forked from matplotlib/matplotlib
-
Notifications
You must be signed in to change notification settings - Fork 0
/
cntr.c
1759 lines (1618 loc) · 56.3 KB
/
cntr.c
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
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
/*
cntr.c
General purpose contour tracer for quadrilateral meshes.
Handles single level contours, or region between a pair of levels.
The routines that do all the work, as well as the explanatory
comments, came from gcntr.c, part of the GIST package. The
original mpl interface was also based on GIST. The present
interface uses parts of the original, but places them in
the entirely different framework of a Python type. It
was written by following the Python "Extending and Embedding"
tutorial.
$Id$
*/
#include <Python.h>
#include "structmember.h"
#include <stdlib.h>
#include <stdio.h>
#include "numerix.h"
/* Note that all arrays in these routines are Fortran-style,
in the sense that the "i" index varies fastest; the dimensions
of the corresponding C array are z[jmax][imax] in the notation
used here. We can identify i and j with the x and y dimensions,
respectively.
*/
/* What is a contour?
*
* Given a quadrilateral mesh (x,y), and values of a z at the points
* of that mesh, we seek a set of polylines connecting points at a
* particular value of z. Each point on such a contour curve lies
* on an edge of the mesh, at a point linearly interpolated to the
* contour level z0 between the given values of z at the endpoints
* of the edge.
*
* Identifying these points is easy. Figuring out how to connect them
* into a curve -- or possibly a set of disjoint curves -- is difficult.
* Each disjoint curve may be either a closed circuit, or it may begin
* and end on a mesh boundary.
*
* One of the problems with a quadrilateral mesh is that when the z
* values at one pair of diagonally opposite points lie below z0, and
* the values at the other diagonal pair of the same zone lie above z0,
* all four edges of the zone are cut, and there is an ambiguity in
* how we should connect the points. I call this a saddle zone.
* The problem is that two disjoint curves cut through a saddle zone
* (I reject the alternative of connecting the opposite points to make
* a single self-intersecting curve, since those make ugly contour plots
* -- I've tried it). The real problem with saddle zones is that you
* need to communicate the connectivity decision you make back to the
* calling routine, since for the next contour level, we need to tell
* the contour tracer to make the same decision as on the previous
* level. The input/output triangulation array is the solution to this
* nasty problem.
*
* Another complicating factor is that there may be logical holes in
* the mesh -- zones which do not exist. We want our contours to stop
* if they hit the edge of such a zone, just as if they'd hit the edge
* of the whole mesh. The input region array addresses this issue.
*
* Yet another complication: We may want a list of closed polygons which
* outline the region between two contour levels z0 and z1. These may
* include sections of the mesh boundary (including edges of logical
* holes defined by the region array), in addition to sections of the
* contour curves at one or both levels. This introduces a huge
* topological problem -- if one of the closed contours (possibly
* including an interior logical hole in the mesh, but not any part of
* the boundary of the whole mesh) encloses a region which is not
* between z0 and z1, that curve must be connected by a slit (or "branch
* cut") to the enclosing curve, so that the list of disjoint polygons
* we return is each simply connected.
*
* Okay, one final stunning difficulty: For the two level case, no
* individual polygon should have more than a few thousand sides, since
* huge filled polygons place an inordinate load on rendering software,
* which needs an amount of scratch space proportional to the number
* of sides it needs to fill. So in the two level case, we want to
* chunk the mesh into rectangular pieces of no more than, say, 30x30
* zones, which keeps each returned polygon to less than a few thousand
* sides (the worst case is very very bad -- you can easily write down
* a function and two level values which produce a polygon that cuts
* every edge of the mesh twice).
*/
/*
* Here is the numbering scheme for points, edges, and zones in
* the mesh -- note that each ij corresponds to one point, one zone,
* one i-edge (i=constant edge) and one j-edge (j=constant edge):
*
* (ij-1)-------(ij)-------(ij)
* | |
* | |
* | |
* (ij-1) (ij) (ij)
* | |
* | |
* | |
* (ij-iX-1)----(ij-iX)----(ij-iX)
*
* At each point, the function value is either 0, 1, or 2, depending
* on whether it is below z0, between z0 and z1, or above z1.
* Each zone either exists (1) or not (0).
* From these three bits of data, all of the curve connectivity follows.
