%%BeginResource: procset LoutFigPrependGraphic
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% PostScript @SysPrependGraphic file for @Fig Jeffrey H. Kingston %
% Version 2.0 (includes CIRCUM label) January 1992 %
% %
% To assist in avoiding name clashes, the names of all symbols %
% defined here begin with "lfig". However, this is not feasible %
% with user-defined labels and some labels used by users. %
% %
% <point> is two numbers, a point. %
% <length> is one number, a length %
% <angle> is one number, an angle in degrees %
% <dashlength> is one number, the preferred length of a dash %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
errordict begin
/handleerror
{
{ /Times-Roman findfont 8 pt scalefont setfont
0 setgray 4 pt 4 pt moveto
$error /errorname get
dup lfigdict exch known
{ lfigdict exch get }
{ 30 string cvs } ifelse
show
( Command: ) show
$error /command get 30 string cvs show
} stopped {} if
showpage stop
} def
end
% concat strings: <string> <string> lfigconcat <string>
% must be defined outside lfigdict since used in lfigpromotelabels
/lfigconcat
{ 2 copy length exch length add string
dup 0 4 index putinterval
dup 3 index length 3 index putinterval
3 1 roll pop pop
} def
% <string> lfigdebugprint -
% must be defined outside lfigdict since used in arbitrary places
% /lfigdebugprint
% { print
% (; operand stack:\n) print
% count copy
% count 2 idiv
% { ==
% (\n) print
% } repeat
% (\n) print
% } def
/lfigdict 120 dict def
lfigdict begin
% error messages
/dictfull (dictfull error: too many labels?) def
/dictstackoverflow (dictstackoverflow error: labels nested too deeply?) def
/execstackoverflow (execstackoverflow error: figure nested too deeply?) def
/limitcheck (limitcheck error: figure nested too deeply or too large?) def
/syntaxerror (syntaxerror error: syntax error in text of figure?) def
/typecheck (typecheck error: syntax error in text of figure?) def
/undefined (undefined error: unknown or misspelt label?) def
/VMError (VMError error: run out of memory?) def
% push pi onto stack: - lfigpi <num>
/lfigpi 3.14159 def
% arc directions
/clockwise false def
/anticlockwise true def
% maximum of two numbers: <num> <num> lfigmax <num>
/lfigmax { 2 copy gt { pop } { exch pop } ifelse } def
% minimum of two numbers: <num> <num> lfigmin <num>
/lfigmin { 2 copy lt { pop } { exch pop } ifelse } def
% add two points: <point> <point> lfigpadd <point>
/lfigpadd { exch 3 1 roll add 3 1 roll add exch } def
% subtract first point from second: <point> <point> lfigpsub <point>
/lfigpsub { 3 2 roll sub 3 1 roll exch sub exch } def
% max two points: <point> <point> lfigpmax <point>
/lfigpmax { exch 3 1 roll lfigmax 3 1 roll lfigmax exch } def
% min two points: <point> <point> lfigpmin <point>
/lfigpmin { exch 3 1 roll lfigmin 3 1 roll lfigmin exch } def
% scalar multiplication: <point> <num> lfigpmul <point>
/lfigpmul { dup 3 1 roll mul 3 1 roll mul exch } def
% point at angle and distance: <point> <length> <angle> lfigatangle <point>
/lfigatangle { 2 copy cos mul 3 1 roll sin mul lfigpadd } def
% angle from one point to another: <point> <point> lfigangle <angle>
/lfigangle { lfigpsub 2 copy 0 eq exch 0 eq and {pop} {exch atan} ifelse } def
% distance between two points: <point> <point> lfigdistance <length>
/lfigdistance { lfigpsub dup mul exch dup mul add sqrt } def
% difference in x coords: <point> <point> lfigxdistance <length>
/lfigxdistance { pop 3 1 roll pop sub } def
%difference in y coords: <point> <point> lfigydistance <length>
/lfigydistance { 3 1 roll pop sub exch pop } def
% stroke a solid line: <length> <dashlength> lfigsolid -
/lfigsolid
{ pop pop [] 0 setdash stroke
} def
% stroke a lfigdashed line: <length> <dashlength> lfigdashed -
/lfigdashed
{ 2 copy div 2 le 1 index 0 le or
{ exch pop 1 pt lfigmax [ exch dup ] 0 setdash }
{ dup [ exch 4 2 roll 2 copy div
1 sub 2 div ceiling dup 4 1 roll
1 add mul sub exch div ] 0 setdash
} ifelse stroke
} def
% stroke a lfigcdashed line: <length> <dashlength> lfigcdashed -
/lfigcdashed
{ 2 copy le 1 index 0 le or
{ exch pop 1 pt lfigmax [ exch dup ] dup 0 get 2 div setdash }
{ dup [ 4 2 roll exch 2 copy exch div
2 div ceiling div 1 index sub
] exch 2 div setdash
} ifelse stroke
} def
% stroke a dotted line: <length> <dashlength> lfigdotted -
/lfigdotted
{ 2 copy le 1 index 0 le or
{ exch pop 1 pt lfigmax [ exch 0 exch ] 0 setdash }
{ 1 index exch div ceiling div
[ 0 3 2 roll ] 0 setdash
} ifelse stroke
} def
% stroke a noline line: <length> <dashlength> lfignoline -
/lfignoline
{ pop pop
} def
% painting (i.e. filling): - lfigwhite - (etc.)
