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%
/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
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%
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%initialisation of angle (using 1st order approx = TvZ's code)
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% (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)
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% 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
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% if D almost equals targetLength, we stop
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% 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
%
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/a1 ED % angle
gsave
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newpath
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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
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a2 cos rx mul x add
a2 sin ry mul y add
a1 cos rx mul x add
a1 sin ry mul y 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 -------------------%%
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%% PostScript prologue for pstricks.tex.
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%%
%% Timothy Van Zandt <tvz@Princeton.EDU>
%%
%% Modified by Etienne Riga - Dec. 16, 1999
%% Modified by Herbert Voss (hv) - 2004/12/27
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%-------------- hv begin 2004/07/25 from: er 2003/03/24
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const mul dup cos amp4 mul exch sin amp4 mul x1 inc add const mul dup
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mul exch sin amp6 mul x1 inc 0.6 mul add const mul dup cos amp1 mul
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mul exch sin amp7 mul dr inc 0.1 mul sub const mul dup cos amp3 mul
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mul 0 translate /arrowspec load flip { -90 }{ 90 } ifelse arrow1 0
y11 dr 1 arrowpos sub mul y11 dashline linesep 0 ne { 0 y22 dr 1 arrowpos
sub mul y22 dashline } if grestore } def
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mul def dsize 0 eq { linesep 0 eq { 0 0 radius 0 darc dasharc } { 0
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0 translate /arrowspec load flip { 0 } { 180 } ifelse arrow1 grestore
} def
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stroke grestore } def
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} def
/gcirc{ gsw /gcolor ed /radius ed translate 1 setgray newpath 0 0
radius 0 360 arc fill gcolor setgray newpath 0 0 radius 0 360 arc fill
0 setgray newpath 0 0 radius 0 360 arc stroke grestore } def
/ccirc1{ gsw /radius ed translate newpath 0 0 radius 0 360 arc fill
grestore } def
/ccirc2{ gsw /radius ed translate newpath 0 0 radius 0 360 arc stroke
grestore } def
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/bbox{ gsw p2 p1 gsave 1 setgray abox fill grestore abox stroke grestore
} def
/gbox{ gsw /gcolor ed p2 p1 1 setgray abox fill gcolor setgray abox
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def
/ptext{ gs /text ed /fsize ed /mode ed 3 1 roll translate rotate mode
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/fsize text stringwidth pop def mode 1 eq { fsize 2 div neg 0 translate
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show grestore } def
/goval{ gsw /gcolor ed /x1 ed /x2 ed /radius ed translate x1 rotate
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gcolor setgray newpath 0 0 radius 0 360 arc fill 0 setgray newpath
0 0 radius 0 360 arc stroke grestore } def
/coval1{ gsw /x1 ed /x2 ed /radius ed translate x1 rotate x2 radius
div 1.0 scale newpath 0 0 radius 0 360 arc fill grestore } def
/coval2{ gsw /x1 ed /x2 ed /radius ed translate x1 rotate x2 radius
div 1.0 scale newpath 0 0 radius 0 360 arc stroke grestore } def
/oval{ gsw /x1 ed /x2 ed /radius ed translate x1 rotate x2 radius
div 1.0 scale newpath 0 0 radius 0 360 arc stroke grestore } def
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/makecurve{ gsw /points ed /ss points length 2 idiv 2 mul def newpath
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/y3 y2 y1 sub x2 x1 sub div y1 y0 sub x1 x0 sub div sub 2 mul x2 x1
sub dup mul x2 x0 sub div mul y2 2 mul add y1 sub def docurve } { ss
4 eq { points 0 get points 1 get moveto points 2 get points 3 get lineto
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/makedashcurve{ gsw /dsize ed /points ed /ss points length 2 idiv
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/x2 points 2 get def /y2 points 3 get def /x3 points 4 get def /y3
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} { ss 4 eq { points 0 get points 1 get moveto points 2 get points
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/pathlength{ flattenpath /dist 0 def { /yfirst ed /xfirst ed /ymoveto
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/centerdash{ /pathlen pathlength def /jj pathlen dsize div 2.0 div
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/logaxis{ gsw /offset ed /hashsize ed /nlogs ed normalizeline /rr
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/linaxis{ gsw /offset ed /hashsize ed /perdec ed /numdec ed normalizeline
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def /y1 rr numdec div def /offset offset x1 mul def 0 1 numdec { y1
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cvi 1 numdec perdec mul offset add { x1 mul offset sub dup 0 ge { dup
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grestore } def
/dashbezier{ gsw /dsize ed p4 p3 p2 p1 dsize 0 ne { [dsize dsize]
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@fedspecial end
%%BeginFont: CMMI10
%!PS-AdobeFont-1.1: CMMI10 1.100
%%CreationDate: 1996 Jul 23 07:53:57
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
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readonly def
/FontBBox{-32 -250 1048 750}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMR12
%!PS-AdobeFont-1.1: CMR12 1.0
%%CreationDate: 1991 Aug 20 16:38:05
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
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end readonly def
/FontName /CMR12 def
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/FontMatrix [0.001 0 0 0.001 0 0] readonly def
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readonly def
/FontBBox{-34 -251 988 750}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMMI12
%!PS-AdobeFont-1.1: CMMI12 1.100
%%CreationDate: 1996 Jul 27 08:57:55
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
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end readonly def
/FontName /CMMI12 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
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dup 13 /gamma put
dup 22 /mu put
dup 23 /nu put
dup 28 /tau put
dup 59 /comma put
dup 87 /W put
dup 90 /Z put
readonly def
/FontBBox{-30 -250 1026 750}readonly def
currentdict end
currentfile eexec
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mchrzasz