*
* The tracing algorithm is naturally edge-based: Either you are at a
* point where a level cuts an edge, ready to step across a zone to
* another edge, or you are drawing the edge itself, if it happens to
* be a boundary with at least one section between z0 and z1.
*
* In either case, the edge is a directed edge -- either the zone
* you are advancing into is to its left or right, or you are actually
* drawing it. I always trace curves keeping the region between z0 and
* z1 to the left of the curve. If I'm tracing a boundary, I'm always
* moving CCW (counter clockwise) around the zone that exists. And if
* I'm about to cross a zone, I'll make the direction of the edge I'm
* sitting on be such that the zone I'm crossing is to its left.
*
* I start tracing each curve near its lower left corner (mesh oriented
* as above), which is the first point I encounter scanning through the
* mesh in order. When I figure the 012 z values and zonal existence,
* I also mark the potential starting points: Each edge may harbor a
* potential starting point corresponding to either direction, so there
* are four start possibilities at each ij point. Only the following
* possibilities need to be marked as potential starting edges:
*
* +-+-+-+
* | | | |
* A-0-C-+ One or both levels cut E and have z=1 above them, and
* | EZ| | 0A is cut and either 0C is cut or CD is cut.
* +-B-D-+ Or, one or both levels cut E and E is a boundary edge.
* | | | | (and Z exists)
* +-+-+-+
*
* +-+-+-+
* | | | |
* +-A-0-C One or both levels cut E and have z=1 below them, and
* | |ZE | 0A is cut and either 0C is cut or CD is cut.
* +-+-B-D Or, one or both levels cut E and E is a boundary edge.
* | | | | (and Z exists)
* +-+-+-+
*
* +-+-+-+
* | | | |
* +-+-+-+ E is a boundary edge, Z exists, at some point on E
* | |Z| | lies between the levels.
* +-+E+-+
* | | | |
* +-+-+-+
*
* +-+-+-+
* | | | |
* +-+E+-+ E is a boundary edge, Z exists, at some point on E
* | |Z| | lies between the levels.
* +-+-+-+
* | | | |
* +-+-+-+
*
* During the first tracing pass, the start mark is erased whenever
* any non-starting edge is encountered, reducing the number of points
* that need to be considered for the second pass. The first pass
* makes the basic connectivity decisions. It figures out how many
* disjoint curves there will be, and identifies slits for the two level
* case or open contours for the single level case, and removes all but
* the actual start markers. A second tracing pass can perform the
* actual final trace.
*/
/* ------------------------------------------------------------------------ */
/* the data about edges, zones, and points -- boundary or not, exists
* or not, z value 0, 1, or 2 -- is kept in a mesh sized data array */
typedef short Cdata;
/* here is the minimum structure required to tell where we are in the
* mesh sized data array */
typedef struct Csite Csite;
struct Csite
{
long edge; /* ij of current edge */
long left; /* +-1 or +-imax as the zone is to right, left, below,
* or above the edge */
long imax; /* imax for the mesh */
long jmax; /* jmax for the mesh */
long n; /* number of points marked on this curve so far */
long count; /* count of start markers visited */
double zlevel[2]; /* contour levels, zlevel[1]<=zlevel[0]
* signals single level case */
short *triangle; /* triangulation array for the mesh */
char *reg; /* region array for the mesh (was int) */
Cdata *data; /* added by EF */
long edge0, left0; /* starting site on this curve for closure */
int level0; /* starting level for closure */
long edge00; /* site needing START_ROW mark */
/* making the actual marks requires a bunch of other stuff */
const double *x, *y, *z; /* mesh coordinates and function values */
double *xcp, *ycp; /* output contour points */
};
void print_Csite(Csite *Csite)
{
Cdata *data = Csite->data;
int i, j, ij;
int nd = Csite->imax * (Csite->jmax + 1) + 1;
