summaryrefslogtreecommitdiff
path: root/Master/texmf-dist/asymptote/contour.asy
blob: 8c6dbba86b37c5f079b748e4ff194f217258d656 (plain)
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
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
// Contour routines written by Radoslav Marinov and John Bowman.

import graph_settings;

real eps=10000*realEpsilon;

//                         1
//             6 +-------------------+ 5
//               | \               / |
//               |   \          /    |
//               |     \       /     |
//               |       \   /       |
//             2 |         X         | 0
//               |       /   \       |
//               |     /       \     |
//               |   /           \   |
//               | /               \ |
//             7 +-------------------+ 4 or 8
//                         3

private struct segment
{
  bool active;
  pair a,b;        // Endpoints; a is always an edge point if one exists.
  int c;           // Contour value.
  int edge;        // -1: interior, 0 to 3: edge,
                   // 4-8: single-vertex edge, 9: double-vertex edge.
}

// Case 1: line passes through two vertices of a triangle
private segment case1(pair p0, pair p1, int edge)
{
  // Will cause a duplicate guide; luckily case1 is rare
  segment rtrn;
  rtrn.active=true;
  rtrn.a=p0;
  rtrn.b=p1;
  rtrn.edge=edge;
  return rtrn;
}

// Case 2: line passes through a vertex and a side of a triangle
// (the first vertex passed and the side between the other two)
private segment case2(pair p0, pair p1, pair p2,
                      real v0, real v1, real v2, int edge)
{
  segment rtrn;
  pair val=interp(p1,p2,abs(v1/(v2-v1)));
  rtrn.active=true;
  if(edge < 4) {
    rtrn.a=val;
    rtrn.b=p0;
  } else {
    rtrn.a=p0;
    rtrn.b=val;
  }
  rtrn.edge=edge;
  return rtrn;
}

// Case 3: line passes through two sides of a triangle
// (through the sides formed by the first & second, and second & third
// vertices)
private segment case3(pair p0, pair p1, pair p2,
                      real v0, real v1, real v2, int edge=-1)
{
  segment rtrn;
  rtrn.active=true;
  rtrn.a=interp(p1,p0,abs(v1/(v0-v1)));
  rtrn.b=interp(p1,p2,abs(v1/(v2-v1)));
  rtrn.edge=edge;
  return rtrn;
}

// Check if a line passes through a triangle, and draw the required line.
private segment checktriangle(pair p0, pair p1, pair p2,
                              real v0, real v1, real v2, int edge=-1)
{
  // default null return
  static segment dflt;

  real eps=eps*max(abs(v0),abs(v1),abs(v2));

  if(v0 < -eps) {
    if(v1 < -eps) {
      if(v2 < -eps) return dflt; // nothing to do
      else if(v2 <= eps) return dflt; // nothing to do
      else return case3(p0,p2,p1,v0,v2,v1);
    } else if(v1 <= eps) {
      if(v2 < -eps) return dflt; // nothing to do
      else if(v2 <= eps) return case1(p1,p2,5+edge);
      else return case2(p1,p0,p2,v1,v0,v2,5+edge);
    } else {
      if(v2 < -eps) return case3(p0,p1,p2,v0,v1,v2,edge);
      else if(v2 <= eps)
        return case2(p2,p0,p1,v2,v0,v1,edge);
      else return case3(p1,p0,p2,v1,v0,v2,edge);
    }
  } else if(v0 <= eps) {
    if(v1 < -eps) {
      if(v2 < -eps) return dflt; // nothing to do
      else if(v2 <= eps) return case1(p0,p2,4+edge);
      else return case2(p0,p1,p2,v0,v1,v2,4+edge);
    } else if(v1 <= eps) {
      if(v2 < -eps) return case1(p0,p1,9);
      else if(v2 <= eps) return dflt; // use finer partitioning.
      else return case1(p0,p1,9);
    } else {
      if(v2 < -eps) return case2(p0,p1,p2,v0,v1,v2,4+edge);
      else if(v2 <= eps) return case1(p0,p2,4+edge);
      else return dflt; // nothing to do
    }
  } else {
    if(v1 < -eps) {
      if(v2 < -eps) return case3(p1,p0,p2,v1,v0,v2,edge);
      else if(v2 <= eps)
        return case2(p2,p0,p1,v2,v0,v1,edge);
      else return case3(p0,p1,p2,v0,v1,v2,edge);
    } else if(v1 <= eps) {
      if(v2 < -eps) return case2(p1,p0,p2,v1,v0,v2,5+edge);
      else if(v2 <= eps) return case1(p1,p2,5+edge);
      else return dflt; // nothing to do
    } else {
      if(v2 < -eps) return case3(p0,p2,p1,v0,v2,v1);
      else if(v2 <= eps) return dflt; // nothing to do
      else return dflt; // nothing to do
    }
  }
}

