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[carveJwlIkooP6JGAAIwe30JlM.git] / rigidbody.h
1 /*
2 * Resources: Box2D - Erin Catto
3 * qu3e - Randy Gaul
4 */
5
6 #include "common.h"
7 #include "bvh.h"
8 #include "scene.h"
9
10 static void rb_tangent_basis( v3f n, v3f tx, v3f ty );
11 static bh_system bh_system_rigidbodies;
12
13 #ifndef RIGIDBODY_H
14 #define RIGIDBODY_H
15
16 /*
17 * -----------------------------------------------------------------------------
18 * (K)onstants
19 * -----------------------------------------------------------------------------
20 */
21
22 static const float
23 k_rb_rate = 60.0f,
24 k_rb_delta = (1.0f/k_rb_rate),
25 k_friction = 0.6f,
26 k_damp_linear = 0.05f, /* scale velocity 1/(1+x) */
27 k_damp_angular = 0.1f, /* scale angular 1/(1+x) */
28 k_limit_bias = 0.02f,
29 k_joint_bias = 0.08f, /* positional joints */
30 k_joint_correction = 0.01f,
31 k_penetration_slop = 0.01f,
32 k_inertia_scale = 4.0f;
33
34 /*
35 * -----------------------------------------------------------------------------
36 * structure definitions
37 * -----------------------------------------------------------------------------
38 */
39
40 typedef struct rigidbody rigidbody;
41 typedef struct contact rb_ct;
42
43 struct rigidbody
44 {
45 v3f co, v, w;
46 v4f q;
47
48 enum rb_shape
49 {
50 k_rb_shape_box = 0,
51 k_rb_shape_sphere = 1,
52 k_rb_shape_capsule = 2,
53 k_rb_shape_scene = 3
54 }
55 type;
56
57 union
58 {
59 struct rb_sphere
60 {
61 float radius;
62 }
63 sphere;
64
65 struct rb_capsule
66 {
67 float height, radius;
68 }
69 capsule;
70
71 struct rb_scene
72 {
73 scene *pscene;
74 }
75 scene;
76 }
77 inf;
78
79 v3f right, up, forward;
80
81 int is_world;
82
83 boxf bbx, bbx_world;
84 float inv_mass;
85
86 /* inertia model and inverse world tensor */
87 v3f I;
88 m3x3f iI, iIw;
89
90 m4x3f to_world, to_local;
91 };
92
93 static struct contact
94 {
95 rigidbody *rba, *rbb;
96 v3f co, n;
97 v3f t[2];
98 float p, bias, norm_impulse, tangent_impulse[2],
99 normal_mass, tangent_mass[2];
100
101 u32 element_id;
102 }
103 rb_contact_buffer[256];
104 static int rb_contact_count = 0;
105
106 /*
107 * -----------------------------------------------------------------------------
108 * Math Utils
109 * -----------------------------------------------------------------------------
110 */
111
112 static float sphere_volume( float radius )
113 {
114 float r3 = radius*radius*radius;
115 return (4.0f/3.0f) * VG_PIf * r3;
116 }
117
118 static void rb_tangent_basis( v3f n, v3f tx, v3f ty )
119 {
120 /* Compute tangent basis (box2d) */
121 if( fabsf( n[0] ) >= 0.57735027f )
122 {
123 tx[0] = n[1];
124 tx[1] = -n[0];
125 tx[2] = 0.0f;
126 }
127 else
128 {
129 tx[0] = 0.0f;
130 tx[1] = n[2];
131 tx[2] = -n[1];
132 }
133
134 v3_normalize( tx );
135 v3_cross( n, tx, ty );
136 }
137
138 /*
139 * -----------------------------------------------------------------------------
140 * Debugging
141 * -----------------------------------------------------------------------------
142 */
143
144 static void rb_debug_contact( rb_ct *ct )
145 {
146 v3f p1;
147 v3_muladds( ct->co, ct->n, 0.1f, p1 );
148 vg_line_pt3( ct->co, 0.025f, 0xff0000ff );
149 vg_line( ct->co, p1, 0xffffffff );
150 }
151
152 static void debug_sphere( m4x3f m, float radius, u32 colour )
153 {
154 v3f ly = { 0.0f, 0.0f, radius },
155 lx = { 0.0f, radius, 0.0f },
156 lz = { 0.0f, 0.0f, radius };
157
158 for( int i=0; i<16; i++ )
159 {
160 float t = ((float)(i+1) * (1.0f/16.0f)) * VG_PIf * 2.0f,
161 s = sinf(t),
