pst-eucl (22nov19)

git-svn-id: svn://tug.org/texlive/trunk@52891 c570f23f-e606-0410-a88d-b1316a301751

2 files changed, 269 insertions, 2 deletions

diff --git a/Master/texmf-dist/dvips/pst-eucl/pst-eucl-alt.pro b/Master/texmf-dist/dvips/pst-eucl/pst-eucl-alt.pro
new file mode 100644
index 00000000000..64f01641148
--- /dev/null
+++ b/Master/texmf-dist/dvips/pst-eucl/pst-eucl-alt.pro
@@ -0,0 +1,132 @@
+%!
+% PostScript prologue for pst-eucl.tex.
+% Version 1.00 2011/08/04
+% 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  % --- hv 20110714
+   { pop 0 0 } %% parallel lines             --- hv 20110714
+   {
+    /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
diff --git a/Master/texmf-dist/dvips/pst-eucl/pst-eucl.pro b/Master/texmf-dist/dvips/pst-eucl/pst-eucl.pro
index d45dfca68a9..3d2fe93c80c 100644
--- a/Master/texmf-dist/dvips/pst-eucl/pst-eucl.pro
+++ b/Master/texmf-dist/dvips/pst-eucl/pst-eucl.pro
@@ -1,6 +1,6 @@
 %!
 % PostScript prologue for pst-eucl.tex.
-% Version 1.01 2012/09/21
+% Version 1.02 2012/11/21
 % For distribution, see pstricks.tex.
 %
 /tx@EcldDict 40 dict def tx@EcldDict begin
@@ -69,7 +69,7 @@
   %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 } 
+  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
@@ -129,5 +129,140 @@
 } def
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 /fgeval { /x exch def f g sub } bind def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% calculate the line coefficents Ax+By+C=0
+%% x1 y1 x2 y2 -> A B C
+/LineCoefABC {
+  0 index 3 index sub % A=y2-y1
+  4 index 3 index sub % B=x1-x2
+  3 index 5 index mul 6 index 4 index mul sub % C=x2y1-x1y2
+  7 3 roll pop pop pop pop
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% calculate the 2-order determinant
+%% |a11 a12|
+%% |a21 a22|
+%% a11 a12, a21 a22 -> X
+/DeterminantTwo {
+  4 1 roll mul 3 1 roll mul exch sub
+} def
+%% calculate the 3-order determinant
+%% |a11 a12 a13|
+%% |a21 a22 a23|
+%% |a31 a32 a33|
+%%   8   7   6    5   4   3    2   1   0
+%% a11 a12 a13, a21 a22 a23, a31 a32 a33 -> X
+/DeterminantThree {
+  % |a22 a23, a32 a33| * (-1)^(1+1)a11
+  8 index abs 1E-5 lt { %a11=0
+    0
+  } {
+    4 index 4 index 3 index 3 index DeterminantTwo
+    9 index mul
+  } ifelse
+  % |a12 a13, a32 a33| * (-1)^(1+2)a21
+  6 index abs 1E-5 lt { %a12=0
+    0 sub
+  } {
+    8 index 8 index 4 index 4 index DeterminantTwo
+    7 index mul sub
+  } ifelse
+  % |a12 a13, a22 a23| * (-1)^(1+3)a31
+  3 index abs 1E-5 lt { %a13=0
+    0 add
+  } {
+    8 index 8 index 7 index 7 index DeterminantTwo
+    4 index mul add
+  } ifelse
+  10 1 roll pop pop pop pop pop pop pop pop pop
+} def
+%% calculate the 4-order determinant
+%% |a11 a12 a13 a14|
+%% |a21 a22 a23 a24|
+%% |a31 a32 a33 a34|
+%% |a41 a42 a43 a44|
+%%  15  14  13  12   11  10   9   8    7   6   5   4    3   2   1   0
+%% a11 a12 a13 a14, a21 a22 a23 a24, a31 a32 a33 a34, a41 a42 a43 a44 -> X
+/DeterminantFour {
+  % |a22 a23 a24, a32 a33 a34, a42 a43 a44| * (-1)^(1+1)a11
+  15 index abs 1E-5 lt { %a11=0
+    0
+  } {
+    10 index 10 index 10 index 9 index 9 index 9 index 8 index 8 index 8 index DeterminantThree