/lfignopaint { } def
/lfignochange { fill } def
/lfigdarkblue { 0.0 0.0 0.5 setrgbcolor fill } def
/lfigblue { 0.0 0.0 1.0 setrgbcolor fill } def
/lfiglightblue { 0.5 0.5 1.0 setrgbcolor fill } def
/lfigdarkgreen { 0.0 0.5 0.0 setrgbcolor fill } def
/lfiggreen { 0.0 1.0 0.0 setrgbcolor fill } def
/lfiglightgreen { 0.5 1.0 0.5 setrgbcolor fill } def
/lfigdarkred { 0.5 0.0 0.0 setrgbcolor fill } def
/lfigred { 1.0 0.0 0.0 setrgbcolor fill } def
/lfiglightred { 1.0 0.5 0.5 setrgbcolor fill } def
/lfigdarkcyan { 0.0 0.5 0.5 setrgbcolor fill } def
/lfigcyan { 0.0 1.0 1.0 setrgbcolor fill } def
/lfiglightcyan { 0.5 1.0 1.0 setrgbcolor fill } def
/lfigdarkmagenta { 0.5 0.0 0.5 setrgbcolor fill } def
/lfigmagenta { 1.0 0.0 1.0 setrgbcolor fill } def
/lfiglightmagenta { 1.0 0.5 1.0 setrgbcolor fill } def
/lfigdarkyellow { 0.5 0.5 0.0 setrgbcolor fill } def
/lfigyellow { 1.0 1.0 0.0 setrgbcolor fill } def
/lfiglightyellow { 1.0 1.0 0.5 setrgbcolor fill } def
/lfigdarkgray { 0.2 0.2 0.2 setrgbcolor fill } def
/lfiggray { 0.5 0.5 0.5 setrgbcolor fill } def
/lfiglightgray { 0.8 0.8 0.8 setrgbcolor fill } def
/lfigdarkgrey { 0.2 0.2 0.2 setrgbcolor fill } def
/lfiggrey { 0.5 0.5 0.5 setrgbcolor fill } def
/lfiglightgrey { 0.8 0.8 0.8 setrgbcolor fill } def
/lfigblack { 0.0 0.0 0.0 setrgbcolor fill } def
/lfigwhite { 1.0 1.0 1.0 setrgbcolor fill } def
% line caps (and joins, not currently used)
/lfigbutt 0 def
/lfiground 1 def
/lfigprojecting 2 def
/lfigmiter 0 def
/lfigbevel 2 def
% shape and labels of the @Box symbol
/lfigbox
{
0 0 /SW lfigpointdef
xsize 0 /SE lfigpointdef
xsize ysize /NE lfigpointdef
0 ysize /NW lfigpointdef
SE 0.5 lfigpmul /S lfigpointdef
NW 0.5 lfigpmul /W lfigpointdef
W SE lfigpadd /E lfigpointdef
S NW lfigpadd /N lfigpointdef
NE 0.5 lfigpmul /CTR lfigpointdef
[ CTR NE lfigpsub /lfigboxcircum cvx ] lfigcircumdef
SW SE NE NW SW
} def
% shape and labels of the @CurveBox symbol
/lfigcurvebox
{
xsize 0.5 mul ysize 0.5 mul /CTR lfigpointdef
xsize 0.5 mul 0 /S lfigpointdef
xsize ysize 0.5 mul /E lfigpointdef
xsize 0.5 mul ysize /N lfigpointdef
0 ysize 0.5 mul /W lfigpointdef
xmark 0.293 mul xmark 0.293 mul /SW lfigpointdef
xsize xmark 0.293 mul sub xmark 0.293 mul /SE lfigpointdef
xsize xmark 0.293 mul sub ysize xmark 0.293 mul sub /NE lfigpointdef
xmark 0.293 mul ysize xmark 0.293 mul sub /NW lfigpointdef
[ xsize ysize 0.5 lfigpmul xmark /lfigcurveboxcircum cvx ] lfigcircumdef
xmark 0
xsize xmark sub 0