162 c = cosf(t);
163
164 v3f py = { s*radius, 0.0f, c*radius },
165 px = { s*radius, c*radius, 0.0f },
166 pz = { 0.0f, s*radius, c*radius };
167
168 v3f p0, p1, p2, p3, p4, p5;
169 m4x3_mulv( m, py, p0 );
170 m4x3_mulv( m, ly, p1 );
171 m4x3_mulv( m, px, p2 );
172 m4x3_mulv( m, lx, p3 );
173 m4x3_mulv( m, pz, p4 );
174 m4x3_mulv( m, lz, p5 );
175
176 vg_line( p0, p1, colour == 0x00? 0xff00ff00: colour );
177 vg_line( p2, p3, colour == 0x00? 0xff0000ff: colour );
178 vg_line( p4, p5, colour == 0x00? 0xffff0000: colour );
179
180 v3_copy( py, ly );
181 v3_copy( px, lx );
182 v3_copy( pz, lz );
183 }
184 }
185
186 static void debug_capsule( m4x3f m, float radius, float h, u32 colour )
187 {
188 v3f ly = { 0.0f, 0.0f, radius },
189 lx = { 0.0f, radius, 0.0f },
190 lz = { 0.0f, 0.0f, radius };
191
192 float s0 = sinf(0.0f)*radius,
193 c0 = cosf(0.0f)*radius;
194
195 v3f p0, p1, up, right, forward;
196 m3x3_mulv( m, (v3f){0.0f,1.0f,0.0f}, up );
197 m3x3_mulv( m, (v3f){1.0f,0.0f,0.0f}, right );
198 m3x3_mulv( m, (v3f){0.0f,0.0f,-1.0f}, forward );
199 v3_muladds( m[3], up, -h*0.5f+radius, p0 );
200 v3_muladds( m[3], up, h*0.5f-radius, p1 );
201
202 v3f a0, a1, b0, b1;
203 v3_muladds( p0, right, radius, a0 );
204 v3_muladds( p1, right, radius, a1 );
205 v3_muladds( p0, forward, radius, b0 );
206 v3_muladds( p1, forward, radius, b1 );
207 vg_line( a0, a1, colour );
208 vg_line( b0, b1, colour );
209
210 v3_muladds( p0, right, -radius, a0 );
211 v3_muladds( p1, right, -radius, a1 );
212 v3_muladds( p0, forward, -radius, b0 );
213 v3_muladds( p1, forward, -radius, b1 );
214 vg_line( a0, a1, colour );
215 vg_line( b0, b1, colour );
216
217 for( int i=0; i<16; i++ )
218 {
219 float t = ((float)(i+1) * (1.0f/16.0f)) * VG_PIf * 2.0f,
220 s1 = sinf(t)*radius,
221 c1 = cosf(t)*radius;
222
223 v3f e0 = { s0, 0.0f, c0 },
224 e1 = { s1, 0.0f, c1 },
225 e2 = { s0, c0, 0.0f },
226 e3 = { s1, c1, 0.0f },
227 e4 = { 0.0f, c0, s0 },
228 e5 = { 0.0f, c1, s1 };
229
230 m3x3_mulv( m, e0, e0 );
231 m3x3_mulv( m, e1, e1 );
232 m3x3_mulv( m, e2, e2 );
233 m3x3_mulv( m, e3, e3 );
234 m3x3_mulv( m, e4, e4 );
235 m3x3_mulv( m, e5, e5 );
236
237 v3_add( p0, e0, a0 );
238 v3_add( p0, e1, a1 );
239 v3_add( p1, e0, b0 );
240 v3_add( p1, e1, b1 );
241
242 vg_line( a0, a1, colour );
243 vg_line( b0, b1, colour );
244
245 if( c0 < 0.0f )
246 {
247 v3_add( p0, e2, a0 );
248 v3_add( p0, e3, a1 );
249 v3_add( p0, e4, b0 );
250 v3_add( p0, e5, b1 );
251 }
252 else
253 {
254 v3_add( p1, e2, a0 );
255 v3_add( p1, e3, a1 );
256 v3_add( p1, e4, b0 );
257 v3_add( p1, e5, b1 );
258 }
259
260 vg_line( a0, a1, colour );
261 vg_line( b0, b1, colour );
262
263 s0 = s1;
264 c0 = c1;
265 }
266 }
267
268 static void rb_debug( rigidbody *rb, u32 colour )
269 {
270 if( rb->type == k_rb_shape_box )
271 {
272 v3f *box = rb->bbx;
273 vg_line_boxf_transformed( rb->to_world, rb->bbx, colour );
274 }
275 else if( rb->type == k_rb_shape_sphere )
276 {
277 debug_sphere( rb->to_world, rb->inf.sphere.radius, colour );
278 }
279 else if( rb->type == k_rb_shape_capsule )
280 {
281 m4x3f m0, m1;
282 float h = rb->inf.capsule.height,
283 r = rb->inf.capsule.radius;
284
285 debug_capsule( rb->to_world, r, h, colour );
286 }
287 else if( rb->type == k_rb_shape_scene )
288 {
289 vg_line_boxf( rb->bbx, colour );
290 }
291 }
292
293 /*
294 * -----------------------------------------------------------------------------
295 * Integration
296 * -----------------------------------------------------------------------------
297 */
298
