1 |
/* Copyright (c) 1998 Silicon Graphics, Inc. */ |
2 |
|
3 |
#ifndef lint |
4 |
static char SCCSid[] = "$SunId$ SGI"; |
5 |
#endif |
6 |
|
7 |
/* |
8 |
* sm_geom.c |
9 |
*/ |
10 |
|
11 |
#include "standard.h" |
12 |
#include "sm_geom.h" |
13 |
|
14 |
tri_centroid(v0,v1,v2,c) |
15 |
FVECT v0,v1,v2,c; |
16 |
{ |
17 |
/* Average three triangle vertices to give centroid: return in c */ |
18 |
c[0] = (v0[0] + v1[0] + v2[0])/3.0; |
19 |
c[1] = (v0[1] + v1[1] + v2[1])/3.0; |
20 |
c[2] = (v0[2] + v1[2] + v2[2])/3.0; |
21 |
} |
22 |
|
23 |
|
24 |
int |
25 |
vec3_equal(v1,v2) |
26 |
FVECT v1,v2; |
27 |
{ |
28 |
return(EQUAL(v1[0],v2[0]) && EQUAL(v1[1],v2[1])&& EQUAL(v1[2],v2[2])); |
29 |
} |
30 |
|
31 |
|
32 |
int |
33 |
convex_angle(v0,v1,v2) |
34 |
FVECT v0,v1,v2; |
35 |
{ |
36 |
FVECT cp01,cp12,cp; |
37 |
|
38 |
/* test sign of (v0Xv1)X(v1Xv2). v1 */ |
39 |
VCROSS(cp01,v0,v1); |
40 |
VCROSS(cp12,v1,v2); |
41 |
VCROSS(cp,cp01,cp12); |
42 |
if(DOT(cp,v1) < 0) |
43 |
return(FALSE); |
44 |
return(TRUE); |
45 |
} |
46 |
|
47 |
/* calculates the normal of a face contour using Newell's formula. e |
48 |
|
49 |
a = SUMi (yi - yi+1)(zi + zi+1) |
50 |
b = SUMi (zi - zi+1)(xi + xi+1) |
51 |
c = SUMi (xi - xi+1)(yi + yi+1) |
52 |
*/ |
53 |
double |
54 |
tri_normal(v0,v1,v2,n,norm) |
55 |
FVECT v0,v1,v2,n; |
56 |
char norm; |
57 |
{ |
58 |
double mag; |
59 |
|
60 |
n[0] = (v0[2] + v1[2]) * (v0[1] - v1[1]) + |
61 |
(v1[2] + v2[2]) * (v1[1] - v2[1]) + |
62 |
(v2[2] + v0[2]) * (v2[1] - v0[1]); |
63 |
|
64 |
n[1] = (v0[2] - v1[2]) * (v0[0] + v1[0]) + |
65 |
(v1[2] - v2[2]) * (v1[0] + v2[0]) + |
66 |
(v2[2] - v0[2]) * (v2[0] + v0[0]); |
67 |
|
68 |
|
69 |
n[2] = (v0[1] + v1[1]) * (v0[0] - v1[0]) + |
70 |
(v1[1] + v2[1]) * (v1[0] - v2[0]) + |
71 |
(v2[1] + v0[1]) * (v2[0] - v0[0]); |
72 |
|
73 |
if(!norm) |
74 |
return(0); |
75 |
|
76 |
|
77 |
mag = normalize(n); |
78 |
|
79 |
return(mag); |
80 |
} |
81 |
|
82 |
|
83 |
tri_plane_equation(v0,v1,v2,n,nd,norm) |
84 |
FVECT v0,v1,v2,n; |
85 |
double *nd; |
86 |
char norm; |
87 |
{ |
88 |
tri_normal(v0,v1,v2,n,norm); |
89 |
|
90 |
*nd = -(DOT(n,v0)); |
91 |
} |
92 |
|
93 |
int |
94 |
point_relative_to_plane(p,n,nd) |
95 |
FVECT p,n; |
96 |
double nd; |
97 |
{ |
98 |
double d; |
99 |
|
100 |
d = p[0]*n[0] + p[1]*n[1] + p[2]*n[2] + nd; |
101 |
if(d < 0) |
102 |
return(-1); |
103 |
if(ZERO(d)) |
104 |
return(0); |
105 |
else |
106 |
return(1); |
107 |
} |
108 |
|
109 |
/* From quad_edge-code */ |
110 |
int |
111 |
point_in_circle_thru_origin(p,p0,p1) |
112 |
FVECT p; |
113 |
FVECT p0,p1; |
114 |
{ |
115 |
|
116 |
double dp0,dp1; |
117 |
double dp,det; |
118 |
|
119 |
dp0 = DOT_VEC2(p0,p0); |
120 |
dp1 = DOT_VEC2(p1,p1); |
121 |
dp = DOT_VEC2(p,p); |
122 |
|
123 |
det = -dp0*CROSS_VEC2(p1,p) + dp1*CROSS_VEC2(p0,p) - dp*CROSS_VEC2(p0,p1); |
124 |
|
125 |
return (det > 0); |
126 |
} |
127 |
|
128 |
|
129 |
|
130 |
point_on_sphere(ps,p,c) |
131 |
FVECT ps,p,c; |
132 |
{ |
133 |
