1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
|
%% BEGIN pst-bspline.tex
%% Author: Michael Sharpe (msharpe at ucsd.edu)
%%
%\message{ v\fileversion, \filedate}
\csname PSTBsplineLoaded\endcsname
\let\PSTBsplineLoaded\endinput
\ifx\PSTricksLoaded\endinput \else\input pstricks \fi
\ifx\PSTnodeLoaded\endinput \else\input pst-node \fi
\ifx\PSTXKeyLoaded\endinput \else\input pst-xkey \fi
\def\fileversion{1.41}
\def\filedate{2010/10/19}
\message{`pst-bspline' v\fileversion, \filedate\space Bspline routines for pstricks (ms)}
%
\edef\TheAtCode{\the\catcode`\@} \catcode`\@=11\relax
\pst@addfams{pst-bspline}
\SpecialCoor
%\newcount\pst@args%used in several macros--now defined in pst-node.tex
\def\PST@root{}
\newcount\bsp@args
\newcount\bsp@cntA
\newcount\bsp@cntB
\newif\ifbsp@omitends
\newif\ifbsp@closed
%\newif\ifbsp@showpoints
%\newif\ifbsp@doubleline
\newif\ifbsp@seq
\newif\ifbsp@per %flag for periodic interpolation
%
\def\bsp@init{%these items are used only within the plotting macros
\def\bsp@arrowA{}%
\def\bsp@arrowB{}%
}%
\def\refreshbspopts{%
\bsp@closedfalse%
\bsp@omitendsfalse%
\bsp@seqfalse%
}%
% showframe key and its default are global
\define@boolkey[psset]{pst-bspline}[Pst@]{showframe}[true]{}
\psset[pst-bspline]{showframe=false}%
\define@boolkey[psset]{pst-bspline}[Pst@]{reverseclip}[true]{}
\psset[pst-bspline]{reverseclip=false}%
%
%Bspline drawing macros
\def\psBsplineNodes{\def\pst@par{}\pst@object{psBsplineNodes}}%
\def\psBsplineNodesC{\def\pst@par{}\pst@object{psBsplineCNodes}}%
\def\psBsplineNodesE{\def\pst@par{}\pst@object{psBsplineENodes}}%
\def\psBsplineC{\def\pst@par{}\pst@object{psBsplineC}}%
\def\psBsplineE{\def\pst@par{}\pst@object{psBsplineE}}%
\def\psBspline{\def\pst@par{}\pst@object{psBspline}}%
%Bspline internal macros, level 1
\def\psBsplineC@i{\bsp@init\refreshbspopts\bsp@closedtrue\ps@bspline}%
\def\psBsplineE@i{\bsp@init\refreshbspopts\bsp@omitendstrue\ps@bspline}%
\def\psBspline@i{\bsp@init\refreshbspopts\ps@bspline}%
\def\psBsplineNodes@i{\bsp@init\refreshbspopts\bsp@seqtrue\ps@bsplineNodes}%
\def\psBsplineCNodes@i{\bsp@init\refreshbspopts\bsp@seqtrue\bsp@closedtrue%
\ps@bsplineNodes}%
\def\psBsplineENodes@i{\bsp@init\refreshbspopts\bsp@seqtrue\bsp@omitendstrue%
\ps@bsplineNodes}%
%Bspline internal macros, level 2
\def\ps@bsplineNodes#1#2{%noderoot, endindex
\def\bsp@root{#1}%
\bsp@args=#2\relax%
\next@Point%
}%
%
\def\ps@bspline{\bsp@args=0\relax%
\@ifnextchar({\psBspline@read{pn@de}}{\psBspline@read}}%
%
\def\psBspline@read#1{%
\def\bsp@root{#1}%
\next@Point%
}%
%
\def\next@Point{\@ifnextchar({\next@Point@i}{\psBsplineMain}}%
\def\next@Point@i(#1){%
\pnode(#1){\bsp@root\the\bsp@args}%
\advance\bsp@args by \@ne%
\next@Point}%
% The main drawing routine
\def\psBsplineMain{%done reading nodes
\pst@killglue%
\begingroup%
\use@par%
\ifbsp@closed\begin@ClosedObj \else \begin@OpenObj \fi%
\let\bsp@linecolor\pslinecolor%
\let\bsp@arrowA\psk@arrowA%