[ xsize xmark sub xmark ]
xsize xmark
xsize ysize xmark sub
[ xsize xmark sub ysize xmark sub ]
xsize xmark sub ysize
xmark ysize
[ xmark ysize xmark sub ]
0 ysize xmark sub
0 xmark
[ xmark xmark ]
xmark 0
} def
% shadow of the @ShadowBox symbol
% its shape and labels are done, somewhat inaccurately, with lfigbox
/lfigshadow
{ xmark 2 mul 0 moveto xsize 0 lineto
xsize ysize xmark 2 mul sub lineto
xsize xmark sub ysize xmark 2 mul sub lineto
xsize xmark sub xmark lineto
xmark 2 mul xmark lineto closepath fill
} def
% shape and labels of the @Square symbol
/lfigsquare
{
xsize ysize 0.5 lfigpmul /CTR lfigpointdef
CTR xsize xsize ysize ysize lfigpmax 0.5 lfigpmul lfigpadd /NE lfigpointdef
CTR 0 0 CTR NE lfigdistance 135 lfigatangle lfigpadd /NW lfigpointdef
CTR 0 0 CTR NE lfigdistance 225 lfigatangle lfigpadd /SW lfigpointdef
CTR 0 0 CTR NE lfigdistance 315 lfigatangle lfigpadd /SE lfigpointdef
SW 0.5 lfigpmul SE 0.5 lfigpmul lfigpadd /S lfigpointdef
NW 0.5 lfigpmul NE 0.5 lfigpmul lfigpadd /N lfigpointdef
SW 0.5 lfigpmul NW 0.5 lfigpmul lfigpadd /W lfigpointdef
SE 0.5 lfigpmul NE 0.5 lfigpmul lfigpadd /E lfigpointdef
[ CTR NE lfigpsub /lfigboxcircum cvx ] lfigcircumdef
SW SE NE NW SW
} def
% shape and labels of the @Diamond symbol
/lfigdiamond
{
xsize 0 0.5 lfigpmul /S lfigpointdef
0 ysize 0.5 lfigpmul /W lfigpointdef
S W lfigpadd /CTR lfigpointdef
CTR W lfigpadd /N lfigpointdef
CTR S lfigpadd /E lfigpointdef
[ xsize ysize 0.5 lfigpmul /lfigdiamondcircum cvx ] lfigcircumdef
S E N W S
} def
% shape and labels of the @Ellipse symbol
/lfigellipse
{
xsize 0 0.5 lfigpmul /S lfigpointdef
0 ysize 0.5 lfigpmul /W lfigpointdef
S W lfigpadd /CTR lfigpointdef
CTR W lfigpadd /N lfigpointdef
CTR S lfigpadd /E lfigpointdef
CTR xsize 0 0.3536 lfigpmul lfigpadd 0 ysize 0.3536 lfigpmul lfigpadd /NE lfigpointdef
0 ysize 0.3536 lfigpmul CTR xsize 0 0.3536 lfigpmul lfigpadd lfigpsub /SE lfigpointdef
xsize 0 0.3536 lfigpmul CTR lfigpsub 0 ysize 0.3536 lfigpmul lfigpadd /NW lfigpointdef
0 ysize 0.3536 lfigpmul xsize 0 0.3536 lfigpmul CTR lfigpsub lfigpsub /SW lfigpointdef
[ xsize ysize 0.5 lfigpmul /lfigellipsecircum cvx ] lfigcircumdef
S [ CTR ] E [ CTR ] N [ CTR ] W [ CTR ] S
} def
% shape and labels of the @Circle symbol
/lfigcircle
{
xsize ysize 0.5 lfigpmul /CTR lfigpointdef
CTR xsize 0 ysize 0 lfigpmax 0.5 lfigpmul lfigpadd /E lfigpointdef
CTR 0 0 CTR E lfigdistance 45 lfigatangle lfigpadd /NE lfigpointdef