VSUB(ps,p,c); |
134 |
normalize(ps); |
135 |
} |
136 |
|
137 |
|
138 |
int |
139 |
intersect_vector_plane(v,plane_n,plane_d,pd,r) |
140 |
FVECT v,plane_n; |
141 |
double plane_d; |
142 |
double *pd; |
143 |
FVECT r; |
144 |
{ |
145 |
double t; |
146 |
int hit; |
147 |
/* |
148 |
Plane is Ax + By + Cz +D = 0: |
149 |
plane[0] = A,plane[1] = B,plane[2] = C,plane[3] = D |
150 |
*/ |
151 |
|
152 |
/* line is l = p1 + (p2-p1)t, p1=origin */ |
153 |
|
154 |
/* Solve for t: */ |
155 |
t = plane_d/-(DOT(plane_n,v)); |
156 |
if(t >0 || ZERO(t)) |
157 |
hit = 1; |
158 |
else |
159 |
hit = 0; |
160 |
r[0] = v[0]*t; |
161 |
r[1] = v[1]*t; |
162 |
r[2] = v[2]*t; |
163 |
if(pd) |
164 |
*pd = t; |
165 |
return(hit); |
166 |
} |
167 |
|
168 |
int |
169 |
intersect_ray_plane(orig,dir,plane_n,plane_d,pd,r) |
170 |
FVECT orig,dir; |
171 |
FVECT plane_n; |
172 |
double plane_d; |
173 |
double *pd; |
174 |
FVECT r; |
175 |
{ |
176 |
double t; |
177 |
int hit; |
178 |
/* |
179 |
Plane is Ax + By + Cz +D = 0: |
180 |
plane[0] = A,plane[1] = B,plane[2] = C,plane[3] = D |
181 |
*/ |
182 |
/* A(orig[0] + dxt) + B(orig[1] + dyt) + C(orig[2] + dzt) + pd = 0 */ |
183 |
/* t = -(DOT(plane_n,orig)+ plane_d)/(DOT(plane_n,d)) |
184 |
/* line is l = p1 + (p2-p1)t */ |
185 |
/* Solve for t: */ |
186 |
t = -(DOT(plane_n,orig) + plane_d)/(DOT(plane_n,dir)); |
187 |
if(ZERO(t) || t >0) |
188 |
hit = 1; |
189 |
else |
190 |
hit = 0; |
191 |
|
192 |
VSUM(r,orig,dir,t); |
193 |
|
194 |
if(pd) |
195 |
*pd = t; |
196 |
return(hit); |
197 |
} |
198 |
|
199 |
|
200 |
int |
201 |
point_in_cone(p,p0,p1,p2) |
202 |
FVECT p; |
203 |
FVECT p0,p1,p2; |
204 |
{ |
205 |
FVECT n; |
206 |
FVECT np,x_axis,y_axis; |
207 |
double d1,d2,d; |
208 |
|
209 |
/* Find the equation of the circle defined by the intersection |
210 |
of the cone with the plane defined by p1,p2,p3- project p into |
211 |
that plane and do an in-circle test in the plane |
212 |
*/ |
213 |
|
214 |
/* find the equation of the plane defined by p1-p3 */ |
215 |
tri_plane_equation(p0,p1,p2,n,&d,FALSE); |
216 |
|
217 |
/* define a coordinate system on the plane: the x axis is in |
218 |
the direction of np2-np1, and the y axis is calculated from |
219 |
n cross x-axis |
220 |
*/ |
221 |
/* Project p onto the plane */ |
222 |
if(!intersect_vector_plane(p,n,d,NULL,np)) |
223 |
return(FALSE); |
224 |
|
225 |
/* create coordinate system on plane: p2-p1 defines the x_axis*/ |
226 |
VSUB(x_axis,p1,p0); |
227 |
normalize(x_axis); |
228 |
/* The y axis is */ |
229 |
VCROSS(y_axis,n,x_axis); |
230 |
normalize(y_axis); |
231 |
|
232 |
VSUB(p1,p1,p0); |
233 |
VSUB(p2,p2,p0); |
234 |
VSUB(np,np,p0); |
235 |
|
236 |
p1[0] = VLEN(p1); |
237 |
p1[1] = 0; |
238 |
|
239 |
d1 = DOT(p2,x_axis); |
240 |
d2 = DOT(p2,y_axis); |
241 |
p2[0] = d1; |
242 |
p2[1] = d2; |
243 |
|
244 |
d1 = DOT(np,x_axis); |
245 |
d2 = DOT(np,y_axis); |
246 |
np[0] = d1; |
247 |
np[1] = d2; |
248 |
|
249 |
/* perform the in-circle test in the new coordinate system */ |