// Collect connecting path segments.
private void collect(pair[][][] points, real[] c)
{
  // use to reverse an array, omitting the first point
  int[] reverseF(int n) {return sequence(new int(int x){return n-1-x;},n-1);}
  // use to reverse an array, omitting the last point
  int[] reverseL(int n) {return sequence(new int(int x){return n-2-x;},n-1);}

  for(int cnt=0; cnt < c.length; ++cnt) {
    pair[][] gdscnt=points[cnt];
    for(int i=0; i < gdscnt.length; ++i) {
      pair[] gig=gdscnt[i];
      int Li=gig.length;
      for(int j=i+1; j < gdscnt.length; ++j) {
        pair[] gjg=gdscnt[j];
        int Lj=gjg.length;
        if(abs(gig[0]-gjg[0]) < eps) {
          gdscnt[j]=gjg[reverseF(Lj)];
          gdscnt[j].append(gig);
          gdscnt.delete(i);
          --i;
          break;
        } else if(abs(gig[0]-gjg[Lj-1]) < eps) {
          gig.delete(0);
          gdscnt[j].append(gig);
          gdscnt.delete(i);
          --i;
          break;
        } else if(abs(gig[Li-1]-gjg[0]) < eps) {
          gjg.delete(0);
          gig.append(gjg);
          gdscnt[j]=gig;
          gdscnt.delete(i);
          --i;
          break;
        } else if(abs(gig[Li-1]-gjg[Lj-1]) < eps) {
          gig.append(gjg[reverseL(Lj)]);
          gdscnt[j]=gig;
          gdscnt.delete(i);
          --i;
          break;
        }
      }
    }
  }
}

// Join path segments.
private guide[][] connect(picture pic, pair[][][] points, real[] c,
                          interpolate join)
{
  // set up return value
  guide[][] result=new guide[c.length][];
  for(int cnt=0; cnt < c.length; ++cnt) {
    pair[][] pointscnt=points[cnt];
    guide[] resultcnt=result[cnt]=new guide[pointscnt.length];
    for(int i=0; i < pointscnt.length; ++i) {
      pair[] pts=pointscnt[i];
      guide gd;
      if(pts.length > 0) {
        if(pts.length > 1 && abs(pts[0]-pts[pts.length-1]) < eps) {
          guide[] g=sequence(new guide(int i) {
              return (pic.scale.x.T(pts[i].x), pic.scale.y.T(pts[i].y));
            },pts.length-1);
          g.push(cycle);
          gd=join(...g);
        } else
          gd=join(...sequence(new guide(int i) {
                return (pic.scale.x.T(pts[i].x), pic.scale.y.T(pts[i].y));
              },pts.length));
      }
      resultcnt[i]=gd;
    }
  }
  return result;
}


// Return contour guides for a 2D data array.
// z:         two-dimensional array of nonoverlapping mesh points
// f:         two-dimensional array of corresponding f(z) data values
// midpoint:  optional array containing values of f at cell midpoints
// c:         array of contour values
// join:      interpolation operator (e.g. operator -- or operator ..)
guide[][] contour(picture pic=currentpicture, pair[][] z, real[][] f,
                  real[][] midpoint=new real[][], real[] c,
                  interpolate join=operator --)
{
  int nx=z.length-1;
  if(nx == 0)
    abort("array z must have length >= 2");
  int ny=z[0].length-1;
  if(ny == 0)
    abort("array z[0] must have length >= 2");

  c=sort(c);
  bool midpoints=midpoint.length > 0;

  segment segments[][][]=new segment[nx][ny][];

  // go over region a rectangle at a time
  for(int i=0; i < nx; ++i) {
    pair[] zi=z[i];
    pair[] zp=z[i+1];
    real[] fi=f[i];
    real[] fp=f[i+1];
    real[] midpointi;
    if(midpoints) midpointi=midpoint[i];
    segment[][] segmentsi=segments[i];
    for(int j=0; j < ny; ++j) {
      segment[] segmentsij=segmentsi[j];