printf("zlevels: %8.2lg %8.2lg\n", Csite->zlevel[0], Csite->zlevel[1]);
printf("edge %ld, left %ld, n %ld, count %ld, edge0 %ld, left0 %ld\n",
Csite->edge, Csite->left, Csite->n, Csite->count,
Csite->edge0, Csite->left0);
printf(" level0 %d, edge00 %ld\n", Csite->level0, Csite->edge00);
printf("%04x\n", data[nd-1]);
for (j = Csite->jmax; j >= 0; j--)
{
for (i=0; i < Csite->imax; i++)
{
ij = i + j * Csite->imax;
printf("%04x ", data[ij]);
}
printf("\n");
}
printf("\n");
}
/* triangle only takes values of -1, 0, 1, so it could be a signed char. */
/* most or all of the longs probably could be converted to ints with no loss */
/* the Cdata array consists of the following bits:
* Z_VALUE (2 bits) 0, 1, or 2 function value at point
* ZONE_EX 1 zone exists, 0 zone doesn't exist
* I_BNDY this i-edge (i=constant edge) is a mesh boundary
* J_BNDY this j-edge (i=constant edge) is a mesh boundary
* I0_START this i-edge is a start point into zone to left
* I1_START this i-edge is a start point into zone to right
* J0_START this j-edge is a start point into zone below
* J1_START this j-edge is a start point into zone above
* START_ROW next start point is in current row (accelerates 2nd pass)
* SLIT_UP marks this i-edge as the beginning of a slit upstroke
* SLIT_DN marks this i-edge as the beginning of a slit downstroke
* OPEN_END marks an i-edge start point whose other endpoint is
* on a boundary for the single level case
* ALL_DONE marks final start point
*/
#define Z_VALUE 0x0003
#define ZONE_EX 0x0004
#define I_BNDY 0x0008
#define J_BNDY 0x0010
#define I0_START 0x0020
#define I1_START 0x0040
#define J0_START 0x0080
#define J1_START 0x0100
#define START_ROW 0x0200
#define SLIT_UP 0x0400
#define SLIT_DN 0x0800
#define OPEN_END 0x1000
#define ALL_DONE 0x2000
/* some helpful macros to find points relative to a given directed
* edge -- points are designated 0, 1, 2, 3 CCW around zone with 0 and
* 1 the endpoints of the current edge */
#define FORWARD(left,ix) ((left)>0?((left)>1?1:-(ix)):((left)<-1?-1:(ix)))
#define POINT0(edge,fwd) ((edge)-((fwd)>0?fwd:0))
#define POINT1(edge,fwd) ((edge)+((fwd)<0?fwd:0))
#define IS_JEDGE(edge,left) ((left)>0?((left)>1?1:0):((left)<-1?1:0))
#define ANY_START (I0_START|I1_START|J0_START|J1_START)
#define START_MARK(left) \
((left)>0?((left)>1?J1_START:I1_START):((left)<-1?J0_START:I0_START))
/* ------------------------------------------------------------------------ */
/* these actually mark points */
static int zone_crosser (Csite * site, int level, int pass2);
static int edge_walker (Csite * site, int pass2);
static int slit_cutter (Csite * site, int up, int pass2);
/* this calls the first three to trace the next disjoint curve
* -- return value is number of points on this curve, or
* 0 if there are no more curves this pass
* -(number of points) on first pass if:
* this is two level case, and the curve closed on a hole
* this is single level case, curve is open, and will start from
* a different point on the second pass
* -- in both cases, this curve will be combined with another
* on the second pass */
static long curve_tracer (Csite * site, int pass2);
/* this initializes the data array for curve_tracer */
static void data_init (Csite * site, int region, long nchunk);
/* ------------------------------------------------------------------------ */
/* zone_crosser assumes you are sitting at a cut edge about to cross
* the current zone. It always marks the initial point, crosses at
* least one zone, and marks the final point. On non-boundary i-edges,
* it is responsible for removing start markers on the first pass. */
static int
zone_crosser (Csite * site, int level, int pass2)
{
Cdata * data = site->data;
long edge = site->edge;
long left = site->left;
long n = site->n;
long fwd = FORWARD (left, site->imax);
long p0, p1;
int jedge = IS_JEDGE (edge, left);
long edge0 = site->edge0;
long left0 = site->left0;
int level0 = site->level0 == level;