250 |
return(point_in_circle_thru_origin(np,p1,p2)); |
251 |
} |
252 |
|
253 |
int |
254 |
test_point_against_spherical_tri(v0,v1,v2,p,n,nset,which,sides) |
255 |
FVECT v0,v1,v2,p; |
256 |
FVECT n[3]; |
257 |
char *nset; |
258 |
char *which; |
259 |
char sides[3]; |
260 |
|
261 |
{ |
262 |
float d; |
263 |
|
264 |
/* Find the normal to the triangle ORIGIN:v0:v1 */ |
265 |
if(!NTH_BIT(*nset,0)) |
266 |
{ |
267 |
VCROSS(n[0],v1,v0); |
268 |
SET_NTH_BIT(*nset,0); |
269 |
} |
270 |
/* Test the point for sidedness */ |
271 |
d = DOT(n[0],p); |
272 |
|
273 |
if(ZERO(d)) |
274 |
sides[0] = GT_EDGE; |
275 |
else |
276 |
if(d > 0) |
277 |
{ |
278 |
sides[0] = GT_OUT; |
279 |
sides[1] = sides[2] = GT_INVALID; |
280 |
return(FALSE); |
281 |
} |
282 |
else |
283 |
sides[0] = GT_INTERIOR; |
284 |
|
285 |
/* Test next edge */ |
286 |
if(!NTH_BIT(*nset,1)) |
287 |
{ |
288 |
VCROSS(n[1],v2,v1); |
289 |
SET_NTH_BIT(*nset,1); |
290 |
} |
291 |
/* Test the point for sidedness */ |
292 |
d = DOT(n[1],p); |
293 |
if(ZERO(d)) |
294 |
{ |
295 |
sides[1] = GT_EDGE; |
296 |
/* If on plane 0-and on plane 1: lies on edge */ |
297 |
if(sides[0] == GT_EDGE) |
298 |
{ |
299 |
*which = 1; |
300 |
sides[2] = GT_INVALID; |
301 |
return(GT_EDGE); |
302 |
} |
303 |
} |
304 |
else if(d > 0) |
305 |
{ |
306 |
sides[1] = GT_OUT; |
307 |
sides[2] = GT_INVALID; |
308 |
return(FALSE); |
309 |
} |
310 |
else |
311 |
sides[1] = GT_INTERIOR; |
312 |
/* Test next edge */ |
313 |
if(!NTH_BIT(*nset,2)) |
314 |
{ |
315 |
|
316 |
VCROSS(n[2],v0,v2); |
317 |
SET_NTH_BIT(*nset,2); |
318 |
} |
319 |
/* Test the point for sidedness */ |
320 |
d = DOT(n[2],p); |
321 |
if(ZERO(d)) |
322 |
{ |
323 |
sides[2] = GT_EDGE; |
324 |
|
325 |
/* If on plane 0 and 2: lies on edge 0*/ |
326 |
if(sides[0] == GT_EDGE) |
327 |
{ |
328 |
*which = 0; |
329 |
return(GT_EDGE); |
330 |
} |
331 |
/* If on plane 1 and 2: lies on edge 2*/ |
332 |
if(sides[1] == GT_EDGE) |
333 |
{ |
334 |
*which = 2; |
335 |
return(GT_EDGE); |
336 |
} |
337 |
/* otherwise: on face 2 */ |
338 |
else |
339 |
{ |
340 |
*which = 2; |
341 |
return(GT_FACE); |
342 |
} |
343 |
} |
344 |
else if(d > 0) |
345 |
{ |
346 |
sides[2] = GT_OUT; |
347 |
return(FALSE); |
348 |
} |
349 |
/* If on edge */ |
350 |
else |
351 |
sides[2] = GT_INTERIOR; |
352 |
|
353 |
/* If on plane 0 only: on face 0 */ |
354 |
if(sides[0] == GT_EDGE) |
355 |
{ |
356 |
*which = 0; |
357 |
return(GT_FACE); |
358 |
} |
359 |
/* If on plane 1 only: on face 1 */ |
360 |
if(sides[1] == GT_EDGE) |
361 |
{ |
362 |
*which = 1; |
363 |
return(GT_FACE); |
364 |
} |
365 |
/* Must be interior to the pyramid */ |
366 |
return(GT_INTERIOR); |
367 |
} |
368 |
|
369 |
|
370 |
|
371 |
|
372 |
int |
373 |
test_single_point_against_spherical_tri(v0,v1,v2,p,which) |
374 |
FVECT v0,v1,v2,p; |
375 |
char *which; |
376 |
{ |
377 |
float d; |
378 |
FVECT n; |
379 |
char sides[3]; |
380 |
|
381 |
