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+%!
+% PostScript prologue for pst-eucl.tex.
+% Version 2002.12, 2002/12/01
+% For distribution, see pstricks.tex.
+%
+/tx@EcldDict 40 dict def tx@EcldDict begin
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Pi
+/Pi 3.14159265359 def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% e
+/E 2.718281828459045 def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% x -> true (if |x| < 1E-6)
+/ZeroEq { abs 1E-6 lt } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% x1 y1 x2 y2 -> a b c (ax-by+c=0 with a^2+b^2=1)
+/EqDr {
+ 4 copy 3 -1 roll sub 7 1 roll exch sub 5 1 roll 4 -1 roll
+ mul 3 1 roll mul exch sub
+ 2 index dup mul 2 index dup mul add sqrt
+ 4 -1 roll 1 index div exch
+ 4 -1 roll 1 index div exch
+ 4 -1 roll 1 index div exch pop
+} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% orthogonal projection of M1 onto (OM2)
+%% x1 y1 x2 y2 -> x3 y3
+/Project {
+ 2 copy dup mul exch dup mul add 5 1 roll 2 copy 5 -1 roll mul exch
+ 5 -1 roll mul add 4 -1 roll div dup 4 -1 roll mul exch 3 -1 roll mul
+} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a b c (ax2+bx+c=0) -> x1 y1
+/SolvTrin {
+ /c exch def /b exch def /a exch def
+ b dup mul a c mul 4 mul sub dup 0 lt
+ { pop 0 0 } %% no solutions
+ {sqrt dup b neg add a 2 mul div exch b add neg 2 a mul div }
+ ifelse } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% x1 y1 x2 y2 -> Dist
+/ABDist { 3 -1 roll sub dup mul 3 1 roll sub dup mul add sqrt } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% x1 y1 x2 y2 -> x1-x2 y1-y2
+/ABVect { 3 -1 roll exch sub 3 1 roll sub exch } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% x1 y1 x2 y2 x3 y3 x4 y4 -> x y
+/InterLines {
+ EqDr /D1c exch def /D1b exch def /D1a exch def
+ EqDr /D2c exch def /D2b exch def /D2a exch def
+ D1a D2b mul D1b D2a mul sub dup ZeroEq
+ { pop pop pop 0 0 } %% parallel lines
+ {
+ /Det exch def
+ D1b D2c mul D1c D2b mul sub Det div
+ D1a D2c mul D2a D1c mul sub Det div
+ }
+ ifelse } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% a b c R -> x1 y1 x2 y2
+/InterLineCircle {
+ /CR exch def /Dc exch def neg /Db exch def /Da exch def
+ ABVect /Vy exch def /Vx exch def
+ %% Dc==0 then O belong to the line
+ %% First project O on the line -> M (-ca;-cb)
+ %% l'abscisse de M sur (OM) divisée par R donne le cosinus
+ %Dc neg dup Db mul exch Da mul 2 copy 0 0
+ %ABDist dup CR gt { pop pop pop 0 0 0 0 }
+ %{ ZeroEq { pop pop Db Da } if Atan /alpha exch def
+ Dc abs CR gt { 0 0 0 0 }
+ { Db neg Da neg Atan /alpha exch def
+ Dc CR div dup dup mul 1 exch sub sqrt exch Atan /beta exch def
+ alpha beta add dup cos CR mul exch sin CR mul
+ alpha beta sub dup cos CR mul exch sin CR mul
+ 4 copy ABVect Vy mul 0 le exch Vx mul 0 le and
+ { 4 2 roll } if } ifelse
+ } def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% R R' OO' -> x1 y1 x2 y2
+/InterCircles {
+ /OOP exch def /CRP exch def /CR exch def
+ OOP dup mul CRP dup mul sub CR dup mul add OOP div 2 div
+ dup dup mul CR dup mul exch sub dup
+ 0 lt { pop pop 0 0 0 0 } { sqrt 2 copy neg } ifelse
+} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% x y theta -> x' y' (rotation of theta)
+/Rotate {
+ dup sin /sintheta exch def cos /costheta exch def /y exch def /x exch def
+ x costheta mul y sintheta mul sub
+ y costheta mul x sintheta mul add
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% N -> x y
+/GetNode {
+ tx@NodeDict begin
+ tx@NodeDict 1 index known { load GetCenter } { pop 0 0 } ifelse
+ end
+} bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% x -> ch(x)
+/ch { dup Ex exch neg Ex add 2 div } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% x -> sh(x)
+/sh { dup Ex exch neg Ex sub 2 div } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% x -> e^(x)
+/Ex { E exch exp } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% x f g -> x y n
+/NewtonSolving {
+ /g exch def /f exch def 0
+ { %%% STACK: x0 n
+ 1 add exch %% one more loop
+ dup ZeroEq
+ { dup 0.0005 add fgeval
+ 1 index 0.0005 sub fgeval sub .001 div }
+ { dup 1.0005 mul fgeval
+ 1 index 0.9995 mul fgeval sub .001 2 index mul div } ifelse %%% STACK: n x0 fg'(x0)
+ %%% compute x1=x0-fg(x0)/fg'(x0)
+ 1 index fgeval exch div dup 4 1 roll sub exch %% stack: dx x0 n
+ 3 -1 roll ZeroEq %% exit if root found
+ 1 index 100 eq or { exit } if %% or looping for more than 100 times
+ } loop
+ dup 100 lt { exch dup /x exch def f } { pop 0 0 } ifelse
+ 3 -1 roll
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+/fgeval { /x exch def f g sub } bind def
+end
+% END ps-euclide.pro