\let\bsp@arrowB\psk@arrowB%
\let\bsp@linestyle\pslinestyle%
\ifbsp@seq\advance\bsp@args by \@ne\fi%
\ifbsp@closed%
\psset{doubleline=false}%
\pnode(\bsp@root0){\bsp@root\the\bsp@args}%
\advance\bsp@args by \@ne%
\pnode(\bsp@root1){\bsp@root\the\bsp@args}%
\advance\bsp@args by \@ne%
\fi%
\advance\bsp@args by \m@ne%
% Define the left and right bezier control points in each interval. These are
% denoted (root+) R0, L1, R1, L2, R2, etc
\multido{\ia=0+1,\ib=1+1}{\bsp@args}{%
\ifPst@showframe%
\ncline[linestyle=dashed,linecolor=gray,arrows=*-*]{\bsp@root\ia}{\bsp@root\ib}%
\fi%
\nodexn{.667(\bsp@root\ia)+.333(\bsp@root\ib)}{\bsp@root R\ia}%
\nodexn{.333(\bsp@root\ia)+.667(\bsp@root\ib)}{\bsp@root L\ib}%
}%
%Finally, define the bezier endpoints for each interval
\advance\bsp@args by \m@ne%
\mmultido{\ia=0+1}{\bsp@args}{%
\ifPst@showframe%
\ncline[linestyle=solid,linecolor=red]{\bsp@root L\ia}{\bsp@root R\ia}%
\fi%
\midAB(\bsp@root L\ia)(\bsp@root R\ia){\bsp@root S\ia}%
\ifPst@showframe%
\psdot[linecolor=red](\bsp@root S\ia)%
\fi%
}%
\ifbsp@closed%
\pnode(\bsp@root S\the\bsp@args){\bsp@root S0}%
\else%
\advance\bsp@args by \@ne%
\pnode(\bsp@root0){\bsp@root S0}%
\pnode(\bsp@root\the\bsp@args){\bsp@root S\the\bsp@args}%
\fi%
\advance\bsp@args by \m@ne%
%the pieces of bezier curve
\ifbsp@closed%
\pscustom[arrows=-]{%
\psbezier[showpoints=false](\bsp@root S0)(\bsp@root R0)(\bsp@root L1)(\bsp@root S1)%
\multido{\ia=1+1,\ib=2+1}{\bsp@args}{\psbezier(\bsp@root R\ia)(\bsp@root L\ib)%
(\bsp@root S\ib)}%
%within \pscustom, \psbezier takes 3 args, using last point of previous
}%
\else %open curve---make arrows, don't use \pscustom
\advance\bsp@args by \m@ne%
\ifbsp@omitends \bsp@cntA=2\relax \bsp@cntB=\@ne \advance\bsp@args by -2\relax%
\else \bsp@cntA=\@ne\bsp@cntB=\z@ \fi%
\psbezier[arrows=-\bsp@arrowA,showpoints=false](\bsp@root S\the\bsp@cntA)%
(\bsp@root L\the\bsp@cntA)(\bsp@root R\the\bsp@cntB)(\bsp@root S\the\bsp@cntB)%
\mmultido{\ia=\the\bsp@cntA+1,\ib=\the\bsp@cntB+1}{\bsp@args}%
{\psbezier[arrows=-,showpoints=false](\bsp@root S\ib)(\bsp@root R\ib)%
(\bsp@root L\ia)(\bsp@root S\ia)}%
%
\ifbsp@omitends \advance\bsp@args by \@ne \fi%
\advance\bsp@args by \@ne%
\bsp@cntA=\bsp@args%
\bsp@cntB=\bsp@cntA%
\advance\bsp@cntB by \@ne%
\psbezier[arrows=-\bsp@arrowB,showpoints=false](\bsp@root S\the\bsp@cntA)%
(\bsp@root R\the\bsp@cntA)(\bsp@root L\the\bsp@cntB)(\bsp@root S\the\bsp@cntB)%
\ifPst@showframe \psdot[linecolor=red](\bsp@root L\the\bsp@cntB) \fi%
\fi% end \ifbsp@closed
\ifPst@showframe%
\psdot[linecolor=red](\bsp@root R0)%
\psdot[linecolor=red](\bsp@root L\the\bsp@args)%
\fi%
\ifshowpoints%
\multido{\i=0+1}{\bsp@args}{\psdot(\bsp@root S\i)}%
\fi%
\ifbsp@closed%
\end@ClosedObj%
\else%
\end@OpenObj%
\fi%
\endgroup%
\ignorespaces%
}
%
\def\psbspline{\def\pst@par{}\pst@object{psbspline}}%
\def\psbspline@i{\pst@getarrows\psbspline@ii}%
\def\psbspline@ii{%
\pnodesX%make the following sequences into nodes named S@0,...
