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
|
/*
GRAPH0.C
Define graphics related functions.
$Id$
*/
/* Copyright (c) 1994. The Regents of the University of California.
All rights reserved. */
#include "ydata.h"
extern long QuickMeshZone(double xx, double yy, double *x, double *y,
int *reg, long ix, long ijx, long i,
long *bndy, long nbndy);
extern long *BuildMeshBndy(double *x, double *y, int *reg,
long ix, long ijx, long *nbndy);
/*--------------------------------------------------------------------------*/
/* return -1 if (xx,yy) not within ix-by-jx mesh (x,y),
else 0-origin zone index -- reg==0 is allowed, and reg
need not have overreach zones
i is an initial guess, or <0 for no guess
if bndy==0, may return -1 erroniously */
long QuickMeshZone(double xx, double yy, double *x, double *y,
int *reg, long ix, long ijx, long i,
long *bndy, long nbndy)
{
/* coordinates of zone corners relative to (xx,yy) */
double xz[4], yz[4], ar[4], sn, sd;
double xr, yr;
int wind, edge, negative, bcheck;
long w= 0;
/* algorithm:
(1) let (xx,yy) be the coordinate origin
(2) compute the midpoints of the two diagonals
of the initial guess zone, and take the one
with the largest absolute value coordinate as
a reference point R
(3) walk in a straight line from R to (xx,yy) (==0)
by examining the intersections of the four zone
edges with this line
(a) examine all four edges of the initial guess
if they wind around (xx,yy), done, otherwise
take the edge which intersects 0R closest to
0 and step across into that zone
(b) examine the other three edges of the new zone
to find whether they wind around 0; if not
take another step and repeat
(4) if encounter a boundary, quit and report failure
(5) if bndy array exists, check if (xx,yy) is really
outside mesh -- if inside, repeat search starting
from boundary zone with closest edge intersection
of x=xx to (xx,yy)
*/
if (i<0) goto check;
bcheck= 0;
start:
/* find corners of first zone */
xz[0]= x[i-ix-1]-xx; yz[0]= y[i-ix-1]-yy;
xz[1]= x[i-ix]-xx; yz[1]= y[i-ix]-yy;
xz[2]= x[i]-xx; yz[2]= y[i]-yy;
xz[3]= x[i-1]-xx; yz[3]= y[i-1]-yy;
if (!bcheck) {
/* compute midpoint of 02 diagonal */
xr= 0.5*(xz[0]+xz[2]);
yr= 0.5*(yz[0]+yz[2]);
/* use 13 diagonal midpoint if that is further from (xx,yy) */
{
double t1= xr<0.? -xr : xr;
double t2= yr<0.? -yr : yr;
double t3= 0.5*(xz[1]+xz[3]);
double t4= 0.5*(yz[1]+yz[3]);
if (t2>t1) t1= t2;
t2= t3<0.? -t3 : t3;
if (t4<0.? (-t4>t2) : (t4>t2)) t2= t4;
if (t2 > t1) {
xr= t3;
yr= t4;
}
}
/* allow for pathological case of (xx,yy) precisely at the
center of a perfect parallelogram */
if (xr==0.0 && yr==0.0) return i;
}
/* compute the first four areas */
ar[0]= xz[0]*yr - xr*yz[0];
ar[1]= xz[1]*yr - xr*yz[1];
ar[2]= xz[2]*yr - xr*yz[2];
ar[3]= xz[3]*yr - xr*yz[3];
/* compute winding number for any crossed edge
and edge number of intersection nearest (xx,yy) */
wind= 0;
negative= ar[0]<0.;
if ((ar[1]<0.)!=negative) {