/* First test if point coincides with any of the vertices */ |
382 |
if(EQUAL_VEC3(p,v0)) |
383 |
{ |
384 |
*which = 0; |
385 |
return(GT_VERTEX); |
386 |
} |
387 |
if(EQUAL_VEC3(p,v1)) |
388 |
{ |
389 |
*which = 1; |
390 |
return(GT_VERTEX); |
391 |
} |
392 |
if(EQUAL_VEC3(p,v2)) |
393 |
{ |
394 |
*which = 2; |
395 |
return(GT_VERTEX); |
396 |
} |
397 |
VCROSS(n,v1,v0); |
398 |
/* Test the point for sidedness */ |
399 |
d = DOT(n,p); |
400 |
if(ZERO(d)) |
401 |
sides[0] = GT_EDGE; |
402 |
else |
403 |
if(d > 0) |
404 |
return(FALSE); |
405 |
else |
406 |
sides[0] = GT_INTERIOR; |
407 |
/* Test next edge */ |
408 |
VCROSS(n,v2,v1); |
409 |
/* Test the point for sidedness */ |
410 |
d = DOT(n,p); |
411 |
if(ZERO(d)) |
412 |
{ |
413 |
sides[1] = GT_EDGE; |
414 |
/* If on plane 0-and on plane 1: lies on edge */ |
415 |
if(sides[0] == GT_EDGE) |
416 |
{ |
417 |
*which = 1; |
418 |
return(GT_VERTEX); |
419 |
} |
420 |
} |
421 |
else if(d > 0) |
422 |
return(FALSE); |
423 |
else |
424 |
sides[1] = GT_INTERIOR; |
425 |
|
426 |
/* Test next edge */ |
427 |
VCROSS(n,v0,v2); |
428 |
/* Test the point for sidedness */ |
429 |
d = DOT(n,p); |
430 |
if(ZERO(d)) |
431 |
{ |
432 |
sides[2] = GT_EDGE; |
433 |
|
434 |
/* If on plane 0 and 2: lies on edge 0*/ |
435 |
if(sides[0] == GT_EDGE) |
436 |
{ |
437 |
*which = 0; |
438 |
return(GT_VERTEX); |
439 |
} |
440 |
/* If on plane 1 and 2: lies on edge 2*/ |
441 |
if(sides[1] == GT_EDGE) |
442 |
{ |
443 |
*which = 2; |
444 |
return(GT_VERTEX); |
445 |
} |
446 |
/* otherwise: on face 2 */ |
447 |
else |
448 |
{ |
449 |
return(GT_FACE); |
450 |
} |
451 |
} |
452 |
else if(d > 0) |
453 |
return(FALSE); |
454 |
/* Must be interior to the pyramid */ |
455 |
return(GT_FACE); |
456 |
} |
457 |
|
458 |
int |
459 |
test_vertices_for_tri_inclusion(t0,t1,t2,p0,p1,p2,nset,n,avg,pt_sides) |
460 |
FVECT t0,t1,t2,p0,p1,p2; |
461 |
char *nset; |
462 |
FVECT n[3]; |
463 |
FVECT avg; |
464 |
char pt_sides[3][3]; |
465 |
|
466 |
{ |
467 |
char below_plane[3],on_edge,test; |
468 |
char which; |
469 |
|
470 |
SUM_3VEC3(avg,t0,t1,t2); |
471 |
on_edge = 0; |
472 |
*nset = 0; |
473 |
/* Test vertex v[i] against triangle j*/ |
474 |
/* Check if v[i] lies below plane defined by avg of 3 vectors |
475 |
defining triangle |
476 |
*/ |
477 |
|
478 |
/* test point 0 */ |
479 |
if(DOT(avg,p0) < 0) |
480 |
below_plane[0] = 1; |
481 |
else |
482 |
below_plane[0]=0; |
483 |
/* Test if b[i] lies in or on triangle a */ |
484 |
test = test_point_against_spherical_tri(t0,t1,t2,p0, |
485 |
n,nset,&which,pt_sides[0]); |
486 |
/* If pts[i] is interior: done */ |
487 |
if(!below_plane[0]) |
488 |
{ |
489 |
if(test == GT_INTERIOR) |
490 |
return(TRUE); |
491 |
/* Remember if b[i] fell on one of the 3 defining planes */ |
492 |
if(test) |
493 |
on_edge++; |
494 |
} |
495 |
/* Now test point 1*/ |
496 |
|
497 |
if(DOT(avg,p1) < 0) |
498 |
below_plane[1] = 1; |
499 |
else |
500 |
below_plane[1]=0; |
501 |
/* Test if b[i] lies in or on triangle a */ |