CTR 0 0 CTR E lfigdistance 90 lfigatangle lfigpadd /N lfigpointdef
CTR 0 0 CTR E lfigdistance 135 lfigatangle lfigpadd /NW lfigpointdef
CTR 0 0 CTR E lfigdistance 180 lfigatangle lfigpadd /W lfigpointdef
CTR 0 0 CTR E lfigdistance 225 lfigatangle lfigpadd /SW lfigpointdef
CTR 0 0 CTR E lfigdistance 270 lfigatangle lfigpadd /S lfigpointdef
CTR 0 0 CTR E lfigdistance 315 lfigatangle lfigpadd /SE lfigpointdef
[ S E lfigpsub /lfigellipsecircum cvx ] lfigcircumdef
S [ CTR ] E [ CTR ] N [ CTR ] W [ CTR ] S
} def
% shape and labels of the @HLine and @HArrow symbols
/lfighline
{
0 ymark lfigprevious /FROM lfigpointdef
xsize ymark lfigprevious /TO lfigpointdef
} def
% shape and labels of the @VLine and @VArrow symbols
/lfigvline
{
xmark ysize lfigprevious /FROM lfigpointdef
xmark 0 lfigprevious /TO lfigpointdef
} def
% points of a polygon around base with given no of sides, vert init angle:
% <sides> <angle> figpolygon <point> ... <point>
/lfigpolygon
{ xsize ysize 0.5 lfigpmul /CTR lfigpointdef
90 sub CTR 2 copy lfigmax 5 3 roll
[ 4 copy pop /lfigpolycircum cvx ] lfigcircumdef
exch dup 360 exch div exch
1 1 3 2 roll
{ 4 string cvs (P) exch lfigconcat cvn
6 copy pop pop lfigatangle 2 copy 10 2 roll
3 2 roll lfigpointdef
dup 3 1 roll add exch
} for
pop lfigatangle
} def
% next array element: <array> <index> lfiggetnext <array> <index> <any> true
% or <array> <index> false
/lfiggetnext
{ 2 copy exch length ge
{ false }
{ 2 copy get exch 1 add exch true } ifelse
} def
% check whether thing is number: <any> lfigisnumbertype <any> <bool>
/lfigisnumbertype
{ dup type dup
/integertype eq exch /realtype eq or
} def
% check whether thing is an array: <any> lfigisarraytype <any> <bool>
/lfigisarraytype { dup type /arraytype eq } def
% get next item: <array> <index> lfiggetnextitem <array> <index> 0
% or <array> <index> <array> 1
% or <array> <index> <point> 2
/lfiggetnextitem
{ lfiggetnext
{ lfigisarraytype
{ 1
}
{ lfigisnumbertype
{ 3 1 roll
lfiggetnext
{ lfigisnumbertype
{ 4 3 roll exch 2
}
{ pop 3 2 roll pop 0
} ifelse
}
{ 3 2 roll pop 0
} ifelse
}
{ pop 0
} ifelse
} ifelse
}
{ 0
} ifelse
} def
% set arc path: bool x1 y1 x2 y2 x0 y0 lfigsetarc <angle> <angle> <dist>
% the path goes from x1 y1 to x2 y2 about centre x0 y0,
% anticlockwise if bool is true else clockwise.
% The orientations of backwards pointing and forwards pointing
% arrowheads are returned in the two angles, and
% the length of the arc is returned in <dist>.