299 /*
300 * Update world space bounding box based on local one
301 */
302 static void rb_update_bounds( rigidbody *rb )
303 {
304 box_copy( rb->bbx, rb->bbx_world );
305 m4x3_transform_aabb( rb->to_world, rb->bbx_world );
306 }
307
308 /*
309 * Commit transform to rigidbody. Updates matrices
310 */
311 static void rb_update_transform( rigidbody *rb )
312 {
313 q_normalize( rb->q );
314 q_m3x3( rb->q, rb->to_world );
315 v3_copy( rb->co, rb->to_world[3] );
316
317 m4x3_invert_affine( rb->to_world, rb->to_local );
318
319 m3x3_mulv( rb->to_world, (v3f){1.0f,0.0f, 0.0f}, rb->right );
320 m3x3_mulv( rb->to_world, (v3f){0.0f,1.0f, 0.0f}, rb->up );
321 m3x3_mulv( rb->to_world, (v3f){0.0f,0.0f,-1.0f}, rb->forward );
322
323 m3x3_mul( rb->iI, rb->to_local, rb->iIw );
324 m3x3_mul( rb->to_world, rb->iIw, rb->iIw );
325
326 rb_update_bounds( rb );
327 }
328
329 /*
330 * Initialize rigidbody and calculate masses, inertia
331 */
332 static void rb_init( rigidbody *rb )
333 {
334 float volume = 1.0f;
335
336 if( rb->type == k_rb_shape_box )
337 {
338 v3f dims;
339 v3_sub( rb->bbx[1], rb->bbx[0], dims );
340 volume = dims[0]*dims[1]*dims[2];
341 }
342 else if( rb->type == k_rb_shape_sphere )
343 {
344 volume = sphere_volume( rb->inf.sphere.radius );
345 v3_fill( rb->bbx[0], -rb->inf.sphere.radius );
346 v3_fill( rb->bbx[1], rb->inf.sphere.radius );
347 }
348 else if( rb->type == k_rb_shape_capsule )
349 {
350 float r = rb->inf.capsule.radius,
351 h = rb->inf.capsule.height;
352 volume = sphere_volume( r ) + VG_PIf * r*r * (h - r*2.0f);
353
354 v3_fill( rb->bbx[0], -rb->inf.sphere.radius );
355 v3_fill( rb->bbx[1], rb->inf.sphere.radius );
356 rb->bbx[0][1] = -h;
357 rb->bbx[1][1] = h;
358 }
359 else if( rb->type == k_rb_shape_scene )
360 {
361 rb->is_world = 1;
362 box_copy( rb->inf.scene.pscene->bbx, rb->bbx );
363 }
364
365 if( rb->is_world )
366 {
367 rb->inv_mass = 0.0f;
368 v3_zero( rb->I );
369 m3x3_zero(rb->iI);
370 }
371 else
372 {
373 float mass = 2.0f*volume;
374 rb->inv_mass = 1.0f/mass;
375
376 v3f extent;
377 v3_sub( rb->bbx[1], rb->bbx[0], extent );
378 v3_muls( extent, 0.5f, extent );
379
380 /* local intertia tensor */
381 float scale = k_inertia_scale;
382 float ex2 = scale*extent[0]*extent[0],
383 ey2 = scale*extent[1]*extent[1],
384 ez2 = scale*extent[2]*extent[2];
385
386 rb->I[0] = ((1.0f/12.0f) * mass * (ey2+ez2));
387 rb->I[1] = ((1.0f/12.0f) * mass * (ex2+ez2));
388 rb->I[2] = ((1.0f/12.0f) * mass * (ex2+ey2));
389
390 m3x3_identity( rb->iI );
391 rb->iI[0][0] = rb->I[0];
392 rb->iI[1][1] = rb->I[1];
393 rb->iI[2][2] = rb->I[2];
394 m3x3_inv( rb->iI, rb->iI );
395 }
396
397 v3_zero( rb->v );
398 v3_zero( rb->w );
399
400 rb_update_transform( rb );
401 }
402
403 static void rb_iter( rigidbody *rb )
404 {
405 v3f gravity = { 0.0f, -9.8f, 0.0f };
406 v3_muladds( rb->v, gravity, k_rb_delta, rb->v );
407
408 /* intergrate velocity */
409 v3_muladds( rb->co, rb->v, k_rb_delta, rb->co );
410 v3_lerp( rb->w, (v3f){0.0f,0.0f,0.0f}, 0.0025f, rb->w );
411
412 /* inegrate inertia */
413 if( v3_length2( rb->w ) > 0.0f )
414 {
415 v4f rotation;
416 v3f axis;
417 v3_copy( rb->w, axis );
418
419 float mag = v3_length( axis );
420 v3_divs( axis, mag, axis );
421 q_axis_angle( rotation, axis, mag*k_rb_delta );
422 q_mul( rotation, rb->q, rb->q );
423 }
424
425 /* damping */
426 v3_muls( rb->v, 1.0f/(1.0f+k_rb_delta*k_damp_linear), rb->v );
427 v3_muls( rb->w, 1.0f/(1.0f+k_rb_delta*k_damp_angular), rb->w );
428 }
429
430 /*