      // define points
      pair bleft=zi[j];
      pair bright=zp[j];
      pair tleft=zi[j+1];
      pair tright=zp[j+1];
      pair middle=0.25*(bleft+bright+tleft+tright);

      real f00=fi[j];
      real f01=fi[j+1];
      real f10=fp[j];
      real f11=fp[j+1];
      real fmm=midpoints ? midpoint[i][j] : 0.25*(f00+f01+f10+f11);

      // optimization: we make sure we don't work with empty rectangles
      int checkcell(int cnt) {
        real C=c[cnt];
        real vertdat0=f00-C;  // bottom-left vertex
        real vertdat1=f10-C;  // bottom-right vertex
        real vertdat2=f01-C;  // top-left vertex
        real vertdat3=f11-C;  // top-right vertex

        // optimization: we make sure we don't work with empty rectangles
        int countm=0;
        int countz=0;
        int countp=0;

        void check(real vertdat) {
          if(vertdat < -eps) ++countm;
          else {
            if(vertdat <= eps) ++countz;
            else ++countp;
          }
        }

        check(vertdat0);
        check(vertdat1);
        check(vertdat2);
        check(vertdat3);

        if(countm == 4) return 1;  // nothing to do
        if(countp == 4) return -1; // nothing to do
        if((countm == 3 || countp == 3) && countz == 1) return 0;

        // go through the triangles

        void addseg(segment seg) {
          if(seg.active) {
            seg.c=cnt;
            segmentsij.push(seg);
          }
        }
        real vertdat4=fmm-C;
        addseg(checktriangle(bright,tright,middle,
                             vertdat1,vertdat3,vertdat4,0));
        addseg(checktriangle(tright,tleft,middle,
                             vertdat3,vertdat2,vertdat4,1));
        addseg(checktriangle(tleft,bleft,middle,
                             vertdat2,vertdat0,vertdat4,2));
        addseg(checktriangle(bleft,bright,middle,
                             vertdat0,vertdat1,vertdat4,3));
        return 0;
      }

      void process(int l, int u) {
        if(l >= u) return;
        int i=quotient(l+u,2);
        int sign=checkcell(i);
        if(sign == -1) process(i+1,u);
        else if(sign == 1) process(l,i);
        else {
          process(l,i);
          process(i+1,u);
        }
      }

      process(0,c.length);
    }
  }

  // set up return value
  pair[][][] points=new pair[c.length][][];

  for(int i=0; i < nx; ++i) {
    segment[][] segmentsi=segments[i];
    for(int j=0; j < ny; ++j) {
      segment[] segmentsij=segmentsi[j];
      for(int k=0; k < segmentsij.length; ++k) {
        segment C=segmentsij[k];

        if(!C.active) continue;

        pair[] g=new pair[] {C.a,C.b};
        segmentsij[k].active=false;

        int forward(int I, int J, bool first=true) {
          if(I >= 0 && I < nx && J >= 0 && J < ny) {
            segment[] segmentsIJ=segments[I][J];
            for(int l=0; l < segmentsIJ.length; ++l) {
              segment D=segmentsIJ[l];
              if(!D.active) continue;
              if(abs(D.a-g[g.length-1]) < eps) {
                g.push(D.b);
                segmentsIJ[l].active=false;
                if(D.edge >= 0 && !first) return D.edge;
                first=false;
                l=-1;
              } else if(abs(D.b-g[g.length-1]) < eps) {
                g.push(D.a);
                segmentsIJ[l].active=false;
                if(D.edge >= 0 && !first) return D.edge;
                first=false;
                l=-1;
              }
            }
          }
          return -1;
        }

        int backward(int I, int J, bool first=true) {
          if(I >= 0 && I < nx && J >= 0 && J < ny) {
            segment[] segmentsIJ=segments[I][J];
            for(int l=0; l < segmentsIJ.length; ++l) {
              segment D=segmentsIJ[l];
              if(!D.active) continue;
              if(abs(D.a-g[0]) < eps) {
                g.insert(0,D.b);
                segmentsIJ[l].active=false;
                if(D.edge >= 0 && !first) return D.edge;
                first=false;
                l=-1;
              } else if(abs(D.b-g[0]) < eps) {
                g.insert(0,D.a);
                segmentsIJ[l].active=false;
                if(D.edge >= 0 && !first) return D.edge;
                first=false;
                l=-1;
              }
            }
          }
          return -1;
        }