int two_levels = site->zlevel[1] > site->zlevel[0];
short *triangle = site->triangle;
const double *x = pass2 ? site->x : 0;
const double *y = pass2 ? site->y : 0;
const double *z = pass2 ? site->z : 0;
double zlevel = pass2 ? site->zlevel[level] : 0.0;
double *xcp = pass2 ? site->xcp : 0;
double *ycp = pass2 ? site->ycp : 0;
int z0, z1, z2, z3;
int keep_left = 0; /* flag to try to minimize curvature in saddles */
int done = 0;
if (level)
level = 2;
for (;;)
{
/* set edge endpoints */
p0 = POINT0 (edge, fwd);
p1 = POINT1 (edge, fwd);
/* always mark cut on current edge */
if (pass2)
{
/* second pass actually computes and stores the point */
double zcp = (zlevel - z[p0]) / (z[p1] - z[p0]);
xcp[n] = zcp * (x[p1] - x[p0]) + x[p0];
ycp[n] = zcp * (y[p1] - y[p0]) + y[p0];
}
if (!done && !jedge)
{
if (n)
{
/* if this is not the first point on the curve, and we're
* not done, and this is an i-edge, check several things */
if (!two_levels && !pass2 && (data[edge] & OPEN_END))
{
/* reached an OPEN_END mark, skip the n++ */
done = 4; /* same return value 4 used below */
break;
}
/* check for curve closure -- if not, erase any start mark */
if (edge == edge0 && left == left0)
{
/* may signal closure on a downstroke */
if (level0)
done = (!pass2 && two_levels && left < 0) ? 5 : 3;
}
else if (!pass2)
{
Cdata start =
data[edge] & (fwd > 0 ? I0_START : I1_START);
if (start)
{
data[edge] &= ~start;
site->count--;
}
if (!two_levels)
{
start = data[edge] & (fwd > 0 ? I1_START : I0_START);
if (start)
{
data[edge] &= ~start;
site->count--;
}
}
}
}
}
n++;
if (done)
break;
/* cross current zone to another cut edge */
z0 = (data[p0] & Z_VALUE) != level; /* 1 if fill toward p0 */
z1 = !z0; /* know level cuts edge */
z2 = (data[p1 + left] & Z_VALUE) != level;
z3 = (data[p0 + left] & Z_VALUE) != level;
if (z0 == z2)
{
if (z1 == z3)
{
/* this is a saddle zone, need triangle to decide
* -- set triangle if not already decided for this zone */
long zone = edge + (left > 0 ? left : 0);
if (triangle)
{
if (!triangle[zone])
{
if (keep_left)
triangle[zone] = jedge ? -1 : 1;
else
triangle[zone] = jedge ? 1 : -1;
}
if (triangle[zone] > 0 ? !jedge : jedge)
goto bkwd;
}
else
{
if (keep_left)
goto bkwd;
}
}
/* bend forward (right along curve) */
keep_left = 1;
jedge = !jedge;
edge = p1 + (left > 0 ? left : 0);
{
long tmp = fwd;
fwd = -left;
left = tmp;
}
}
else if (z1 == z3)
{
bkwd:
/* bend backward (left along curve) */
keep_left = 0;
jedge = !jedge;
edge = p0 + (left > 0 ? left : 0);
{
long tmp = fwd;
fwd = left;
left = -tmp;
}
}
else
{
/* straight across to opposite edge */
edge += left;
}
/* after crossing zone, edge/left/fwd is oriented CCW relative to
* the next zone, assuming we will step there */
/* now that we've taken a step, check for the downstroke
* of a slit on the second pass (upstroke checked above)
* -- taking step first avoids a race condition */
if (pass2 && two_levels && !jedge)
{
if (left > 0)
{
if (data[edge] & SLIT_UP)
done = 6;
}
else
{
if (data[edge] & SLIT_DN)
done = 5;
}
}
if (!done)
{
/* finally, check if we are on a boundary */
if (data[edge] & (jedge ? J_BNDY : I_BNDY))
{
done = two_levels ? 2 : 4;
/* flip back into the zone that exists */
left = -left;
fwd = -fwd;
if (!pass2 && (edge != edge0 || left != left0))
{
Cdata start = data[edge] & START_MARK (left);
if (start)
{
data[edge] &= ~start;
site->count--;
}
}
}
}
}
site->edge = edge;
site->n = n;
site->left = left;
return done > 4 ? slit_cutter (site, done - 5, pass2) : done;
}
/* edge_walker assumes that the current edge is being drawn CCW
* around the current zone. Since only boundary edges are drawn
* and we always walk around with the filled region to the left,
* no edge is ever drawn CW. We attempt to advance to the next
* edge on this boundary, but if current second endpoint is not
* between the two contour levels, we exit back to zone_crosser.
* Note that we may wind up marking no points.