sn= xz[0]*yz[1] - xz[1]*yz[0];
if (sn > 0.) { wind++; edge= 0; }
else { wind--; sn= -sn; edge= 4; }
sd= ar[0] - ar[1];
if (negative) sd= -sd;
negative= !negative;
} else {
sn= 1.0;
sd= 0.0;
edge= 8;
}
if ((ar[2]<0.)!=negative) {
double sn0= xz[1]*yz[2] - xz[2]*yz[1];
double sd0= ar[1] - ar[2];
int plus= sn0 > 0.;
if (plus) wind++;
else { wind--; sn0= -sn0; }
if (negative) sd0= -sd0;
negative= !negative;
if (sn0*sd<sn*sd0) {
sn= sn0;
sd= sd0;
edge= plus? 1 : 5;
}
}
if ((ar[3]<0.)!=negative) {
double sn0= xz[2]*yz[3] - xz[3]*yz[2];
double sd0= ar[2] - ar[3];
int plus= sn0 > 0.;
if (plus) wind++;
else { wind--; sn0= -sn0; }
if (negative) sd0= -sd0;
negative= !negative;
if (sn0*sd<sn*sd0) {
sn= sn0;
sd= sd0;
edge= plus? 2 : 6;
}
}
if ((ar[0]<0.)!=negative) {
double sn0= xz[3]*yz[0] - xz[0]*yz[3];
double sd0= ar[3] - ar[0];
int plus= sn0 > 0.;
if (plus) wind++;
else { wind--; sn0= -sn0; }
if (negative) sd0= -sd0;
if (sn0*sd<sn*sd0) {
sn= sn0;
sd= sd0;
edge= plus? 3 : 7;
}
}
for (;;) {
/* quit if we're lost */
if (edge&8) break;
/* quit if we have a winding number */
if (wind) return i;
/* set winding number for edge we just crossed */
if (edge&4) {
/* decremented wind on other side, increment here */
wind++;
edge-= 4;
} else {
/* incremented wind on other side, decrement here */
wind--;
}
/* move into the new zone and find exit edge
-- one case for each of the four possible edges */
if (edge==0) {
i-= ix;
if (i<=ix || (reg && !reg[i])) break;
xz[2]= xz[1]; yz[2]= yz[1];
xz[3]= xz[0]; yz[3]= yz[0];
xz[0]= x[i-ix-1]-xx; yz[0]= y[i-ix-1]-yy;
xz[1]= x[i-ix]-xx; yz[1]= y[i-ix]-yy;
ar[2]= ar[1];
ar[3]= ar[0];
ar[0]= xz[0]*yr - xr*yz[0];
ar[1]= xz[1]*yr - xr*yz[1];
negative= ar[0]<0.;
if ((ar[1]<0.)!=negative) {
sn= xz[0]*yz[1] - xz[1]*yz[0];
if (sn > 0.) { wind++; edge= 0; }
else { wind--; sn= -sn; edge= 4; }
sd= ar[0] - ar[1];
if (negative) sd= -sd;
negative= !negative;
} else {
edge= 8;
}
if ((ar[2]<0.)!=negative) {
double sn0= xz[1]*yz[2] - xz[2]*yz[1];
double sd0= ar[1] - ar[2];
int plus= sn0 > 0.;
if (plus) wind++;
else { wind--; sn0= -sn0; }
if (negative) sd0= -sd0;
negative= !negative;
if ((edge&8) || sn0*sd<sn*sd0) {
sn= sn0;
sd= sd0;
edge= plus? 1 : 5;
}
}
negative= !negative; /* we know we crossed edge 2 */
if ((ar[0]<0.)!=negative) {
double sn0= xz[3]*yz[0] - xz[0]*yz[3];
double sd0= ar[3] - ar[0];
int plus= sn0 > 0.;
if (plus) wind++;
else { wind--; sn0= -sn0; }
if (negative) sd0= -sd0;
if ((edge&8) || sn0*sd<sn*sd0) {
sn= sn0;
sd= sd0;
edge= plus? 3 : 7;
}
}
} else if (edge==1) {
i+= 1;
if (!(i%ix) || (reg && !reg[i])) break;
xz[0]= xz[1]; yz[0]= yz[1];
xz[3]= xz[2]; yz[3]= yz[2];
xz[1]= x[i-ix]-xx; yz[1]= y[i-ix]-yy;
xz[2]= x[i]-xx; yz[2]= y[i]-yy;
ar[0]= ar[1];
ar[3]= ar[2];
ar[1]= xz[1]*yr - xr*yz[1];
ar[2]= xz[2]*yr - xr*yz[2];
negative= ar[0]<0.;
if ((ar[1]<0.)!=negative) {
sn= xz[0]*yz[1] - xz[1]*yz[0];
if (sn > 0.) { wind++; edge= 0; }
else { wind--; sn= -sn; edge= 4; }