%last index=\pst@args
}%
\def\psbspline@iii{%
\pst@killglue%
\psBsplineInterp{S@}{\the\pst@args}%creates S@B0...
\begingroup%
\use@par%
\psBsplineNodes{S@B}{\the\pst@args}%draw curve
\endgroup\ignorespaces}%
%
\def\pnodesX{%version of \pnodes where the last step moves to \psbspline@iii
\pst@args=\z@%
\def\PST@root{S@}%
\next@NodeX}%
%
\def\next@NodeX{\@ifnextchar({\next@NodeX@i}{\advance\pst@args by \m@ne\typeout{Defined nodes \PST@root0 .. \PST@root\the\pst@args.}\psbspline@iii}}%
%
\def\next@NodeX@i(#1){%
\pnode(#1){\PST@root\the\pst@args}%
\advance\pst@args\@ne%
\next@NodeX}%
%
\def\make@mcoeff#1{%
\pstVerb{ tx@Dict begin /mcoeff #1\space 1 add array def %
mcoeff 1 0.25 put %
1 1 #1\space 1 sub %
{/j exch def %j is counter
mcoeff j 1 add 1 4 mcoeff j get sub div put } for end }}%
%
\def\psBsplineInterp#1#2{{%
% #1=node name root to interpolate, #2=end index,
% eg, if we want to interpolate S0,..., S100, #1=S, #2=100,
\pst@killglue
\global\bsp@perfalse %
\newcount\top@mone \top@mone=#2\relax%100
\newcount\top@ndx \top@ndx=\top@mone%
\advance\top@ndx by -1\relax%99
\advance\top@mone by -2\relax%98
\newcount\top@mtwo \top@mtwo=\top@mone \advance\top@mtwo by \m@ne%97
\make@mcoeff{#2}%
\def\noderoot{#1}%
\pnode(\noderoot 0){\noderoot B0}%
\pnode(\noderoot #2){\noderoot B#2}%
\ifnum\top@mone>\m@ne% at least 3 points to interpolate
\ifnum\top@mone>\z@% we started with 4 or more points to interpolate
\psLCNode(\noderoot 1){6}(\noderoot 0){-1}{\noderoot B1}% 6*S1-S0->SB1
\multido{\iA=2+1,\iAA=1+1}{\top@mone}{\psLCNodeVar(\noderoot\iA)(\noderoot B\iAA)(! 6 mcoeff \iAA\space get neg ){\noderoot B\iA}}%2 to n-2, 6*S_k-m_{k-1}*SB_{k-1}->SB_k
\psLCNodeVar(\noderoot \the\top@ndx)(\noderoot #2)(! mcoeff \the\top@ndx\space get dup 6 mul exch neg ){tmp@node}%m_{99}*(6*S99-S100)->tmp@node
\psLCNodeVar(tmp@node)(\noderoot B\the\top@mone)(! 1 mcoeff \the\top@ndx\space get mcoeff \the\top@mone\space get mul neg ){\noderoot B\the\top@ndx}% temp@node -m_{98}*m_{99}*SB98->SB99
\multido{\iA=\the\top@mone+-1,\iAA=\the\top@ndx+-1}{\the\top@mone}{\psLCNodeVar(\noderoot B\iA)(\noderoot B\iAA)(! mcoeff \iA\space get dup neg ){\noderoot B\iA}% m_k*SB_k-m_k*SB_{k+1}->SB_k, k=98 downto 1
}% end multido
\else% exactly 3 points to interpolate
\nodexn{1.5(\noderoot1)-.25(\noderoot0)-.25(\noderoot2)}{\noderoot B1}%
\fi\fi%
}\ignorespaces}% end def
%
\def\psBsplineInterpC#1#2{{%
% #1=node name root, #2=top index,
% eg, if we want to interpolate S0,..., S100, #1=S, #2=100
% interpolation in this case is periodic (closed curve)
\pst@killglue
\global\bsp@pertrue %
\pst@cnta=\csname#1nodecount\endcsname\advance\pst@cnta \@ne %
\newcount\top@mone \top@mone=#2\relax%
\ifnum \top@mone<\pst@cnta %