/lfigsetarc
{
20 dict begin
matrix currentmatrix 8 1 roll
2 copy translate 2 copy 8 2 roll
4 2 roll lfigpsub 6 2 roll lfigpsub
dup /y1 exch def dup mul /y1s exch def
dup /x1 exch def dup mul /x1s exch def
dup /y2 exch def dup mul /y2s exch def
dup /x2 exch def dup mul /x2s exch def
y1s y2s eq
{ -1
}
{ y1s x2s mul y2s x1s mul sub y1s y2s sub div
} ifelse
/da exch def
x1s x2s eq
{ -1
}
{ x1s y2s mul x2s y1s mul sub x1s x2s sub div
} ifelse
/db exch def
da 0 gt db 0 gt and
{ /LMax da sqrt db sqrt lfigmax def
/scalex da sqrt LMax div def
/scaley db sqrt LMax div def
scalex scaley scale
0 0 LMax
0 0 x1 scalex mul y1 scaley mul lfigangle
0 0 x2 scalex mul y2 scaley mul lfigangle
2 copy eq { 360 add } if
2 copy 8 2 roll
5 index { arc } { arcn } ifelse
2 index 1 index
{ 90 sub } { 90 add } ifelse
dup sin scaley mul exch cos scalex mul atan
2 index 2 index
{ 90 add } { 90 sub } ifelse
dup sin scaley mul exch cos scalex mul atan
5 2 roll % res1 res2 ang1 ang2 anticlockwise
{ exch sub } { sub } ifelse
dup 0 le { 360 add } if lfigpi mul LMax mul 180 div
}
{ 0 0 x1 y1 lfigdistance 0 0 x2 y2 lfigdistance eq
0 0 x1 y1 lfigdistance 0 gt and
{ 0 0
0 0 x1 y1 lfigdistance
0 0 x1 y1 lfigangle
0 0 x2 y2 lfigangle
2 copy eq { 360 add } if
2 copy 8 2 roll
5 index { arc } { arcn } ifelse
2 index 1 index
{ 90 sub } { 90 add } ifelse
2 index 2 index
{ 90 add } { 90 sub } ifelse
5 2 roll % res1 res2 ang1 ang2 clockwise
{ exch sub } { sub } ifelse
dup 0 le { 360 add } if lfigpi mul 0 0 x1 y1 lfigdistance mul 180 div
}
{ x2 y2 lineto pop
x2 y2 x1 y1 lfigangle
x1 y1 x2 y2 lfigangle
x1 y1 x2 y2 lfigdistance
} ifelse
} ifelse
4 -1 roll setmatrix
end
} def
% lfigsetcurve: set up a Bezier curve from x0 y0 to x3 y3
% and return arrowhead angles and length of curve (actually 0)
% x0 y0 x1 y1 x2 y2 x3 y3 lfigsetcurve <angle> <angle> <length>
/lfigsetcurve
{ 8 copy curveto pop pop
lfigangle
5 1 roll
4 2 roll lfigangle
exch
0
} def
% lfigpaintpath: paint a path of the given shape
% /paint [ shape ] lfigpaintpath -
/lfigpaintpath
{
10 dict begin
0 newpath
/prevseen false def
/curveseen false def
{ lfiggetnextitem
dup 0 eq { pop exit }
{ 1 eq
{ /curveseen true def
/curve exch def
curve length 0 eq { /curveseen false def } if
}
{ /ycurr exch def
/xcurr exch def
prevseen
{ curveseen
{ curve length 4 eq
{ xprev yprev
curve 0 get curve 1 get
curve 2 get curve 3 get
xcurr ycurr
lfigsetcurve pop pop pop
}
{ xprev yprev xcurr ycurr
curve length 1 ge { curve 0 get } { 0 } ifelse
curve length 2 ge { curve 1 get } { 0 } ifelse
curve length 3 ge { curve 2 get } { true } ifelse
7 1 roll
lfigsetarc pop pop pop
} ifelse
}
{ xcurr ycurr lineto
} ifelse
}
{ xcurr ycurr moveto
} ifelse
/xprev xcurr def
/yprev ycurr def
/prevseen true def
/curveseen false def
} ifelse
} ifelse
} loop pop pop cvx exec
end
} def
% stroke a path of the given shape in the given linestyle and dash length.
% Return the origin and angle of the backward and forward arrow heads.