* -- edge_walker is never called for single level case */
static int
edge_walker (Csite * site, int pass2)
{
Cdata * data = site->data;
long edge = site->edge;
long left = site->left;
long n = site->n;
long fwd = FORWARD (left, site->imax);
long p0 = POINT0 (edge, fwd);
long p1 = POINT1 (edge, fwd);
int jedge = IS_JEDGE (edge, left);
long edge0 = site->edge0;
long left0 = site->left0;
int level0 = site->level0 == 2;
int marked;
const double *x = pass2 ? site->x : 0;
const double *y = pass2 ? site->y : 0;
double *xcp = pass2 ? site->xcp : 0;
double *ycp = pass2 ? site->ycp : 0;
int z0, z1, heads_up = 0;
for (;;)
{
/* mark endpoint 0 only if value is 1 there, and this is a
* two level task */
z0 = data[p0] & Z_VALUE;
z1 = data[p1] & Z_VALUE;
marked = 0;
if (z0 == 1)
{
/* mark current boundary point */
if (pass2)
{
xcp[n] = x[p0];
ycp[n] = y[p0];
}
marked = 1;
}
else if (!n)
{
/* if this is the first point is not between the levels
* must do the job of the zone_crosser and mark the first cut here,
* so that it will be marked again by zone_crosser as it closes */
if (pass2)
{
double zcp = site->zlevel[(z0 != 0)];
zcp = (zcp - site->z[p0]) / (site->z[p1] - site->z[p0]);
xcp[n] = zcp * (x[p1] - x[p0]) + x[p0];
ycp[n] = zcp * (y[p1] - y[p0]) + y[p0];
}
marked = 1;
}
if (n)
{
/* check for closure */
if (level0 && edge == edge0 && left == left0)
{
site->edge = edge;
site->left = left;
site->n = n + marked;
/* if the curve is closing on a hole, need to make a downslit */
if (fwd < 0 && !(data[edge] & (jedge ? J_BNDY : I_BNDY)))
return slit_cutter (site, 0, pass2);
return 3;
}
else if (pass2)
{
if (heads_up || (fwd < 0 && (data[edge] & SLIT_DN)))
{
site->edge = edge;
site->left = left;
site->n = n + marked;
return slit_cutter (site, heads_up, pass2);
}
}
else
{
/* if this is not first point, clear start mark for this edge */
Cdata start = data[edge] & START_MARK (left);
if (start)
{
data[edge] &= ~start;
site->count--;
}
}
}
if (marked)
n++;
/* if next endpoint not between levels, need to exit to zone_crosser */
if (z1 != 1)
{
site->edge = edge;
site->left = left;
site->n = n;
return (z1 != 0); /* return level closest to p1 */
}
/* step to p1 and find next edge
* -- turn left if possible, else straight, else right
* -- check for upward slit beginning at same time */
edge = p1 + (left > 0 ? left : 0);
if (pass2 && jedge && fwd > 0 && (data[edge] & SLIT_UP))
{
jedge = !jedge;
heads_up = 1;
}
else if (data[edge] & (jedge ? I_BNDY : J_BNDY))
{
long tmp = fwd;
fwd = left;
left = -tmp;
jedge = !jedge;
}
else
{
edge = p1 + (fwd > 0 ? fwd : 0);
if (pass2 && !jedge && fwd > 0 && (data[edge] & SLIT_UP))
{
heads_up = 1;
}
else if (!(data[edge] & (jedge ? J_BNDY : I_BNDY)))
{
edge = p1 - (left < 0 ? left : 0);
jedge = !jedge;
{
long tmp = fwd;
fwd = -left;
left = tmp;
}
}
}
p0 = p1;
p1 = POINT1 (edge, fwd);
}
}
/* -- slit_cutter is never called for single level case */
static int
slit_cutter (Csite * site, int up, int pass2)
{
Cdata * data = site->data;
long imax = site->imax;
long n = site->n;
const double *x = pass2 ? site->x : 0;
const double *y = pass2 ? site->y : 0;
double *xcp = pass2 ? site->xcp : 0;
double *ycp = pass2 ? site->ycp : 0;
if (up)
{
/* upward stroke of slit proceeds up left side of slit until
* it hits a boundary or a point not between the contour levels
* -- this never happens on the first pass */
long p1 = site->edge;
int z1;
for (;;)
{
z1 = data[p1] & Z_VALUE;
if (z1 != 1)
{
site->edge = p1;
site->left = -1;
site->n = n;
return (z1 != 0);
}
else if (data[p1] & J_BNDY)
{
/* this is very unusual case of closing on a mesh hole */
site->edge = p1;
site->left = -imax;
site->n = n;
return 2;
}
xcp[n] = x[p1];
ycp[n] = y[p1];
n++;
p1 += imax;
}
}
else
{
/* downward stroke proceeds down right side of slit until it
* hits a boundary or point not between the contour levels */
long p0 = site->edge;
int z0;
/* at beginning of first pass, mark first i-edge with SLIT_DN */
data[p0] |= SLIT_DN;
p0 -= imax;
for (;;)
{
z0 = data[p0] & Z_VALUE;
if (!pass2)
{
if (z0 != 1 || (data[p0] & I_BNDY) || (data[p0 + 1] & J_BNDY))
{
/* at end of first pass, mark final i-edge with SLIT_UP */
data[p0 + imax] |= SLIT_UP;