        void follow(int f(int, int, bool first=true), int edge) {
          int I=i;
          int J=j;
          while(true) {
            static int ix[]={1,0,-1,0};
            static int iy[]={0,1,0,-1};
            if(edge >= 0 && edge < 4) {
              I += ix[edge];
              J += iy[edge];
              edge=f(I,J);
            } else {
              if(edge == -1) break;
              if(edge < 9) {
                int edge0=(edge-5) % 4;
                int edge1=(edge-4) % 4;
                int ix0=ix[edge0];
                int iy0=iy[edge0];
                I += ix0;
                J += iy0;
                // Search all 3 corner cells
                if((edge=f(I,J)) == -1) {
                  I += ix[edge1];
                  J += iy[edge1];
                  if((edge=f(I,J)) == -1) {
                    I -= ix0;
                    J -= iy0;
                    edge=f(I,J);
                  }
                }
              } else {
                // Double-vertex edge: search all 8 surrounding cells
                void search() {
                  for(int i=-1; i <= 1; ++i) {
                    for(int j=-1; j <= 1; ++j) {
                      if((edge=f(I+i,J+j,false)) >= 0) {
                        I += i;
                        J += j;
                        return;
                      }
                    }
                  }
                }
                search();
              }
            }
          }
        }

        // Follow contour in cell
        int edge=forward(i,j,first=false);

        // Follow contour forward outside of cell
        follow(forward,edge);

        // Follow contour backward outside of cell
        follow(backward,C.edge);

        points[C.c].push(g);
      }
    }
  }

  collect(points,c); // Required to join remaining case1 cycles.

  return connect(pic,points,c,join);
}

// Return contour guides for a 2D data array on a uniform lattice
// f:         two-dimensional array of real data values
// midpoint:  optional array containing data values at cell midpoints
// a,b:       diagonally opposite vertices of rectangular domain
// c:         array of contour values
// join:      interpolation operator (e.g. operator -- or operator ..)
guide[][] contour(picture pic=currentpicture, real[][] f,
                  real[][] midpoint=new real[][], pair a, pair b, real[] c,
                  interpolate join=operator --)
{
  int nx=f.length-1;
  if(nx == 0)
    abort("array f must have length >= 2");
  int ny=f[0].length-1;
  if(ny == 0)
    abort("array f[0] must have length >= 2");

  pair[][] z=new pair[nx+1][ny+1];
  for(int i=0; i <= nx; ++i) {
    pair[] zi=z[i];
    real xi=interp(a.x,b.x,i/nx);
    for(int j=0; j <= ny; ++j) {
      zi[j]=(xi,interp(a.y,b.y,j/ny));
    }
  }
  return contour(pic,z,f,midpoint,c,join);
}

// return contour guides for a real-valued function
// f:        real-valued function of two real variables
// a,b:      diagonally opposite vertices of rectangular domain
// c:        array of contour values
// nx,ny:    number of subdivisions in x and y directions (determines accuracy)
// join:     interpolation operator (e.g. operator -- or operator ..)
guide[][] contour(picture pic=currentpicture, real f(real, real), pair a,
                  pair b, real[] c, int nx=ngraph, int ny=nx,
                  interpolate join=operator --)
{
  // evaluate function at points and midpoints
  real[][] dat=new real[nx+1][ny+1];
  real[][] midpoint=new real[nx+1][ny+1];

  for(int i=0; i <= nx; ++i) {
    real x=interp(a.x,b.x,i/nx);
    real x2=interp(a.x,b.x,(i+0.5)/nx);
    real[] dati=dat[i];
    real[] midpointi=midpoint[i];
    for(int j=0; j <= ny; ++j) {
      dati[j]=f(x,interp(a.y,b.y,j/ny));
      midpointi[j]=f(x2,interp(a.y,b.y,(j+0.5)/ny));
    }
  }

  return contour(pic,dat,midpoint,a,b,c,join);
}

void draw(picture pic=currentpicture, Label[] L=new Label[],
          guide[][] g, pen[] p)
{
  begingroup(pic);
  for(int cnt=0; cnt < g.length; ++cnt) {
    guide[] gcnt=g[cnt];
    pen pcnt=p[cnt];
    for(int i=0; i < gcnt.length; ++i)
      draw(pic,gcnt[i],pcnt);
    if(L.length > 0) {
      Label Lcnt=L[cnt];
      for(int i=0; i < gcnt.length; ++i) {
        if(Lcnt.s != "" && size(gcnt[i]) > 1)
          label(pic,Lcnt,gcnt[i],pcnt);
      }
    }
  }
  endgroup(pic);
}

void draw(picture pic=currentpicture, Label[] L=new Label[],
          guide[][] g, pen p=currentpen)
{
  draw(pic,L,g,sequence(new pen(int) {return p;},g.length));
}