+    16 index mul
+  } ifelse
+  % |a12 a13 a14, a32 a33 a34, a42 a43 a44| * (-1)^(1+2)a21
+  12 index abs 1E-5 lt { %a21=0
+    0 sub
+  } {
+    15 index 15 index 15 index 10 index 10 index 10 index 9 index 9 index 9 index DeterminantThree
+    13 index mul sub
+  } ifelse
+  % |a12 a13 a14, a22 a23 a24, a42 a43 a44| * (-1)^(1+3)a31
+  8 index abs 1E-5 lt { %a31=0
+    0 add
+  } {
+    15 index 15 index 15 index 14 index 14 index 14 index 9 index 9 index 9 index DeterminantThree
+    9 index mul add
+  } ifelse
+  % |a12 a13 a14, a22 a23 a24, a32 a33 a34| * (-1)^(1+4)a41
+  4 index abs 1E-5 lt { %a41=0
+    0 sub
+  } {
+    15 index 15 index 15 index 14 index 14 index 14 index 13 index 13 index 13 index DeterminantThree
+    5 index mul sub
+  } ifelse
+  17 1 roll pop pop pop pop pop pop pop pop
+  pop pop pop pop pop pop pop pop
+} def
+%% calculate the 5-order determinant
+%% |a11 a12 a13 a14 a15|
+%% |a21 a22 a23 a24 a25|
+%% |a31 a32 a33 a34 a35|
+%% |a41 a42 a43 a44 a45|
+%% |a51 a52 a53 a54 a55|
+%%  24  23  22  21  20   19  18  17  16  15   14  13  12  11  10    9   8   7   6   5    4   3   2   1   0
+%% a11 a12 a13 a14 a15, a21 a22 a23 a24 a25, a31 a32 a33 a34 a35, a41 a42 a43 a44 a45, a51 a52 a53 a54 a55-> X
+/DeterminantFive {
+  % |a22 a23 a24 a25, a32 a33 a34 a35, a42 a43 a44 a45, a52 a53 a54 a55| * (-1)^(1+1)a11
+  24 index abs 1E-5 lt { %a11=0
+    0
+  } {
+    18 index 18 index 18 index 18 index 17 index 17 index 17 index 17 index 16 index 16 index 16 index 16 index 15 index 15 index 15 index 15 index DeterminantFour
+    25 index mul
+  } ifelse
+  % |a12 a13 a14 a15, a32 a33 a34 a35, a42 a43 a44 a45, a52 a53 a54 a55| * (-1)^(1+2)a21
+  20 index abs 1E-5 lt { %a21=0
+    0 sub
+  } {
+    24 index 24 index 24 index 24 index 18 index 18 index 18 index 18 index 17 index 17 index 17 index 17 index 16 index 16 index 16 index 16 index DeterminantFour
+    21 index mul sub
+  } ifelse
+  % |a12 a13 a14 a15, a22 a23 a24 a25, a42 a43 a44 a45, a52 a53 a54 a55| * (-1)^(1+3)a31
+  15 index abs 1E-5 lt { %a31=0
+    0 add
+  } {
+    24 index 24 index 24 index 24 index 23 index 23 index 23 index 23 index 17 index 17 index 17 index 17 index 16 index 16 index 16 index 16 index DeterminantFour
+    16 index mul add
+  } ifelse
+  % |a12 a13 a14 a15, a22 a23 a24 a25, a32 a33 a34 a35, a52 a53 a54 a55| * (-1)^(1+4)a41
+  10 index abs 1E-5 lt { %a41=0
+    0 sub
+  } {
+    24 index 24 index 24 index 24 index 23 index 23 index 23 index 23 index 22 index 22 index 22 index 22 index 16 index 16 index 16 index 16 index DeterminantFour
+    11 index mul sub
+  } ifelse
+  % |a12 a13 a14 a15, a22 a23 a24 a25, a32 a33 a34 a35, a42 a43 a44 a45| * (-1)^(1+5)a51
+  5 index abs 1E-5 lt { %a51=0
+    0 add
+  } {
+    24 index 24 index 24 index 24 index 23 index 23 index 23 index 23 index 22 index 22 index 22 index 22 index 21 index 21 index 21 index 21 index DeterminantFour
+    6 index mul add
+  } ifelse
+  26 1 roll pop pop pop pop pop pop pop pop pop pop
+  pop pop pop pop pop pop pop pop pop pop
+  pop pop pop pop pop
+} def
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 end
 % END ps-euclide.pro