%! % 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