\expandafter\xdef \csname #1nodecount\endcsname {\the\pst@cnta}%
\typeout{Changed #1nodecount to \the\pst@cnta}%
%\top@mone=\pst@cnta %
\else%
\ifnum \top@mone>\pst@cnta \top@mone=\pst@cnta\advance\top@mone \m@ne\fi
\fi%
\newcount\top@ndx \top@ndx=\top@mone%
\advance\top@ndx by \@ne%number of nodes to interpolate
\
\newcount\top@mtwo \top@mtwo=\top@mone \advance\top@mtwo\m@ne%
% After copying S0 to S101, \top@ndx, \top@mone, \top@mtwo are top index, top index-1, top index-two---101, 100, 99 in the example
\make@mcoeff{\the\top@ndx}%
\def\noderoot{#1}%
\pstVerb{ tx@Dict begin /bcoeff #2\space 2 add array def /ccoeff #2\space 2 add array def /xcoeff #2\space 2 add array def /ycoeff #2\space 2 add array def %
%% initialize b, c, x ,y values
1 1 \the\top@ndx\space %1 add
{/j exch def %j is counter
ccoeff j 0 put bcoeff j 0 put } for %
bcoeff 1 1 put bcoeff #2\space 1 put bcoeff #2\space 1 add 4 put %
ccoeff 1 0.25 put ccoeff #2\space 1 put end }%
%end \pstVerb
\pnode(\noderoot 0){\noderoot\the\top@ndx}%copy node 0 to top end
\pstVerb{ tx@Dict begin xcoeff 1 1 put ycoeff 1 1.5 put end }%
\pnode(! \psGetNodeCenter{\noderoot 1} xcoeff 1 \noderoot 1.x 1.5 mul put ycoeff 1 \noderoot 1.y 1.5 mul put 1 1){temp@}% 1.5=6*0.25
\multido{\iA=2+1}{\the\top@mone}{\pnode(! ycoeff \iA\space xcoeff \iA\space \psGetNodeCenter{#1\iA} #1\iA.x 6 mul put #1\iA.y 6 mul put 1 1){temp@}}% move x, y coords times 6 to arrays
\multido{\iA=2+1,\iB=1+1}{\the\top@mtwo}{\pstVerb{ tx@Dict begin %
ccoeff \iA\space ccoeff \iA\space get ccoeff \iB\space get sub mcoeff \iA\space get mul put %
xcoeff \iA\space xcoeff \iA\space get xcoeff \iB\space get sub mcoeff \iA\space get mul put %
ycoeff \iA\space ycoeff \iA\space get ycoeff \iB\space get sub mcoeff \iA\space get mul put
bcoeff \iA\space bcoeff \iA\space get bcoeff \iB\space get mcoeff \iB\space get mul sub put
bcoeff \the\top@ndx\space bcoeff \the\top@ndx\space get bcoeff \iB\space get ccoeff \iB\space get mul sub put
xcoeff \the\top@ndx\space xcoeff \the\top@ndx\space get xcoeff \iB\space get bcoeff \iB\space get mul sub put
ycoeff \the\top@ndx\space ycoeff \the\top@ndx\space get ycoeff \iB\space get bcoeff \iB\space get mul sub put end %
}% end \pstVerb
}% end \multido
\pstVerb{ tx@Dict begin %
bcoeff \the\top@ndx\space bcoeff \the\top@ndx\space get bcoeff \the\top@mone\space get
ccoeff \the\top@mone\space get mul sub put %b(n)=b(n)-b(n-1)*c(n-1)
xcoeff \the\top@ndx\space xcoeff \the\top@ndx\space get xcoeff \the\top@mone\space get bcoeff \the\top@mone\space get mul sub bcoeff \the\top@ndx\space get div put %x(n)=(x(n)-x(n-1)*b(n-1))/b(n)