502 |
test = test_point_against_spherical_tri(t0,t1,t2,p1, |
503 |
n,nset,&which,pt_sides[1]); |
504 |
/* If pts[i] is interior: done */ |
505 |
if(!below_plane[1]) |
506 |
{ |
507 |
if(test == GT_INTERIOR) |
508 |
return(TRUE); |
509 |
/* Remember if b[i] fell on one of the 3 defining planes */ |
510 |
if(test) |
511 |
on_edge++; |
512 |
} |
513 |
|
514 |
/* Now test point 2 */ |
515 |
if(DOT(avg,p2) < 0) |
516 |
below_plane[2] = 1; |
517 |
else |
518 |
below_plane[2]=0; |
519 |
/* Test if b[i] lies in or on triangle a */ |
520 |
test = test_point_against_spherical_tri(t0,t1,t2,p2, |
521 |
n,nset,&which,pt_sides[2]); |
522 |
|
523 |
/* If pts[i] is interior: done */ |
524 |
if(!below_plane[2]) |
525 |
{ |
526 |
if(test == GT_INTERIOR) |
527 |
return(TRUE); |
528 |
/* Remember if b[i] fell on one of the 3 defining planes */ |
529 |
if(test) |
530 |
on_edge++; |
531 |
} |
532 |
|
533 |
/* If all three points below separating plane: trivial reject */ |
534 |
if(below_plane[0] && below_plane[1] && below_plane[2]) |
535 |
return(FALSE); |
536 |
/* Accept if all points lie on a triangle vertex/edge edge- accept*/ |
537 |
if(on_edge == 3) |
538 |
return(TRUE); |
539 |
/* Now check vertices in a against triangle b */ |
540 |
return(FALSE); |
541 |
} |
542 |
|
543 |
|
544 |
set_sidedness_tests(t0,t1,t2,p0,p1,p2,test,sides,nset,n) |
545 |
FVECT t0,t1,t2,p0,p1,p2; |
546 |
char test[3]; |
547 |
char sides[3][3]; |
548 |
char nset; |
549 |
FVECT n[3]; |
550 |
{ |
551 |
char t; |
552 |
double d; |
553 |
|
554 |
|
555 |
/* p=0 */ |
556 |
test[0] = 0; |
557 |
if(sides[0][0] == GT_INVALID) |
558 |
{ |
559 |
if(!NTH_BIT(nset,0)) |
560 |
VCROSS(n[0],t1,t0); |
561 |
/* Test the point for sidedness */ |
562 |
d = DOT(n[0],p0); |
563 |
if(d >= 0) |
564 |
SET_NTH_BIT(test[0],0); |
565 |
} |
566 |
else |
567 |
if(sides[0][0] != GT_INTERIOR) |
568 |
SET_NTH_BIT(test[0],0); |
569 |
|
570 |
if(sides[0][1] == GT_INVALID) |
571 |
{ |
572 |
if(!NTH_BIT(nset,1)) |
573 |
VCROSS(n[1],t2,t1); |
574 |
/* Test the point for sidedness */ |
575 |
d = DOT(n[1],p0); |
576 |
if(d >= 0) |
577 |
SET_NTH_BIT(test[0],1); |
578 |
} |
579 |
else |
580 |
if(sides[0][1] != GT_INTERIOR) |
581 |
SET_NTH_BIT(test[0],1); |
582 |
|
583 |
if(sides[0][2] == GT_INVALID) |
584 |
{ |
585 |
if(!NTH_BIT(nset,2)) |
586 |
VCROSS(n[2],t0,t2); |
587 |
/* Test the point for sidedness */ |
588 |
d = DOT(n[2],p0); |
589 |
if(d >= 0) |
590 |
SET_NTH_BIT(test[0],2); |
591 |
} |
592 |
else |
593 |
if(sides[0][2] != GT_INTERIOR) |
594 |
SET_NTH_BIT(test[0],2); |
595 |
|
596 |
/* p=1 */ |
597 |
test[1] = 0; |
598 |
/* t=0*/ |
599 |
if(sides[1][0] == GT_INVALID) |
600 |
{ |
601 |
if(!NTH_BIT(nset,0)) |
602 |
VCROSS(n[0],t1,t0); |
603 |
/* Test the point for sidedness */ |
604 |
d = DOT(n[0],p1); |
605 |
if(d >= 0) |
606 |
SET_NTH_BIT(test[1],0); |
607 |
} |
608 |
else |
609 |
if(sides[1][0] != GT_INTERIOR) |
610 |
SET_NTH_BIT(test[1],0); |
611 |
|
612 |
/* t=1 */ |