431 * -----------------------------------------------------------------------------
432 * Closest point functions
433 * -----------------------------------------------------------------------------
434 */
435
436 /*
437 * These closest point tests were learned from Real-Time Collision Detection by
438 * Christer Ericson
439 */
440 static float closest_segment_segment( v3f p1, v3f q1, v3f p2, v3f q2,
441 float *s, float *t, v3f c1, v3f c2)
442 {
443 v3f d1,d2,r;
444 v3_sub( q1, p1, d1 );
445 v3_sub( q2, p2, d2 );
446 v3_sub( p1, p2, r );
447
448 float a = v3_length2( d1 ),
449 e = v3_length2( d2 ),
450 f = v3_dot( d2, r );
451
452 const float kEpsilon = 0.0001f;
453
454 if( a <= kEpsilon && e <= kEpsilon )
455 {
456 *s = 0.0f;
457 *t = 0.0f;
458 v3_copy( p1, c1 );
459 v3_copy( p2, c2 );
460
461 v3f v0;
462 v3_sub( c1, c2, v0 );
463
464 return v3_length2( v0 );
465 }
466
467 if( a<= kEpsilon )
468 {
469 *s = 0.0f;
470 *t = vg_clampf( f / e, 0.0f, 1.0f );
471 }
472 else
473 {
474 float c = v3_dot( d1, r );
475 if( e <= kEpsilon )
476 {
477 *t = 0.0f;
478 *s = vg_clampf( -c / a, 0.0f, 1.0f );
479 }
480 else
481 {
482 float b = v3_dot(d1,d2),
483 d = a*e-b*b;
484
485 if( d != 0.0f )
486 {
487 *s = vg_clampf((b*f - c*e)/d, 0.0f, 1.0f);
488 }
489 else
490 {
491 *s = 0.0f;
492 }
493
494 *t = (b*(*s)+f) / e;
495
496 if( *t < 0.0f )
497 {
498 *t = 0.0f;
499 *s = vg_clampf( -c / a, 0.0f, 1.0f );
500 }
501 else if( *t > 1.0f )
502 {
503 *t = 1.0f;
504 *s = vg_clampf((b-c)/a,0.0f,1.0f);
505 }
506 }
507 }
508
509 v3_muladds( p1, d1, *s, c1 );
510 v3_muladds( p2, d2, *t, c2 );
511
512 v3f v0;
513 v3_sub( c1, c2, v0 );
514 return v3_length2( v0 );
515 }
516
517 static void closest_point_aabb( v3f p, boxf box, v3f dest )
518 {
519 v3_maxv( p, box[0], dest );
520 v3_minv( dest, box[1], dest );
521 }
522
523 static void closest_point_obb( v3f p, rigidbody *rb, v3f dest )
524 {
525 v3f local;
526 m4x3_mulv( rb->to_local, p, local );
527 closest_point_aabb( local, rb->bbx, local );
528 m4x3_mulv( rb->to_world, local, dest );
529 }
530
531 static float closest_point_segment( v3f a, v3f b, v3f point, v3f dest )
532 {
533 v3f v0, v1;
534 v3_sub( b, a, v0 );
535 v3_sub( point, a, v1 );
536
537 float t = v3_dot( v1, v0 ) / v3_length2(v0);
538 t = vg_clampf(t,0.0f,1.0f);
539 v3_muladds( a, v0, t, dest );
540 return t;
541 }
542
543 static void closest_on_triangle( v3f p, v3f tri[3], v3f dest )
544 {
545 v3f ab, ac, ap;
546 float d1, d2;
547
548 /* Region outside A */
549 v3_sub( tri[1], tri[0], ab );
550 v3_sub( tri[2], tri[0], ac );
551 v3_sub( p, tri[0], ap );
552
553 d1 = v3_dot(ab,ap);
554 d2 = v3_dot(ac,ap);
555 if( d1 <= 0.0f && d2 <= 0.0f )
556 {
557 v3_copy( tri[0], dest );
558 v3_copy( (v3f){INFINITY,INFINITY,INFINITY}, dest );
559 return;
560 }
561
562 /* Region outside B */
563 v3f bp;
564 float d3, d4;
565
566 v3_sub( p, tri[1], bp );
567 d3 = v3_dot( ab, bp );
568 d4 = v3_dot( ac, bp );
569
570 if( d3 >= 0.0f && d4 <= d3 )
571 {
572 v3_copy( tri[1], dest );
573 v3_copy( (v3f){INFINITY,INFINITY,INFINITY}, dest );
574 return;
575 }
576
577 /* Edge region of AB */
578 float vc = d1*d4 - d3*d2;
579 if( vc <= 0.0f && d1 >= 0.0f && d3 <= 0.0f )
580 {
581 float v = d1 / (d1-d3);
582 v3_muladds( tri[0], ab, v, dest );
583 v3_copy( (v3f){INFINITY,INFINITY,INFINITY}, dest );
584 return;
585 }
586
587 /* Region outside C */
588 v3f cp;
589 float d5, d6;
590 v3_sub( p, tri[2], cp );
591 d5 = v3_dot(ab, cp);
592 d6 = v3_dot(ac, cp);
593
594 if( d6 >= 0.0f && d5 <= d6 )
595 {
596 v3_copy( tri[2], dest );