% dashlength /linestyle [shape] lfigdopath [<point> <angle>] [<point> <angle>]
/lfigdopath
{
10 dict begin
0
/prevseen false def
/curveseen false def
/backarrow [] def
/fwdarrow [] def
{
lfiggetnextitem
dup 0 eq { pop exit }
{
1 eq
{ /curveseen true def
/curve exch def
curve length 0 eq { /prevseen false def } if
}
{ /ycurr exch def
/xcurr exch def
prevseen
{ newpath xprev yprev moveto
curveseen
{ curve length 4 eq
{ xprev yprev
curve 0 get curve 1 get
curve 2 get curve 3 get
xcurr ycurr lfigsetcurve
}
{ xprev yprev xcurr ycurr
curve length 1 ge { curve 0 get } { 0 } ifelse
curve length 2 ge { curve 1 get } { 0 } ifelse
curve length 3 ge { curve 2 get } { true } ifelse
7 1 roll
lfigsetarc
} ifelse
}
{ xcurr ycurr lineto
xcurr ycurr xprev yprev lfigangle dup 180 sub
xprev yprev xcurr ycurr lfigdistance
} ifelse
6 index 6 index cvx exec
[ xprev yprev 5 -1 roll ]
backarrow length 0 eq
{ /backarrow exch def }
{ pop } ifelse
[ xcurr ycurr 4 -1 roll ] /fwdarrow exch def
} if
/xprev xcurr def
/yprev ycurr def
/prevseen true def
/curveseen false def
} ifelse
} ifelse
} loop
pop pop pop pop
backarrow length 0 eq { [ 0 0 0 ] } { backarrow } ifelse
fwdarrow length 0 eq { [ 0 0 0 ] } { fwdarrow } ifelse
end
} def
% lfigdoarrow: draw an arrow head of given form
% dashlength /lstyle /pstyle hfrac height width [ <point> <angle> ] lfigdoarrow -
/lfigdoarrow
{ matrix currentmatrix 8 1 roll
dup 0 get 1 index 1 get translate
2 get rotate
[ 2 index neg 2 index 0 0
3 index 3 index neg
1 index 10 index mul 0
7 index 7 index ]
4 1 roll pop pop pop
dup 3 1 roll
gsave lfigpaintpath grestore lfigdopath pop pop
setmatrix
} def
% arrow head styles
/lfigopen 0.0 def
/lfighalfopen 0.5 def
/lfigclosed 1.0 def
% stroke no arrows, forward, back, and both
/lfignoarrow { pop pop pop pop pop pop pop pop } def
/lfigforward { 7 -1 roll lfigdoarrow pop } def
/lfigback { 8 -2 roll pop lfigdoarrow } def
/lfigboth { 8 -1 roll 7 copy lfigdoarrow pop 7 -1 roll lfigdoarrow } def
% lfigprevious: return previous point on path
/lfigprevious
{ lfigisnumbertype
{ 2 copy }
{ lfigisarraytype
{ 2 index 2 index }
{ 0 0 }
ifelse
} ifelse
} def
% label a point in 2nd top dictionary: <point> /name lfigpointdef -
/lfigpointdef
{
% (Entering lfigpointdef) lfigdebugprint
[ 4 2 roll transform
/itransform cvx ] cvx
currentdict end
3 1 roll
% currentdict length currentdict maxlength lt
% { def }
% { exec moveto (too many labels) show stop }
% ifelse
def
begin
% (Leaving lfigpointdef) lfigdebugprint
} def
% promote labels from second top to third top dictionary
% <string> lfigpromotelabels -
/lfigpromotelabels
{
% (Entering lfigpromotelabels) lfigdebugprint
currentdict end exch currentdict end
{ exch 20 string cvs 2 index
(@) lfigconcat exch lfigconcat cvn exch def
} forall pop begin
% (Leaving lfigpromotelabels) lfigdebugprint
} def
% show labels (except CIRCUM): - lfigshowlabels -
/lfigshowlabels
{
% (Entering lfigshowlabels) lfigdebugprint
currentdict end
currentdict
{ 1 index 20 string cvs (CIRCUM) search % if CIRCUM in key
{ pop pop pop pop pop }
{ pop cvx exec 2 copy
newpath 1.5 pt 0 360 arc
0 setgray fill
/Times-Roman findfont 8 pt scalefont setfont
moveto 0.2 cm 0.1 cm rmoveto 20 string cvs show
}
ifelse
} forall
begin
% (Leaving lfigshowlabels) lfigdebugprint
} def
% fix an angle to 0 <= res < 360: <angle> lfigfixangle <angle>