sd= ar[0] - ar[1];
if (negative) sd= -sd;
negative= !negative;
} else {
edge= 8;
}
if ((ar[2]<0.)!=negative) {
double sn0= xz[1]*yz[2] - xz[2]*yz[1];
double sd0= ar[1] - ar[2];
int plus= sn0 > 0.;
if (plus) wind++;
else { wind--; sn0= -sn0; }
if (negative) sd0= -sd0;
negative= !negative;
if ((edge&8) || sn0*sd<sn*sd0) {
sn= sn0;
sd= sd0;
edge= plus? 1 : 5;
}
}
if ((ar[3]<0.)!=negative) {
double sn0= xz[2]*yz[3] - xz[3]*yz[2];
double sd0= ar[2] - ar[3];
int plus= sn0 > 0.;
if (plus) wind++;
else { wind--; sn0= -sn0; }
if (negative) sd0= -sd0;
if ((edge&8) || sn0*sd<sn*sd0) {
sn= sn0;
sd= sd0;
edge= plus? 2 : 6;
}
}
} else if (edge==2) {
i+= ix;
if (i>=ijx || (reg && !reg[i])) break;
xz[0]= xz[3]; yz[0]= yz[3];
xz[1]= xz[2]; yz[1]= yz[2];
xz[2]= x[i]-xx; yz[2]= y[i]-yy;
xz[3]= x[i-1]-xx; yz[3]= y[i-1]-yy;
ar[0]= ar[3];
ar[1]= ar[2];
ar[2]= xz[2]*yr - xr*yz[2];
ar[3]= xz[3]*yr - xr*yz[3];
negative= ar[1]<0.;
if ((ar[2]<0.)!=negative) {
sn= xz[1]*yz[2] - xz[2]*yz[1];
if (sn > 0.) { wind++; edge= 1; }
else { wind--; sn= -sn; edge= 5; }
sd= ar[1] - ar[2];
if (negative) sd= -sd;
negative= !negative;
} else {
edge= 8;
}
if ((ar[3]<0.)!=negative) {
double sn0= xz[2]*yz[3] - xz[3]*yz[2];
double sd0= ar[2] - ar[3];
int plus= sn0 > 0.;
if (plus) wind++;
else { wind--; sn0= -sn0; }
if (negative) sd0= -sd0;
negative= !negative;
if ((edge&8) || sn0*sd<sn*sd0) {
sn= sn0;
sd= sd0;
edge= plus? 2 : 6;
}
}
if ((ar[0]<0.)!=negative) {
double sn0= xz[3]*yz[0] - xz[0]*yz[3];
double sd0= ar[3] - ar[0];
int plus= sn0 > 0.;
if (plus) wind++;
else { wind--; sn0= -sn0; }
if (negative) sd0= -sd0;
if ((edge&8) || sn0*sd<sn*sd0) {
sn= sn0;
sd= sd0;
edge= plus? 3 : 7;
}
}
} else if (edge==3) {
i-= 1;
if (!(i%ix) || (reg && !reg[i])) break;
xz[1]= xz[0]; yz[1]= yz[0];
xz[2]= xz[3]; yz[2]= yz[3];
xz[0]= x[i-ix-1]-xx; yz[0]= y[i-ix-1]-yy;
xz[3]= x[i-1]-xx; yz[3]= y[i-1]-yy;
ar[1]= ar[0];
ar[2]= ar[3];
ar[0]= xz[0]*yr - xr*yz[0];
ar[3]= xz[3]*yr - xr*yz[3];
negative= ar[0]<0.;
if ((ar[1]<0.)!=negative) {
sn= xz[0]*yz[1] - xz[1]*yz[0];
if (sn > 0.) { wind++; edge= 0; }
else { wind--; sn= -sn; edge= 4; }
sd= ar[0] - ar[1];
if (negative) sd= -sd;
negative= !negative;
} else {
edge= 8;
}
negative= !negative; /* we know we crossed edge 1 */
if ((ar[3]<0.)!=negative) {
double sn0= xz[2]*yz[3] - xz[3]*yz[2];
double sd0= ar[2] - ar[3];
int plus= sn0 > 0.;
if (plus) wind++;
else { wind--; sn0= -sn0; }
if (negative) sd0= -sd0;
negative= !negative;
if ((edge&8) || sn0*sd<sn*sd0) {
sn= sn0;
sd= sd0;
edge= plus? 2 : 6;
}
}
if ((ar[0]<0.)!=negative) {
double sn0= xz[3]*yz[0] - xz[0]*yz[3];
double sd0= ar[3] - ar[0];
int plus= sn0 > 0.;
if (plus) wind++;
else { wind--; sn0= -sn0; }
if (negative) sd0= -sd0;
if ((edge&8) || sn0*sd<sn*sd0) {
sn= sn0;
sd= sd0;
edge= plus? 3 : 7;
}
}
}
}
/* if we have a boundary array, we can figure out whether we are
really outside the mesh or if we just need to try harder */