/* one extra count for splicing at outer curve */
site->n = n + 1;
return 4; /* return same special value as for OPEN_END */
}
}
else
{
if (z0 != 1)
{
site->edge = p0 + imax;
site->left = 1;
site->n = n;
return (z0 != 0);
}
else if (data[p0 + 1] & J_BNDY)
{
site->edge = p0 + 1;
site->left = imax;
site->n = n;
return 2;
}
else if (data[p0] & I_BNDY)
{
site->edge = p0;
site->left = 1;
site->n = n;
return 2;
}
}
if (pass2)
{
xcp[n] = x[p0];
ycp[n] = y[p0];
n++;
}
else
{
/* on first pass need to count for upstroke as well */
n += 2;
}
p0 -= imax;
}
}
}
/* ------------------------------------------------------------------------ */
/* curve_tracer finds the next starting point, then traces the curve,
* returning the number of points on this curve
* -- in a two level trace, the return value is negative on the
* first pass if the curve closed on a hole
* -- in a single level trace, the return value is negative on the
* first pass if the curve is an incomplete open curve
* -- a return value of 0 indicates no more curves */
static long
curve_tracer (Csite * site, int pass2)
{
Cdata * data = site->data;
long imax = site->imax;
long edge0 = site->edge0;
long left0 = site->left0;
long edge00 = site->edge00;
int two_levels = site->zlevel[1] > site->zlevel[0];
int level, level0, mark_row;
long n;
/* it is possible for a single i-edge to serve as two actual start
* points, one to the right and one to the left
* -- for the two level case, this happens on the first pass for
* a doubly cut edge, or on a chunking boundary
* -- for single level case, this is impossible, but a similar
* situation involving open curves is handled below
* a second two start possibility is when the edge0 zone does not
* exist and both the i-edge and j-edge boundaries are cut
* yet another possibility is three start points at a junction
* of chunk cuts
* -- sigh, several other rare possibilities,
* allow for general case, just go in order i1, i0, j1, j0 */
int two_starts;
/* printf("curve_tracer pass %d\n", pass2); */
/* print_Csite(site); */
if (left0 == 1)
two_starts = data[edge0] & (I0_START | J1_START | J0_START);
else if (left0 == -1)
two_starts = data[edge0] & (J1_START | J0_START);
else if (left0 == imax)
two_starts = data[edge0] & J0_START;
else
two_starts = 0;
if (pass2 || edge0 == 0)
{
/* zip up to row marked on first pass (or by data_init if edge0==0)
* -- but not for double start case */
if (!two_starts)
{
/* final start point marked by ALL_DONE marker */
int first = (edge0 == 0 && !pass2);
long e0 = edge0;
if (data[edge0] & ALL_DONE)
return 0;
while (!(data[edge0] & START_ROW))
edge0 += imax;
if (e0 == edge0)
edge0++; /* two starts handled specially */
if (first)
/* if this is the very first start point, we want to remove
* the START_ROW marker placed by data_init */
data[edge0 - edge0 % imax] &= ~START_ROW;
}
}
else
{
/* first pass ends when all potential start points visited */
if (site->count <= 0)
{
/* place ALL_DONE marker for second pass */
data[edge00] |= ALL_DONE;
/* reset initial site for second pass */
site->edge0 = site->edge00 = site->left0 = 0;
return 0;
}
if (!two_starts)
edge0++;
}
if (two_starts)
{
/* trace second curve with this start immediately */
if (left0 == 1 && (data[edge0] & I0_START))
{
left0 = -1;
level = (data[edge0] & I_BNDY) ? 2 : 0;
}
else if ((left0 == 1 || left0 == -1) && (data[edge0] & J1_START))
{
left0 = imax;
level = 2;
}
else
{
left0 = -imax;
level = 2;
}
}
else
{
/* usual case is to scan for next start marker
* -- on second pass, this is at most one row of mesh, but first
* pass hits nearly every point of the mesh, since it can't
* know in advance which potential start marks removed */
while (!(data[edge0] & ANY_START))
edge0++;
if (data[edge0] & I1_START)
left0 = 1;
else if (data[edge0] & I0_START)
left0 = -1;
else if (data[edge0] & J1_START)
left0 = imax;
else /*data[edge0]&J0_START */
left0 = -imax;
if (data[edge0] & (I1_START | I0_START))
level = (data[edge0] & I_BNDY) ? 2 : 0;
else
level = 2;
}
/* this start marker will not be unmarked, but it has been visited */
if (!pass2)
site->count--;
/* if this curve starts on a non-boundary i-edge, we need to
* determine the level */
if (!level && two_levels)
level = left0 > 0 ?