/lfigfixangle
{
% (Entering lfigfixangle) lfigdebugprint
{ dup 0 ge { exit } if
360 add
} loop
{ dup 360 lt { exit } if
360 sub
} loop
% (Leaving lfigfixangle) lfigdebugprint
} def
% find point on circumference of box: alpha a b lfigboxcircum x y
/lfigboxcircum
{
% (Entering lfigboxcircum) lfigdebugprint
4 dict begin
/b exch def
/a exch def
lfigfixangle /alpha exch def
0 0 a b lfigangle /theta exch def
% if alpha <= theta, return (a, a*tan(alpha))
alpha theta le
{ a a alpha sin mul alpha cos div }
{
% else if alpha <= 180 - theta, return (b*cot(alpha), b)
alpha 180 theta sub le
{ b alpha cos mul alpha sin div b }
{
% else if alpha <= 180 + theta, return (-a, -a*tan(alpha))
alpha 180 theta add le
{ a neg a neg alpha sin mul alpha cos div }
{
% else if alpha <= 360 - theta, return (-b*cot(alpha), -b)
alpha 360 theta sub le
{ b neg alpha cos mul alpha sin div b neg }
{
% else 360 - theta <= alpha, return (a, a*tan(alpha))
a a alpha sin mul alpha cos div
} ifelse
} ifelse
} ifelse
} ifelse
end
% (Leaving lfigboxcircum) lfigdebugprint
} def
% find quadratic roots (assume a != 0): a b c lfigqroots x1 x2 2
% or x2 1
% or 0
/lfigqroots
{
4 dict begin
/c exch def
/b exch def
/a exch def
/disc b b mul 4 a c mul mul sub def
disc 0 lt
{ 0
}
{ disc 0 eq
{ b neg 2 a mul div
1
}
{ b neg disc sqrt add 2 a mul div
b neg disc sqrt sub 2 a mul div
2
}
ifelse
}
ifelse
end
} def
% work our which quadrant: <angle> lfigquadrant <0-3>
/lfigquadrant
{ dup 90 lt
{ pop 0
}
{ dup 180 lt
{ pop 1
}
{ 270 lt
{ 2
}
{ 3
} ifelse
} ifelse
} ifelse
} def
% find curvebox circum, assuming upper right quadrant: alpha a b xmk lfigcb x y
/lfigcb
{
6 dict begin
/xmk exch def
/b exch def
/a exch def
/alpha exch def
/theta1 0 0 a b xmk sub lfigangle def
/theta2 0 0 a xmk sub b lfigangle def
alpha theta1 le
{ % if alpha <= theta1, return (a, a*tan(alpha))
a a alpha sin mul alpha cos div
}
{ alpha theta2 ge
{ % else if alpha > theta2, return (b*cot(alpha), b)
b alpha cos mul alpha sin div b
}
{
% else, return the intersection of line and circle
a xmk sub b xmk sub xmk 0 0 alpha lfigcircleintersect
dup 0 eq
{ % should never happen, just return any reasonable point
pop
a b 0.5 lfigpmul
}
{ 1 eq
{ % should never happen, just return the point on top of stack
}
{ % the usual case, two points on stack, return the larger
lfigpmax
} ifelse
} ifelse
} ifelse
} ifelse
end
} def
% find point on circumference of curvebox: alpha a b xmk lfigcurveboxcircum x y
/lfigcurveboxcircum
{
% (Entering lfigcurveboxcircum) lfigdebugprint
5 dict begin
/xmk exch def
/b exch def
/a exch def
lfigfixangle /alpha exch def
% work out which quadrant we are in, and reflect accordingly
/quad alpha lfigquadrant def
quad 0 eq
{ alpha a b xmk lfigcb
}
{ quad 1 eq
{ 180 alpha sub a b xmk lfigcb exch neg exch
}
{ quad 2 eq
{ alpha 180 sub a b xmk lfigcb neg exch neg exch
}
{ 360 alpha sub a b xmk lfigcb neg
} ifelse
} ifelse
} ifelse
end
% (Leaving lfigcurveboxcircum) lfigdebugprint
} def
% find point on circumference of diamond: alpha a b lfigdiamondcircum x y
/lfigdiamondcircum
{
% (Entering lfigdiamondcircum) lfigdebugprint
4 dict begin
/b exch def
/a exch def
lfigfixangle /alpha exch def
b alpha cos abs mul a alpha sin abs mul add /denom exch def
a b mul alpha cos mul denom div
a b mul alpha sin mul denom div