ycoeff \the\top@ndx\space ycoeff \the\top@ndx\space get ycoeff \the\top@mone\space get bcoeff \the\top@mone\space get mul sub bcoeff \the\top@ndx\space get div put %y(n)=(y(n)-y(n-1)*b(n-1))/b(n)
xcoeff \the\top@mone\space xcoeff \the\top@mone\space get xcoeff \the\top@ndx\space get ccoeff \the\top@mone\space get mul sub put %x(n-1)=x(n-1)-c(n-1)*x(n)
ycoeff \the\top@mone\space ycoeff \the\top@mone\space get ycoeff \the\top@ndx\space get ccoeff \the\top@mone\space get mul sub put end %y(n-1)=y(n-1)-c(n-1)*y(n)
}% end pstVerb
\mmultido{\iA=\the\top@mone+-1,\iB=\the\top@ndx+-1}{\the\top@mtwo}{%
\pstVerb{ tx@Dict begin xcoeff \iA\space xcoeff \iA\space get mcoeff \iA\space get xcoeff \iB\space get mul sub ccoeff \iA\space get xcoeff \the\top@ndx\space get mul sub put % x(k)=x(k)-m(k)*x(k+1)-c(k)*x(n)
ycoeff \iA\space ycoeff \iA\space get mcoeff \iA\space get ycoeff \iB\space get mul sub ccoeff \iA\space get ycoeff \the\top@ndx\space get mul sub put end %
}}%y(k)=...
\multido{\iA=1+1}{\the\top@ndx}{\pnode(! xcoeff \iA\space get ycoeff \iA\space get )%
{\noderoot B\iA}}%
\pnode(\noderoot B\the\top@ndx){\noderoot B0}%
}\ignorespaces}%
%
\def\thickBspline{\def\pst@par{}\pst@object{thickBspline}}%
\def\thickBspline@i#1#2#3#4{{%
% #1=root | #2=nsegments | #3=thickness | #4=items to clip
\pst@killglue%
\use@par%
%prepare array
\pssetlength{\pst@dimp}{#3}\pst@dimtonum{\pst@dimp}{\thickness}% thickness in TeX pt
\newcount\n@cnt%
\newcount\np@cnt%
\newcount\ary@max \ary@max=\psk@plotpoints \relax%
\multiply\ary@max #2\np@cnt=\ary@max \multiply\ary@max 4\relax%
\advance\ary@max 4\relax %
\n@cnt=\ary@max \advance\n@cnt \m@ne%
\multiply\np@cnt \tw@\advance\np@cnt \tw@% count of points in array
\pstVerb{ gsave tx@Dict begin %
/psxu \pst@number\psxunit\space def /psyu \pst@number\psyunit\space def %
/uratio psyu psxu div def % so that perp to a, b is -b*uratio a
/nseg #2 def /nplotpt \psk@plotpoints\space def %
/clipary #2 nplotpt mul 4 mul 4 add array def %
/lindex 2 def /uindex \the\ary@max\space 1 sub def %
/dt 1 \psk@plotpoints\space div def %
% /halfthck #3 2 div def %
end grestore }%
\multido{\iA=0+1,\iB=1+1}{#2}{%
% pass control points of this segment to PostScript variables
\pstVerb{%
gsave tx@Dict begin %
STV CP T \psGetNodeCenter{#1\iA}\space \psGetNodeCenter{#1BR\iA}\space \psGetNodeCenter{#1BL\iB}\space \psGetNodeCenter{#1\iB}\space %
/bez@1.x #1\iA.x def /bez@1.y #1\iA.y def %initial point on segment
%(START) = bez@1.x = bez@1.y = SB1.x = %
/bez@2.x #1BR\iA.x bez@1.x sub def %adjusted control points (less init pt)
/bez@2.y #1BR\iA.y bez@1.y sub def %
/bez@3.x #1BL\iB.x bez@1.x sub def %
/bez@3.y #1BL\iB.y bez@1.y sub def %
/bez@4.x #1\iB.x bez@1.x sub def %
/bez@4.y #1\iB.y bez@1.y sub def %
/bez@1x bez@2.x 3 mul def % for position--w1=3z1