((data[edge0 - imax] & Z_VALUE) !=
0) : ((data[edge0] & Z_VALUE) != 0);
/* initialize site for this curve */
site->edge = site->edge0 = edge0;
site->left = site->left0 = left0;
site->level0 = level0 = level; /* for open curve detection only */
/* single level case just uses zone_crosser */
if (!two_levels)
level = 0;
/* to generate the curve, alternate between zone_crosser and
* edge_walker until closure or first call to edge_walker in
* single level case */
site->n = 0;
for (;;)
{
if (level < 2)
level = zone_crosser (site, level, pass2);
else if (level < 3)
level = edge_walker (site, pass2);
else
break;
}
n = site->n;
/* single level case may have ended at a boundary rather than closing
* -- need to recognize this case here in order to place the
* OPEN_END mark for zone_crosser, remove this start marker,
* and be sure not to make a START_ROW mark for this case
* two level case may close with slit_cutter, in which case start
* must also be removed and no START_ROW mark made
* -- change sign of return n to inform caller */
if (!pass2 && level > 3 && (two_levels || level0 == 0))
{
if (!two_levels)
data[edge0] |= OPEN_END;
data[edge0] &= ~(left0 > 0 ? I1_START : I0_START);
mark_row = 0; /* do not mark START_ROW */
n = -n;
}
else
{
if (two_levels)
mark_row = !two_starts;
else
mark_row = 1;
}
/* on first pass, must apply START_ROW mark in column above previous
* start marker
* -- but skip if we just did second of two start case */
if (!pass2 && mark_row)
{
data[edge0 - (edge0 - edge00) % imax] |= START_ROW;
site->edge00 = edge0;
}
return n;
}
/* ------------------------------------------------------------------------ */
/* The sole function of the "region" argument is to specify the
value in Csite.reg that denotes a missing zone. We always
use zero.
*/
static void
data_init (Csite * site, int region, long nchunk)
{
Cdata * data = site->data;
long imax = site->imax;
long jmax = site->jmax;
long ijmax = imax * jmax;
const double *z = site->z;
double zlev0 = site->zlevel[0];
double zlev1 = site->zlevel[1];
int two_levels = zlev1 > zlev0;
char *reg = site->reg;
long count = 0;
int started = 0;
int ibndy, jbndy, i_was_chunk;
long icsize = imax - 1;
long jcsize = jmax - 1;
long ichunk, jchunk, irem, jrem, i, j, ij;
if (nchunk && two_levels)
{
/* figure out chunk sizes
* -- input nchunk is square root of maximum allowed zones per chunk
* -- start points for single level case are wrong, so don't try it */
long inum = (nchunk * nchunk) / (jmax - 1);
long jnum = (nchunk * nchunk) / (imax - 1);
if (inum < nchunk)
inum = nchunk;
if (jnum < nchunk)
jnum = nchunk;
/* ijnum= actual number of chunks,
* ijrem= number of those chunks needing one more zone (ijcsize+1) */
inum = (imax - 2) / inum + 1;
icsize = (imax - 1) / inum;
irem = (imax - 1) % inum;
jnum = (jmax - 2) / jnum + 1;
jcsize = (jmax - 1) / jnum;
jrem = (jmax - 1) % jnum;
/* convert ijrem into value of i or j at which to begin adding an
* extra zone */
irem = (inum - irem) * icsize;
jrem = (jnum - jrem) * jcsize;
}
else
{
irem = imax;
jrem = jmax;
}