613 |
if(sides[1][1] == GT_INVALID) |
614 |
{ |
615 |
if(!NTH_BIT(nset,1)) |
616 |
VCROSS(n[1],t2,t1); |
617 |
/* Test the point for sidedness */ |
618 |
d = DOT(n[1],p1); |
619 |
if(d >= 0) |
620 |
SET_NTH_BIT(test[1],1); |
621 |
} |
622 |
else |
623 |
if(sides[1][1] != GT_INTERIOR) |
624 |
SET_NTH_BIT(test[1],1); |
625 |
|
626 |
/* t=2 */ |
627 |
if(sides[1][2] == GT_INVALID) |
628 |
{ |
629 |
if(!NTH_BIT(nset,2)) |
630 |
VCROSS(n[2],t0,t2); |
631 |
/* Test the point for sidedness */ |
632 |
d = DOT(n[2],p1); |
633 |
if(d >= 0) |
634 |
SET_NTH_BIT(test[1],2); |
635 |
} |
636 |
else |
637 |
if(sides[1][2] != GT_INTERIOR) |
638 |
SET_NTH_BIT(test[1],2); |
639 |
|
640 |
/* p=2 */ |
641 |
test[2] = 0; |
642 |
/* t = 0 */ |
643 |
if(sides[2][0] == GT_INVALID) |
644 |
{ |
645 |
if(!NTH_BIT(nset,0)) |
646 |
VCROSS(n[0],t1,t0); |
647 |
/* Test the point for sidedness */ |
648 |
d = DOT(n[0],p2); |
649 |
if(d >= 0) |
650 |
SET_NTH_BIT(test[2],0); |
651 |
} |
652 |
else |
653 |
if(sides[2][0] != GT_INTERIOR) |
654 |
SET_NTH_BIT(test[2],0); |
655 |
/* t=1 */ |
656 |
if(sides[2][1] == GT_INVALID) |
657 |
{ |
658 |
if(!NTH_BIT(nset,1)) |
659 |
VCROSS(n[1],t2,t1); |
660 |
/* Test the point for sidedness */ |
661 |
d = DOT(n[1],p2); |
662 |
if(d >= 0) |
663 |
SET_NTH_BIT(test[2],1); |
664 |
} |
665 |
else |
666 |
if(sides[2][1] != GT_INTERIOR) |
667 |
SET_NTH_BIT(test[2],1); |
668 |
/* t=2 */ |
669 |
if(sides[2][2] == GT_INVALID) |
670 |
{ |
671 |
if(!NTH_BIT(nset,2)) |
672 |
VCROSS(n[2],t0,t2); |
673 |
/* Test the point for sidedness */ |
674 |
d = DOT(n[2],p2); |
675 |
if(d >= 0) |
676 |
SET_NTH_BIT(test[2],2); |
677 |
} |
678 |
else |
679 |
if(sides[2][2] != GT_INTERIOR) |
680 |
SET_NTH_BIT(test[2],2); |
681 |
} |
682 |
|
683 |
|
684 |
int |
685 |
spherical_tri_intersect(a1,a2,a3,b1,b2,b3) |
686 |
FVECT a1,a2,a3,b1,b2,b3; |
687 |
{ |
688 |
char which,test,n_set[2]; |
689 |
char sides[2][3][3],i,j,inext,jnext; |
690 |
char tests[2][3]; |
691 |
FVECT n[2][3],p,avg[2]; |
692 |
|
693 |
/* Test the vertices of triangle a against the pyramid formed by triangle |
694 |
b and the origin. If any vertex of a is interior to triangle b, or |
695 |
if all 3 vertices of a are ON the edges of b,return TRUE. Remember |
696 |
the results of the edge normal and sidedness tests for later. |
697 |
*/ |
698 |
if(test_vertices_for_tri_inclusion(a1,a2,a3,b1,b2,b3, |
699 |
&(n_set[0]),n[0],avg[0],sides[1])) |
700 |
return(TRUE); |
701 |
|
702 |
if(test_vertices_for_tri_inclusion(b1,b2,b3,a1,a2,a3, |
703 |
&(n_set[1]),n[1],avg[1],sides[0])) |
704 |
return(TRUE); |
705 |
|
706 |
|
707 |
set_sidedness_tests(b1,b2,b3,a1,a2,a3,tests[0],sides[0],n_set[1],n[1]); |
708 |
if(tests[0][0]&tests[0][1]&tests[0][2]) |
709 |
return(FALSE); |
710 |
|
711 |
set_sidedness_tests(a1,a2,a3,b1,b2,b3,tests[1],sides[1],n_set[0],n[0]); |
712 |
if(tests[1][0]&tests[1][1]&tests[1][2]) |
713 |
return(FALSE); |
714 |
|
715 |
for(j=0; j < 3;j++) |
716 |
{ |