// Extend palette by the colors below and above at each end.
pen[] extend(pen[] palette, pen below, pen above) {
  pen[] p=copy(palette);
  p.insert(0,below);
  p.push(above);
  return p;
}

// Compute the interior palette for a sequence of cyclic contours
// corresponding to palette.
pen[][] interior(picture pic=currentpicture, guide[][] g, pen[] palette)
{
  if(palette.length != g.length+1)
    abort("Palette array must have length one more than guide array");
  pen[][] fillpalette=new pen[g.length][];
  for(int i=0; i < g.length; ++i) {
    guide[] gi=g[i];
    guide[] gp;
    if(i+1 < g.length) gp=g[i+1];
    guide[] gm;
    if(i > 0) gm=g[i-1];

    pen[] fillpalettei=new pen[gi.length];
    for(int j=0; j < gi.length; ++j) {
      path P=gi[j];
      if(cyclic(P)) {
        int index=i+1;
        bool nextinside;
        for(int k=0; k < gp.length; ++k) {
          path next=gp[k];
          if(cyclic(next)) {
            if(inside(P,point(next,0)))
              nextinside=true;
            else if(inside(next,point(P,0)))
              index=i;
          }
        }
        if(!nextinside) {
          // Check to see if previous contour is inside
          for(int k=0; k < gm.length; ++k) {
            path prev=gm[k];
            if(cyclic(prev)) {
              if(inside(P,point(prev,0)))
                index=i;
            }
          }
        }
        fillpalettei[j]=palette[index];
      }
      fillpalette[i]=fillpalettei;
    }
  }
  return fillpalette;
}

// Fill the interior of cyclic contours with palette
void fill(picture pic=currentpicture, guide[][] g, pen[][] palette)
{
  for(int i=0; i < g.length; ++i) {
    guide[] gi=g[i];
    guide[] gp;
    if(i+1 < g.length) gp=g[i+1];
    guide[] gm;
    if(i > 0) gm=g[i-1];

    for(int j=0; j < gi.length; ++j) {
      path P=gi[j];
      path[] S=P;
      if(cyclic(P)) {
        for(int k=0; k < gp.length; ++k) {
          path next=gp[k];
          if(cyclic(next) && inside(P,point(next,0)))
            S=S^^next;
        }
        for(int k=0; k < gm.length; ++k) {
          path next=gm[k];
          if(cyclic(next) && inside(P,point(next,0)))
            S=S^^next;
        }
        fill(pic,S,palette[i][j]+evenodd);
      }
    }
  }
}

// routines for irregularly spaced points:

// check existing guides and adds new segment to them if possible,
// or otherwise store segment as a new guide
private void addseg(pair[][] gds, segment seg)
{
  if(!seg.active) return;
  // search for a path to extend
  for(int i=0; i < gds.length; ++i) {
    pair[] gd=gds[i];
    if(abs(gd[0]-seg.b) < eps) {
      gd.insert(0,seg.a);
      return;
    } else if(abs(gd[gd.length-1]-seg.b) < eps) {
      gd.push(seg.a);
      return;
    } else if(abs(gd[0]-seg.a) < eps) {
      gd.insert(0,seg.b);
      return;
    } else if(abs(gd[gd.length-1]-seg.a) < eps) {
      gd.push(seg.b);
      return;
    }
  }

  // in case nothing is found
  pair[] segm;
  segm=new pair[] {seg.a,seg.b};
  gds.push(segm);

  return;
}

guide[][] contour(picture pic=currentpicture, real f(pair), pair a, pair b,
                  real[] c, int nx=ngraph, int ny=nx,
                  interpolate join=operator --)
{
  return contour(pic,new real(real x, real y) {return f((x,y));},a,b,c,nx,ny,join);
}

guide[][] contour(picture pic=currentpicture, pair[] z, real[] f, real[] c, interpolate join=operator --)
{
  if(z.length != f.length)
    abort("z and f arrays have different lengths");

  int[][] trn=triangulate(z);

  // array to store guides found so far
  pair[][][] points=new pair[c.length][][];

  for(int cnt=0; cnt < c.length; ++cnt) {
    pair[][] pointscnt=points[cnt];
    real C=c[cnt];
    for(int i=0; i < trn.length; ++i) {
      int[] trni=trn[i];
      int i0=trni[0], i1=trni[1], i2=trni[2];
      addseg(pointscnt,checktriangle(z[i0],z[i1],z[i2],
                                     f[i0]-C,f[i1]-C,f[i2]-C));
    }
  }

  collect(points,c);

  return connect(pic,points,c,join);
}