/bez@1y bez@2.y 3 mul def %
/bez@2x bez@3.x bez@2.x 2 mul sub 3 mul def %position w2=3(z2-2z1)
/bez@2y bez@3.y bez@2.y 2 mul sub 3 mul def %
/bez@2xT bez@2x 2 mul def % for tangent
/bez@2yT bez@2y 2 mul def %
/bez@3x bez@4.x bez@2.x bez@3.x sub 3 mul add def % w3=z3+3z1-3z2
/bez@3y bez@4.y bez@2.y bez@3.y sub 3 mul add def %
/bez@3xT bez@3x 3 mul def % tangent
/bez@3yT bez@3y 3 mul def %
/Func % position
( bez@3x t mul bez@2x add t mul bez@1x add t mul bez@1.x add psxu mul %
bez@3y t mul bez@2y add t mul bez@1y add t mul bez@1.y add psyu mul ) cvx def %
%/FuncT % tangent
% ( bez@1x t bez@2xT mul add t t bez@3xT mul mul add %
% bez@1y t bez@2yT mul add t t bez@3yT mul mul add ) cvx def
/FuncN % unit normal times delta
( bez@2yT t bez@3yT mul add t mul bez@1y add uratio mul neg
bez@2xT t bez@3xT mul add t mul bez@1x add 2 copy Pyth dup %
3 1 roll div 3 1 roll div \thickness\space 2 div dup 3 1 roll mul 3 1 roll mul ) cvx def %
end grestore }%
\ifnum\iA=0 \relax%
\pnode(! /t 0 def FuncN /dy exch def /dx exch def Func 2 copy %
/y0 ED /x0 ED %
clipary 0 x0 dx add put clipary 1 y0 dy add put %
clipary uindex y0 dy sub put clipary uindex 1 sub x0 dx sub put %
/uindex uindex 2 sub def ){tmp@P}%
\fi%
\multido{\i=1+1}{\psk@plotpoints}{%
%make array elements for this segment using #3
\pnode(! /t dt \i\space mul def FuncN /dy ED /dx ED Func 2 copy /y0 ED /x0 ED %
clipary lindex x0 dx add put clipary lindex 1 add y0 dy add put %
clipary uindex y0 dy sub put clipary uindex 1 sub x0 dx sub put %
/lindex lindex 2 add def /uindex uindex 2 sub def ){tmp@P}%
}% end multido \i
}% end multido \iA
% if periodic, we have to adjust 2 points so as not too leave a wege in the
% clipping region. We have to set Q_{nk} to Q_0 and R_{nk} to R_0
% R_{nk} is at position 2*nk, 2*nk+1 and Q_{nk} is at the next pair
%\ifbsp@per %
% \pstVerb{%
% tx@Dict begin /itemcnt #2 nplotpt mul 2 mul def %first item to change is index 2nk
% clipary itemcnt clipary 0 get put /itemcnt itemcnt 1 add def %
% clipary itemcnt clipary 1 get put /itemcnt itemcnt 1 add def %
% clipary itemcnt clipary \the\n@cnt\space 1 sub get put /itemcnt itemcnt 1 add def %
% clipary itemcnt clipary \the\n@cnt\space get put %
% end }%
%\fi%
% make a clipping path in PS and pass commands #4
\ifbsp@per %periodic
\psclip{\pscustom{%
\code{ clipary aload pop moveto nseg nplotpt mul %
{ lineto } repeat closepath %
moveto nseg nplotpt mul { lineto } repeat closepath }}}%
#4
\endpsclip%
\else % not periodic
\psclip{\pscustom{%
\code{ clipary aload pop moveto nseg nplotpt mul 2 mul %
1 add { lineto } repeat closepath %
\ifPst@reverseclip\space reversepath \fi}}}%
#4
\endpsclip%
\fi%
}%
\ignorespaces}%
\catcode`\@=\TheAtCode\relax
\endinput
|