717 |
jnext = (j+1)%3; |
718 |
/* IF edge b doesnt cross any great circles of a, punt */ |
719 |
if(tests[1][j] & tests[1][jnext]) |
720 |
continue; |
721 |
for(i=0;i<3;i++) |
722 |
{ |
723 |
inext = (i+1)%3; |
724 |
/* IF edge a doesnt cross any great circles of b, punt */ |
725 |
if(tests[0][i] & tests[0][inext]) |
726 |
continue; |
727 |
/* Now find the great circles that cross and test */ |
728 |
if((NTH_BIT(tests[0][i],j)^(NTH_BIT(tests[0][inext],j))) |
729 |
&& (NTH_BIT(tests[1][j],i)^NTH_BIT(tests[1][jnext],i))) |
730 |
{ |
731 |
VCROSS(p,n[0][i],n[1][j]); |
732 |
|
733 |
/* If zero cp= done */ |
734 |
if(ZERO_VEC3(p)) |
735 |
continue; |
736 |
/* check above both planes */ |
737 |
if(DOT(avg[0],p) < 0 || DOT(avg[1],p) < 0) |
738 |
{ |
739 |
NEGATE_VEC3(p); |
740 |
if(DOT(avg[0],p) < 0 || DOT(avg[1],p) < 0) |
741 |
continue; |
742 |
} |
743 |
return(TRUE); |
744 |
} |
745 |
} |
746 |
} |
747 |
return(FALSE); |
748 |
} |
749 |
|
750 |
int |
751 |
ray_intersect_tri(orig,dir,v0,v1,v2,pt,wptr) |
752 |
FVECT orig,dir; |
753 |
FVECT v0,v1,v2; |
754 |
FVECT pt; |
755 |
char *wptr; |
756 |
{ |
757 |
FVECT p0,p1,p2,p,n; |
758 |
char type,which; |
759 |
double pd; |
760 |
|
761 |
point_on_sphere(p0,v0,orig); |
762 |
point_on_sphere(p1,v1,orig); |
763 |
point_on_sphere(p2,v2,orig); |
764 |
type = test_single_point_against_spherical_tri(p0,p1,p2,dir,&which); |
765 |
|
766 |
if(type) |
767 |
{ |
768 |
/* Intersect the ray with the triangle plane */ |
769 |
tri_plane_equation(v0,v1,v2,n,&pd,FALSE); |
770 |
intersect_ray_plane(orig,dir,n,pd,NULL,pt); |
771 |
} |
772 |
if(wptr) |
773 |
*wptr = which; |
774 |
|
775 |
return(type); |
776 |
} |
777 |
|
778 |
|
779 |
calculate_view_frustum(vp,hv,vv,horiz,vert,near,far,fnear,ffar) |
780 |
FVECT vp,hv,vv; |
781 |
double horiz,vert,near,far; |
782 |
FVECT fnear[4],ffar[4]; |
783 |
{ |
784 |
double height,width; |
785 |
FVECT t,nhv,nvv,ndv; |
786 |
double w2,h2; |
787 |
/* Calculate the x and y dimensions of the near face */ |
788 |
/* hv and vv are the horizontal and vertical vectors in the |
789 |
view frame-the magnitude is the dimension of the front frustum |
790 |
face at z =1 |
791 |
*/ |
792 |
VCOPY(nhv,hv); |
793 |
VCOPY(nvv,vv); |
794 |
w2 = normalize(nhv); |
795 |
h2 = normalize(nvv); |
796 |
/* Use similar triangles to calculate the dimensions at z=near */ |
797 |
width = near*0.5*w2; |
798 |
height = near*0.5*h2; |
799 |
|
800 |
VCROSS(ndv,nvv,nhv); |
801 |
/* Calculate the world space points corresponding to the 4 corners |
802 |
of the front face of the view frustum |
803 |
*/ |
804 |
fnear[0][0] = width*nhv[0] + height*nvv[0] + near*ndv[0] + vp[0] ; |
805 |
fnear[0][1] = width*nhv[1] + height*nvv[1] + near*ndv[1] + vp[1]; |
806 |
fnear[0][2] = width*nhv[2] + height*nvv[2] + near*ndv[2] + vp[2]; |
807 |
fnear[1][0] = -width*nhv[0] + height*nvv[0] + near*ndv[0] + vp[0]; |
808 |
fnear[1][1] = -width*nhv[1] + height*nvv[1] + near*ndv[1] + vp[1]; |
809 |