597 v3_copy( (v3f){INFINITY,INFINITY,INFINITY}, dest );
598 return;
599 }
600
601 /* Region of AC */
602 float vb = d5*d2 - d1*d6;
603 if( vb <= 0.0f && d2 >= 0.0f && d6 <= 0.0f )
604 {
605 float w = d2 / (d2-d6);
606 v3_muladds( tri[0], ac, w, dest );
607 v3_copy( (v3f){INFINITY,INFINITY,INFINITY}, dest );
608 return;
609 }
610
611 /* Region of BC */
612 float va = d3*d6 - d5*d4;
613 if( va <= 0.0f && (d4-d3) >= 0.0f && (d5-d6) >= 0.0f )
614 {
615 float w = (d4-d3) / ((d4-d3) + (d5-d6));
616 v3f bc;
617 v3_sub( tri[2], tri[1], bc );
618 v3_muladds( tri[1], bc, w, dest );
619 v3_copy( (v3f){INFINITY,INFINITY,INFINITY}, dest );
620 return;
621 }
622
623 /* P inside region, Q via barycentric coordinates uvw */
624 float d = 1.0f/(va+vb+vc),
625 v = vb*d,
626 w = vc*d;
627
628 v3_muladds( tri[0], ab, v, dest );
629 v3_muladds( dest, ac, w, dest );
630 }
631
632 static void closest_on_triangle_1( v3f p, v3f tri[3], v3f dest )
633 {
634 v3f ab, ac, ap;
635 float d1, d2;
636
637 /* Region outside A */
638 v3_sub( tri[1], tri[0], ab );
639 v3_sub( tri[2], tri[0], ac );
640 v3_sub( p, tri[0], ap );
641
642 d1 = v3_dot(ab,ap);
643 d2 = v3_dot(ac,ap);
644 if( d1 <= 0.0f && d2 <= 0.0f )
645 {
646 v3_copy( tri[0], dest );
647 return;
648 }
649
650 /* Region outside B */
651 v3f bp;
652 float d3, d4;
653
654 v3_sub( p, tri[1], bp );
655 d3 = v3_dot( ab, bp );
656 d4 = v3_dot( ac, bp );
657
658 if( d3 >= 0.0f && d4 <= d3 )
659 {
660 v3_copy( tri[1], dest );
661 return;
662 }
663
664 /* Edge region of AB */
665 float vc = d1*d4 - d3*d2;
666 if( vc <= 0.0f && d1 >= 0.0f && d3 <= 0.0f )
667 {
668 float v = d1 / (d1-d3);
669 v3_muladds( tri[0], ab, v, dest );
670 return;
671 }
672
673 /* Region outside C */
674 v3f cp;
675 float d5, d6;
676 v3_sub( p, tri[2], cp );
677 d5 = v3_dot(ab, cp);
678 d6 = v3_dot(ac, cp);
679
680 if( d6 >= 0.0f && d5 <= d6 )
681 {
682 v3_copy( tri[2], dest );
683 return;
684 }
685
686 /* Region of AC */
687 float vb = d5*d2 - d1*d6;
688 if( vb <= 0.0f && d2 >= 0.0f && d6 <= 0.0f )
689 {
690 float w = d2 / (d2-d6);
691 v3_muladds( tri[0], ac, w, dest );
692 return;
693 }
694
695 /* Region of BC */
696 float va = d3*d6 - d5*d4;
697 if( va <= 0.0f && (d4-d3) >= 0.0f && (d5-d6) >= 0.0f )
698 {
699 float w = (d4-d3) / ((d4-d3) + (d5-d6));
700 v3f bc;
701 v3_sub( tri[2], tri[1], bc );
702 v3_muladds( tri[1], bc, w, dest );
703 return;
704 }
705
706 /* P inside region, Q via barycentric coordinates uvw */
707 float d = 1.0f/(va+vb+vc),
708 v = vb*d,
709 w = vc*d;
710
711 v3_muladds( tri[0], ab, v, dest );
712 v3_muladds( dest, ac, w, dest );
713 }
714
715 /*
716 * -----------------------------------------------------------------------------
717 * Boolean shape overlap functions
718 * -----------------------------------------------------------------------------
719 */
720
721 /*
722 * Project AABB, and triangle interval onto axis to check if they overlap
723 */
724 static int rb_box_triangle_interval( v3f extent, v3f axis, v3f tri[3] )
725 {
726 float
727
728 r = extent[0] * fabsf(axis[0]) +
729 extent[1] * fabsf(axis[1]) +
730 extent[2] * fabsf(axis[2]),
731
732 p0 = v3_dot( axis, tri[0] ),
733 p1 = v3_dot( axis, tri[1] ),
734 p2 = v3_dot( axis, tri[2] ),
735
736 e = vg_maxf(-vg_maxf(p0,vg_maxf(p1,p2)), vg_minf(p0,vg_minf(p1,p2)));
737
738 if( e > r ) return 0;
739 else return 1;
740 }
741
742 /*
743 * Seperating axis test box vs triangle
744 */
745 static int rb_box_triangle_sat( rigidbody *rba, v3f tri_src[3] )
746 {
747 v3f tri[3];
748
749 v3f extent, c;