end
% (Leaving lfigdiamondcircum) lfigdebugprint
} def
% find point on circumference of ellipse: alpha a b lfigellipsecircum x y
/lfigellipsecircum
{
% (Entering lfigellipsecircum) lfigdebugprint
4 dict begin
/b exch def
/a exch def
lfigfixangle /alpha exch def
b alpha cos mul dup mul a alpha sin mul dup mul add sqrt /denom exch def
a b mul alpha cos mul denom div
a b mul alpha sin mul denom div
end
% (Leaving lfigellipsecircum) lfigdebugprint
} def
% find point of intersection of two lines each defined by two points
% x1 y1 x2 y2 x3 y3 x4 y4 lfiglineintersect x y
/lfiglineintersect
{
% (Entering lfiglineintersect) lfigdebugprint
13 dict begin
/y4 exch def
/x4 exch def
/y3 exch def
/x3 exch def
/y2 exch def
/x2 exch def
/y1 exch def
/x1 exch def
x2 x1 sub /x21 exch def
x4 x3 sub /x43 exch def
y2 y1 sub /y21 exch def
y4 y3 sub /y43 exch def
y21 x43 mul y43 x21 mul sub /det exch def
% calculate x
y21 x43 mul x1 mul
y43 x21 mul x3 mul sub
y3 y1 sub x21 mul x43 mul add
det div
% calculate y
x21 y43 mul y1 mul
x43 y21 mul y3 mul sub
x3 x1 sub y21 mul y43 mul add
det neg div
end
% (Leaving lfiglineintersect) lfigdebugprint
} def
% find point on circumference of polygon
% alpha radius num theta lfigpolycircum x y
/lfigpolycircum
{
% (Entering lfigpolycircum) lfigdebugprint
13 dict begin
/theta exch def
/num exch def
/radius exch def
/alpha exch def
% calculate delta, the angle from theta to alpha
alpha theta sub lfigfixangle
% calculate the angle which is the multiple of 360/num closest to delta
360 num div div truncate 360 num div mul theta add /anglea exch def
% calculate the next multiple of 360/num after anglea
anglea 360 num div add /angleb exch def
% intersect the line through these two points with the alpha line
anglea cos anglea sin angleb cos angleb sin
0 0 alpha cos 2 mul alpha sin 2 mul
lfiglineintersect radius lfigpmul
end
% (Leaving lfigpolycircum) lfigdebugprint
} def
% find point of intersection of a point and a circle
% x0 y0 r x1 y1 theta lfigcircleintersect xa ya xb yb 2
% or xb yb 1
% or 0
/lfigcircleintersect
{
% (Entering lfigcircleintersect) lfigdebugprint
15 dict begin
/theta exch def
/y1 exch def
/x1 exch def
/r exch def
/y0 exch def
/x0 exch def
% if sin(theta) = 0 then line is horizontal and y must be y1
theta sin abs 0.00001 lt
{
/a 1 def
/b -2 x0 mul def
/c x0 dup mul y1 y0 sub dup mul add r dup mul sub def
a b c lfigqroots dup
0 eq
{ pop
0
}
{ 1 eq
{ y1 1
}
{ y1 exch y1 2
} ifelse
} ifelse
}
{
/ct theta cos theta sin div def
/a ct ct mul 1 add def
/b ct x1 x0 sub mul y1 add y0 sub 2 mul def
/c x1 x0 sub dup mul y1 y0 sub dup mul add r dup mul sub def
a b c lfigqroots dup
0 eq
{ pop
0
}
{ 1 eq
{ y1 add /yb exch def
yb y1 sub ct mul x1 add /xb exch def
xb yb 1
}
{ y1 add /ya exch def
ya y1 sub ct mul x1 add /xa exch def
y1 add /yb exch def
yb y1 sub ct mul x1 add /xb exch def
xa ya xb yb 2
} ifelse
} ifelse
} ifelse
end
% (Leaving lfigcircleintersect) lfigdebugprint
} def
% add CIRCUM operator with this body: <array> lfigcircumdef -
/lfigcircumdef
{ % (Entering lfigcircumdef) lfigdebugprint
/CIRCUM exch cvx
currentdict end
3 1 roll
% currentdict length currentdict maxlength lt
% { def }
% { exec moveto (too many labels) show stop }
% ifelse
def
begin
% (Leaving lfigcircumdef) lfigdebugprint
} def
end
%%EndResource