fnear[1][2] = -width*nhv[2] + height*nvv[2] + near*ndv[2] + vp[2]; |
810 |
fnear[2][0] = -width*nhv[0] - height*nvv[0] + near*ndv[0] + vp[0]; |
811 |
fnear[2][1] = -width*nhv[1] - height*nvv[1] + near*ndv[1] + vp[1]; |
812 |
fnear[2][2] = -width*nhv[2] - height*nvv[2] + near*ndv[2] + vp[2]; |
813 |
fnear[3][0] = width*nhv[0] - height*nvv[0] + near*ndv[0] + vp[0]; |
814 |
fnear[3][1] = width*nhv[1] - height*nvv[1] + near*ndv[1] + vp[1]; |
815 |
fnear[3][2] = width*nhv[2] - height*nvv[2] + near*ndv[2] + vp[2]; |
816 |
|
817 |
/* Now do the far face */ |
818 |
width = far*0.5*w2; |
819 |
height = far*0.5*h2; |
820 |
ffar[0][0] = width*nhv[0] + height*nvv[0] + far*ndv[0] + vp[0] ; |
821 |
ffar[0][1] = width*nhv[1] + height*nvv[1] + far*ndv[1] + vp[1] ; |
822 |
ffar[0][2] = width*nhv[2] + height*nvv[2] + far*ndv[2] + vp[2] ; |
823 |
ffar[1][0] = -width*nhv[0] + height*nvv[0] + far*ndv[0] + vp[0] ; |
824 |
ffar[1][1] = -width*nhv[1] + height*nvv[1] + far*ndv[1] + vp[1] ; |
825 |
ffar[1][2] = -width*nhv[2] + height*nvv[2] + far*ndv[2] + vp[2] ; |
826 |
ffar[2][0] = -width*nhv[0] - height*nvv[0] + far*ndv[0] + vp[0] ; |
827 |
ffar[2][1] = -width*nhv[1] - height*nvv[1] + far*ndv[1] + vp[1] ; |
828 |
ffar[2][2] = -width*nhv[2] - height*nvv[2] + far*ndv[2] + vp[2] ; |
829 |
ffar[3][0] = width*nhv[0] - height*nvv[0] + far*ndv[0] + vp[0] ; |
830 |
ffar[3][1] = width*nhv[1] - height*nvv[1] + far*ndv[1] + vp[1] ; |
831 |
ffar[3][2] = width*nhv[2] - height*nvv[2] + far*ndv[2] + vp[2] ; |
832 |
} |
833 |
|
834 |
|
835 |
|
836 |
|
837 |
int |
838 |
spherical_polygon_edge_intersect(a0,a1,b0,b1) |
839 |
FVECT a0,a1,b0,b1; |
840 |
{ |
841 |
FVECT na,nb,avga,avgb,p; |
842 |
double d; |
843 |
int sb0,sb1,sa0,sa1; |
844 |
|
845 |
/* First test if edge b straddles great circle of a */ |
846 |
VCROSS(na,a0,a1); |
847 |
d = DOT(na,b0); |
848 |
sb0 = ZERO(d)?0:(d<0)? -1: 1; |
849 |
d = DOT(na,b1); |
850 |
sb1 = ZERO(d)?0:(d<0)? -1: 1; |
851 |
/* edge b entirely on one side of great circle a: edges cannot intersect*/ |
852 |
if(sb0*sb1 > 0) |
853 |
return(FALSE); |
854 |
/* test if edge a straddles great circle of b */ |
855 |
VCROSS(nb,b0,b1); |
856 |
d = DOT(nb,a0); |
857 |
sa0 = ZERO(d)?0:(d<0)? -1: 1; |
858 |
d = DOT(nb,a1); |
859 |
sa1 = ZERO(d)?0:(d<0)? -1: 1; |
860 |
/* edge a entirely on one side of great circle b: edges cannot intersect*/ |
861 |
if(sa0*sa1 > 0) |
862 |
return(FALSE); |
863 |
|
864 |
/* Find one of intersection points of the great circles */ |
865 |
VCROSS(p,na,nb); |
866 |
/* If they lie on same great circle: call an intersection */ |
867 |
if(ZERO_VEC3(p)) |
868 |
return(TRUE); |
869 |
|
870 |
VADD(avga,a0,a1); |
871 |
VADD(avgb,b0,b1); |
872 |
if(DOT(avga,p) < 0 || DOT(avgb,p) < 0) |
873 |
{ |
874 |
NEGATE_VEC3(p); |
875 |
if(DOT(avga,p) < 0 || DOT(avgb,p) < 0) |
876 |
return(FALSE); |
877 |
} |
878 |
if((!sb0 || !sb1) && (!sa0 || !sa1)) |
879 |
return(FALSE); |
880 |
return(TRUE); |
881 |
} |
882 |
|