750 v3_sub( rba->bbx[1], rba->bbx[0], extent );
751 v3_muls( extent, 0.5f, extent );
752 v3_add( rba->bbx[0], extent, c );
753
754 for( int i=0; i<3; i++ )
755 {
756 m4x3_mulv( rba->to_local, tri_src[i], tri[i] );
757 v3_sub( tri[i], c, tri[i] );
758 }
759
760 /* u0, u1, u2 */
761 if(!rb_box_triangle_interval( extent, (v3f){1.0f,0.0f,0.0f}, tri )) return 0;
762 if(!rb_box_triangle_interval( extent, (v3f){0.0f,1.0f,0.0f}, tri )) return 0;
763 if(!rb_box_triangle_interval( extent, (v3f){0.0f,0.0f,1.0f}, tri )) return 0;
764
765 v3f v0,v1,v2,n, e0,e1,e2;
766 v3_sub( tri[1], tri[0], v0 );
767 v3_sub( tri[2], tri[0], v1 );
768 v3_sub( tri[2], tri[1], v2 );
769 v3_normalize( v0 );
770 v3_normalize( v1 );
771 v3_normalize( v2 );
772 v3_cross( v0, v1, n );
773 v3_cross( v0, n, e0 );
774 v3_cross( n, v1, e1 );
775 v3_cross( v2, n, e2 );
776
777 /* normal */
778 if(!rb_box_triangle_interval( extent, n, tri )) return 0;
779
780 v3f axis[9];
781 v3_cross( e0, (v3f){1.0f,0.0f,0.0f}, axis[0] );
782 v3_cross( e0, (v3f){0.0f,1.0f,0.0f}, axis[1] );
783 v3_cross( e0, (v3f){0.0f,0.0f,1.0f}, axis[2] );
784 v3_cross( e1, (v3f){1.0f,0.0f,0.0f}, axis[3] );
785 v3_cross( e1, (v3f){0.0f,1.0f,0.0f}, axis[4] );
786 v3_cross( e1, (v3f){0.0f,0.0f,1.0f}, axis[5] );
787 v3_cross( e2, (v3f){1.0f,0.0f,0.0f}, axis[6] );
788 v3_cross( e2, (v3f){0.0f,1.0f,0.0f}, axis[7] );
789 v3_cross( e2, (v3f){0.0f,0.0f,1.0f}, axis[8] );
790
791 for( int i=0; i<9; i++ )
792 if(!rb_box_triangle_interval( extent, axis[i], tri )) return 0;
793
794 return 1;
795 }
796
797 /*
798 * -----------------------------------------------------------------------------
799 * Collision matrix
800 * -----------------------------------------------------------------------------
801 */
802
803 /*
804 * Contact generators
805 *
806 * These do not automatically allocate contacts, an appropriately sized
807 * buffer must be supplied. The function returns the size of the manifold
808 * which was generated.
809 *
810 * The values set on the contacts are: n, co, p, rba, rbb
811 */
812
813 /*
814 * By collecting the minimum(time) and maximum(time) pairs of points, we
815 * build a reduced and stable exact manifold.
816 *
817 * tx: time at point
818 * rx: minimum distance of these points
819 * dx: the delta between the two points
820 *
821 * pairs will only ammend these if they are creating a collision
822 */
823 typedef struct capsule_manifold capsule_manifold;
824 struct capsule_manifold
825 {
826 float t0, t1;
827 float r0, r1;
828 v3f d0, d1;
829 };
830
831 /*
832 * Expand a line manifold with a new pair. t value is the time along segment
833 * on the oriented object which created this pair.
834 */
835 static void rb_capsule_manifold( v3f pa, v3f pb, float t, float r,
836 capsule_manifold *manifold )
837 {
838 v3f delta;
839 v3_sub( pa, pb, delta );
840
841 if( v3_length2(delta) < r*r )
842 {
843 if( t < manifold->t0 )
844 {
845 v3_copy( delta, manifold->d0 );
846 manifold->t0 = t;
847 manifold->r0 = r;
848 }
849
850 if( t > manifold->t1 )
851 {
852 v3_copy( delta, manifold->d1 );
853 manifold->t1 = t;
854 manifold->r1 = r;
855 }
856 }
857 }
858
859 static void rb_capsule_manifold_init( capsule_manifold *manifold )
860 {
861 manifold->t0 = INFINITY;
862 manifold->t1 = -INFINITY;
863 }
864
865 static int rb_capsule_manifold_done( rigidbody *rba, rigidbody *rbb,
866 capsule_manifold *manifold, rb_ct *buf )
867 {
868 float h = rba->inf.capsule.height,
869 ra = rba->inf.capsule.radius;
870
871 v3f p0, p1;
872 v3_muladds( rba->co, rba->up, -h*0.5f+ra, p0 );
