x add y1 add x1 add def
  /Coef 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 def 
  /y y Coef mul def 
  /x x Coef mul def 
  /y1 y1 Coef mul def 
  /x1 x1 Coef mul def
  x1 0 gt y1 0 gt or x 0 gt or y 0 gt and 
    { [ y x y1 x1 ] 1 a sub y mul }
    { [ 1 0 ] 0 } ifelse 
  setdash stroke
} def
%%-------------- DG end patch 15 ---------------%%
/DotLine { 
  /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 { 
      /b b y add def } if 
    } ifelse 
  } 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 
} def
%
/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 
  clip 
  newpath 
  2 setlinecap 
  systemdict
  /setstrokeadjust known { true setstrokeadjust } if 
  x2 x1 sub 1 add { 
    x1 a mul y1 moveto 0 y2 rlineto stroke 
    /x1 x1 1 add 
      hatchWidthInc 0 gt { CLW add } if 
    def 
    hatchSepInc 0 gt hatchWidthInc 0 gt or { 
      /a a hatchSepInc add def
      CLW hatchWidthInc add SLW 
    } if
  } repeat 
  grestore 
  pop pop } def
%
/PenroseFill {%	 on stack: scaling factor
  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 
  newpath 
  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}
 { Z -36.2001 1 33 }{25 E S rlineto}{/q Z dup q G E q 1 + G}{Z 2 2}]{cvx def}forall
  [0 72 1008 {dup sin E cos }F ]1 setlinejoin/s W{/a W{/b I 10{/i I 4{/m I moveto
  i m +/j I 10{/l Z b m l + G a l G sub s m get div .2 + floor .3 + 25
  mul j l + S rmoveto}F i L j L stroke }F}F}F}F 
  grestore 
  pop pop 
} def
%
%gsave abs CLW add /a ED a 0 dtransform round exch round exch
%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25
%% DG/SR modification begin - Dec. 12, 1997 - Patch 2
%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a
%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a
%% DG/SR modification end
%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict
%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1
%% DG/SR modification begin - Jun.  1, 1998 - Patch 3 (from Michael Vulis)
%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore }
%% def
%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore
%pop pop } def
%% DG/SR modification end
%
/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 
  /b ED 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
%
%/NArray { 
%   aload length 2 div dup dup cvi eq not { exch pop } if /n exch
%   cvi def 
%} def
%
/NArray { % holds the coordinates and on top of stack the showpoints boolean
  /showpoints ED 
  counttomark 2 div dup cvi /n ED 
  n eq not { exch pop } if
  showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse 
} 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
%
/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 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def 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
/Diamond { 
  /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
% DG modification begin - Jan. 15, 1997
%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq {
%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2
%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0
%d /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 
  /h h d w h Atan sin Div sub def 
  /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
%
/CC { 
  /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
%
/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
%
/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
%
/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 
  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
%
/ClosedBezier { 
  BezierNArray 
  n 1 eq 
    { pop pop } 
    { moveto n 1 sub 3 idiv 
      { 6 2 roll 4 2 roll curveto } repeat 
      closepath } ifelse 
} 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
%
/Grid { 
  newpath 
  /a 4 string def 
  /b ED /c ED /n ED 
  cvi dup 1 lt { pop 1 } if 
  /s ED 
  s div dup 0 eq { pop 1 } if 
  /dy ED s div dup 0 eq { pop 1 } if
  /dx ED dy div round dy mul 
  /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 
    /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 
  { i dx mul dup y0 moveto 
    b 0 gt 
      { gsave c i a cvs dup stringwidth pop 
        /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse 
	h 0 gt {b neg}{z1} ifelse 
        rmoveto show grestore } if 
    dup t f moveto 
    g t L stroke 
    /i i w add def 
  } repeat 
  grestore 
  gsave 
  n 0 gt
  % DG/SR modification begin - Nov. 7, 1997 - Patch 1
  %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }
    { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
  % DG/SR modification end
    { 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 
  { newpath i dy mul dup x0 exch moveto 
    b 0 gt { gsave c i a cvs dup stringwidth pop 
      /z2 ED 
      w 0 gt {z1 z2 add neg} {z1} ifelse 
      h 0 gt {z1} {b neg} ifelse 
      rmoveto show grestore } if 
    dup f exch t moveto 
    g exch t L stroke 
    /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
%
/Ellipse { /mtrx CM def T scale 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@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 { 
  /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 
} def
%
/BeginOL { 
  dup (all) eq exch TheOL eq or 
    { IfVisible not { Visible /IfVisible true def } if } 
    { IfVisible { Invisible /IfVisible false def } if } ifelse 
} def
%
/InitOL { 
  /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def
  /Visible { CP OLUnit idtransform T moveto } def 
  /Invisible { CP OLUnit neg exch neg exch idtransform T moveto } def 
  /BOL { BeginOL } def
  /IfVisible true def 
} def
%
end
%-----------------------------------------------------------------------------%
%
% END pstricks.pro
