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%!
% PostScript prologue for pst-eucl.tex.
% Version 2001, 2001/12/09
% For distribution, see pstricks.tex.
%
/tx@EcldDict 400 dict def tx@EcldDict begin
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Pi
/Pi 3.14159265359 def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% e
/E 2.718281828459045 def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% x -> true (if |x| < 1E-10)
/ZeroEq { abs 1E-10 lt } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% x1 y1 x2 y2 -> a b c (ax+by+c=0)
/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 } 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 }
{
/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 /Db exch def /Da exch def
Db Da dup ZeroEq { pop Dc dup ZeroEq { pop 1 } if } if div abs
0.0005 lt { InterLineCirclebnull } { InterLineCircleGal }
ifelse
%%dup 3 index lt { 4 2 roll } if
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% case where the line is parallel to (oy)
/InterLineCirclebnull {
Dc Da div neg dup dup mul CR dup mul exch sub dup
0 lt
{ pop pop 0 0 0 0 } { sqrt dup 3 1 roll exch dup 4 1 roll exch neg }
ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% general case
/InterLineCircleGal {
Da dup mul Db dup mul add -2 Dc mul Da mul Dc dup mul CR dup mul Db dup
mul mul sub SolvTrin dup neg exch Da Db div mul Dc Db
div exch sub 3 -1 roll
dup neg exch Da Db div mul Dc Db div exch sub
} bind def
/Glbx 0 def /Glby 0 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
end
% END ps-euclide.pro
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