873 v3_muladds( rba->co, rba->up, h*0.5f-ra, p1 );
874
875 int count = 0;
876 if( manifold->t0 <= 1.0f )
877 {
878 rb_ct *ct = buf;
879
880 v3f pa;
881 v3_muls( p0, 1.0f-manifold->t0, pa );
882 v3_muladds( pa, p1, manifold->t0, pa );
883
884 float d = v3_length( manifold->d0 );
885 v3_muls( manifold->d0, 1.0f/d, ct->n );
886 v3_muladds( pa, ct->n, -ra, ct->co );
887
888 ct->p = manifold->r0 - d;
889 ct->rba = rba;
890 ct->rbb = rbb;
891
892 count ++;
893 }
894
895 if( (manifold->t1 >= 0.0f) && (manifold->t0 != manifold->t1) )
896 {
897 rb_ct *ct = buf+count;
898
899 v3f pa;
900 v3_muls( p0, 1.0f-manifold->t1, pa );
901 v3_muladds( pa, p1, manifold->t1, pa );
902
903 float d = v3_length( manifold->d1 );
904 v3_muls( manifold->d1, 1.0f/d, ct->n );
905 v3_muladds( pa, ct->n, -ra, ct->co );
906
907 ct->p = manifold->r1 - d;
908 ct->rba = rba;
909 ct->rbb = rbb;
910
911 count ++;
912 }
913
914 /*
915 * Debugging
916 */
917
918 if( count == 2 )
919 vg_line( buf[0].co, buf[1].co, 0xff0000ff );
920
921 return count;
922 }
923
924 static int rb_capsule_sphere( rigidbody *rba, rigidbody *rbb, rb_ct *buf )
925 {
926 float h = rba->inf.capsule.height,
927 ra = rba->inf.capsule.radius,
928 rb = rbb->inf.sphere.radius;
929
930 v3f p0, p1;
931 v3_muladds( rba->co, rba->up, -h*0.5f+ra, p0 );
932 v3_muladds( rba->co, rba->up, h*0.5f-ra, p1 );
933
934 v3f c, delta;
935 closest_point_segment( p0, p1, rbb->co, c );
936 v3_sub( c, rbb->co, delta );
937
938 float d2 = v3_length2(delta),
939 r = ra + rb;
940
941 if( d2 < r*r )
942 {
943 float d = sqrtf(d2);
944
945 rb_ct *ct = buf;
946 v3_muls( delta, 1.0f/d, ct->n );
947 ct->p = r-d;
948
949 v3f p0, p1;
950 v3_muladds( c, ct->n, -ra, p0 );
951 v3_muladds( rbb->co, ct->n, rb, p1 );
952 v3_add( p0, p1, ct->co );
953 v3_muls( ct->co, 0.5f, ct->co );
954
955 ct->rba = rba;
956 ct->rbb = rbb;
957
958 return 1;
959 }
960
961 return 0;
962 }
963
964 static int rb_capsule_capsule( rigidbody *rba, rigidbody *rbb, rb_ct *buf )
965 {
966 float ha = rba->inf.capsule.height,
967 hb = rbb->inf.capsule.height,
968 ra = rba->inf.capsule.radius,
969 rb = rbb->inf.capsule.radius,
970 r = ra+rb;
971
972 v3f p0, p1, p2, p3;
973 v3_muladds( rba->co, rba->up, -ha*0.5f+ra, p0 );
974 v3_muladds( rba->co, rba->up, ha*0.5f-ra, p1 );
975 v3_muladds( rbb->co, rbb->up, -hb*0.5f+rb, p2 );
976 v3_muladds( rbb->co, rbb->up, hb*0.5f-rb, p3 );
977
978 capsule_manifold manifold;
979 rb_capsule_manifold_init( &manifold );
980
981 v3f pa, pb;
982 float ta, tb;
983 closest_segment_segment( p0, p1, p2, p3, &ta, &tb, pa, pb );
984 rb_capsule_manifold( pa, pb, ta, r, &manifold );
985
986 ta = closest_point_segment( p0, p1, p2, pa );
987 tb = closest_point_segment( p0, p1, p3, pb );
988 rb_capsule_manifold( pa, p2, ta, r, &manifold );
989 rb_capsule_manifold( pb, p3, tb, r, &manifold );
990
991 closest_point_segment( p2, p3, p0, pa );
992 closest_point_segment( p2, p3, p1, pb );
993 rb_capsule_manifold( p0, pa, 0.0f, r, &manifold );
994 rb_capsule_manifold( p1, pb, 1.0f, r, &manifold );
995
996 return rb_capsule_manifold_done( rba, rbb, &manifold, buf );
997 }
998
999 /*
1000 * Generates up to two contacts; optimised for the most stable manifold
1001 */
1002 static int rb_capsule_box( rigidbody *rba, rigidbody *rbb, rb_ct *buf )
1003 {
1004 float h = rba->inf.capsule.height,
1005 r = rba->inf.capsule.radius;
1006
1007 /*
1008 * Solving this in symetric local space of the cube saves us some time and a
1009 * couple branches when it comes to the quad stage.