check:
if (!w && bndy) {
long imin= nbndy;
double cross, den= 0.;
for (i=0 ; i<nbndy ; i+=2) {
xz[0]= x[bndy[i]] - xx;
xz[1]= x[bndy[i+1]] - xx;
if ((xz[0]<0.)==(xz[1]<0.)) continue;
yz[0]= y[bndy[i]] - yy;
yz[1]= y[bndy[i+1]] - yy;
cross= xz[0]*yz[1] - xz[1]*yz[0];
if (cross > 0.) w++;
else { w--; cross= -cross; }
den= xz[0] - xz[1];
if (xz[0]<0.) den= -den;
if (imin==nbndy || sn*den>sd*cross) {
/* keep track of x=xx boundary crossing nearest to (xx,yy) */
imin= i;
sn= cross;
sd= den;
}
}
if (w) {
/* (xx,yy) is inside the mesh -- start over
from boundary intersection closest to (xx,yy) this time */
long j= bndy[imin+1];
i= bndy[imin];
yr= y[i] + (xx-x[i])/(x[j]-x[i]);
xr= 0.0;
if (i+1 == j) i= j+ix;
else if (i+ix == j) i= j;
else if (i-ix == j) i= i+1;
bcheck= 1;
goto start;
}
}
return -1;
}
/*--------------------------------------------------------------------------*/
long *BuildMeshBndy(double *x, double *y, int *reg,
long ix, long ijx, long *nbndy)
{
Array *barray;
long *bndy;
long i, j, jx= ijx/ix;
long nedges;
if (!reg) {
nedges= 2*(ix+jx) - 4;
} else {
long i0= 0;
nedges= 0;
/* loop over zones */
for (i=ix+1 ; i<ijx ; i++) {
if ((++i0)==ix) { i0= 1; i++; }
/* check if j=lower edge of zone is a boundary */
if ((reg[i-ix]!=0)!=(reg[i]!=0)) nedges++;
/* check if i=lower edge of zone is a boundary */
if ((reg[i-1]!=0)!=(reg[i]!=0)) nedges++;
}
/* check i=upper edge of whole mesh */
for (i=2*ix-1 ; i<ijx ; i+=ix) if (reg[i]!=0) nedges++;
/* check j=upper edge of whole mesh */
for (i=ijx-ix+1 ; i<ijx ; i++) if (reg[i]!=0) nedges++;
}
/* allocate workspace on stack to hold endpoint indices of the
boundary segments */
CheckStack(1);
nedges*= 2;
barray=
PushDataBlock(NewArray(&longStruct,
NewDimension(nedges, 1L, (Dimension *)0)));
bndy= barray->value.l;
*nbndy= nedges;
j= 0;
if (!reg) {
/* walk boundary with mesh to left */
for (i=0 ; i<ix-1 ; i++) {
bndy[j++]= i;
bndy[j++]= i+1;
}
for (i=ix-1 ; i<ijx-ix ; i+=ix) {
bndy[j++]= i;
bndy[j++]= i+ix;
}
for (i=ijx-1 ; i>ijx-ix ; i--) {
bndy[j++]= i;
bndy[j++]= i-1;
}
for (i=ijx-ix ; i>0 ; i-=ix) {
bndy[j++]= i;
bndy[j++]= i-ix;
}
} else {
long i0= 0;
/* loop over zones */
for (i=ix+1 ; i<ijx ; i++) {
if ((++i0)==ix) { i0= 1; i++; }
/* check if j=lower edge of zone is a boundary */
if ((reg[i-ix]!=0)!=(reg[i]!=0)) {
if (reg[i]) {
bndy[j++]= i-ix-1;
bndy[j++]= i-ix;
} else {
bndy[j++]= i-ix;
bndy[j++]= i-ix-1;
}
}
/* check if i=lower edge of zone is a boundary */
if ((reg[i-1]!=0)!=(reg[i]!=0)) {
if (reg[i]) {
bndy[j++]= i-1;
bndy[j++]= i-1-ix;
} else {
bndy[j++]= i-1-ix;
bndy[j++]= i-1;
}
}
}
/* check i=upper edge of whole mesh */
for (i=2*ix-1 ; i<ijx ; i+=ix) if (reg[i]!=0) {
bndy[j++]= i-ix;
bndy[j++]= i;
}
/* check j=upper edge of whole mesh */
for (i=ijx-ix+1 ; i<ijx ; i++) if (reg[i]!=0) {
bndy[j++]= i;
bndy[j++]= i-1;
}
}
return bndy;
}
/*--------------------------------------------------------------------------*/
|