1010 */
1011 v3f centroid;
1012 v3_add( rbb->bbx[0], rbb->bbx[1], centroid );
1013 v3_muls( centroid, 0.5f, centroid );
1014
1015 boxf bbx;
1016 v3_sub( rbb->bbx[0], centroid, bbx[0] );
1017 v3_sub( rbb->bbx[1], centroid, bbx[1] );
1018
1019 v3f pc, p0w, p1w, p0, p1;
1020 v3_muladds( rba->co, rba->up, -h*0.5f+r, p0w );
1021 v3_muladds( rba->co, rba->up, h*0.5f-r, p1w );
1022
1023 m4x3_mulv( rbb->to_local, p0w, p0 );
1024 m4x3_mulv( rbb->to_local, p1w, p1 );
1025 v3_sub( p0, centroid, p0 );
1026 v3_sub( p1, centroid, p1 );
1027 v3_add( p0, p1, pc );
1028 v3_muls( pc, 0.5f, pc );
1029
1030 /*
1031 * Finding an appropriate quad to collide lines with
1032 */
1033 v3f region;
1034 v3_div( pc, bbx[1], region );
1035
1036 v3f quad[4];
1037 if( (fabsf(region[0]) > fabsf(region[1])) &&
1038 (fabsf(region[0]) > fabsf(region[2])) )
1039 {
1040 float px = vg_signf(region[0]) * bbx[1][0];
1041 v3_copy( (v3f){ px, bbx[0][1], bbx[0][2] }, quad[0] );
1042 v3_copy( (v3f){ px, bbx[1][1], bbx[0][2] }, quad[1] );
1043 v3_copy( (v3f){ px, bbx[1][1], bbx[1][2] }, quad[2] );
1044 v3_copy( (v3f){ px, bbx[0][1], bbx[1][2] }, quad[3] );
1045 }
1046 else if( fabsf(region[1]) > fabsf(region[2]) )
1047 {
1048 float py = vg_signf(region[1]) * bbx[1][1];
1049 v3_copy( (v3f){ bbx[0][0], py, bbx[0][2] }, quad[0] );
1050 v3_copy( (v3f){ bbx[1][0], py, bbx[0][2] }, quad[1] );
1051 v3_copy( (v3f){ bbx[1][0], py, bbx[1][2] }, quad[2] );
1052 v3_copy( (v3f){ bbx[0][0], py, bbx[1][2] }, quad[3] );
1053 }
1054 else
1055 {
1056 float pz = vg_signf(region[2]) * bbx[1][2];
1057 v3_copy( (v3f){ bbx[0][0], bbx[0][1], pz }, quad[0] );
1058 v3_copy( (v3f){ bbx[1][0], bbx[0][1], pz }, quad[1] );
1059 v3_copy( (v3f){ bbx[1][0], bbx[1][1], pz }, quad[2] );
1060 v3_copy( (v3f){ bbx[0][0], bbx[1][1], pz }, quad[3] );
1061 }
1062
1063 capsule_manifold manifold;
1064 rb_capsule_manifold_init( &manifold );
1065
1066 v3f c0, c1;
1067 closest_point_aabb( p0, bbx, c0 );
1068 closest_point_aabb( p1, bbx, c1 );
1069
1070 v3f d0, d1, da;
1071 v3_sub( c0, p0, d0 );
1072 v3_sub( c1, p1, d1 );
1073 v3_sub( p1, p0, da );
1074
1075 v3_normalize(d0);
1076 v3_normalize(d1);
1077 v3_normalize(da);
1078
1079 if( v3_dot( da, d0 ) <= 0.01f )
1080 rb_capsule_manifold( p0, c0, 0.0f, r, &manifold );
1081
1082 if( v3_dot( da, d1 ) >= -0.01f )
1083 rb_capsule_manifold( p1, c1, 1.0f, r, &manifold );
1084
1085 for( int i=0; i<4; i++ )
1086 {
1087 int i0 = i,
1088 i1 = (i+1)%4;
1089
1090 v3f ca, cb;
1091 float ta, tb;
1092 closest_segment_segment( p0, p1, quad[i0], quad[i1], &ta, &tb, ca, cb );
1093 rb_capsule_manifold( ca, cb, ta, r, &manifold );
1094 }
1095
1096 /*
1097 * Create final contacts based on line manifold
1098 */
1099 m3x3_mulv( rbb->to_world, manifold.d0, manifold.d0 );
1100 m3x3_mulv( rbb->to_world, manifold.d1, manifold.d1 );
1101
1102 /*
1103 * Debugging
1104 */
1105
1106 #if 0
1107 for( int i=0; i<4; i++ )
1108 {
1109 v3f q0, q1;
1110 int i0 = i,
1111 i1 = (i+1)%4;
1112
1113 v3_add( quad[i0], centroid, q0 );
1114 v3_add( quad[i1], centroid, q1 );
1115
1116 m4x3_mulv( rbb->to_world, q0, q0 );
1117 m4x3_mulv( rbb->to_world, q1, q1 );
1118
1119 vg_line( q0, q1, 0xffffffff );
1120 }
1121 #endif
1122
1123 return rb_capsule_manifold_done( rba, rbb, &manifold, buf );
1124 }
1125
1126 static int rb_sphere_box( rigidbody *rba, rigidbody *rbb, rb_ct *buf )
1127 {
1128 v3f co, delta;
1129
1130 closest_point_obb( rba->co, rbb, co );
1131 v3_sub( rba->co, co, delta );
1132
1133 float d2 = v3_length2(delta),
1134 r = rba->inf.sphere.radius;
1135
1136 if( d2 <= r*r )
1137 {
1138 float d;
1139
1140 rb_ct *ct = buf;
1141 if( d2 <= 0.0001f )
1142 {
1143 v3_sub( rba->co, rbb->co, delta );
1144
1145 /*
1146 * some extra testing is required to find the best axis to push the
1147 * object back outside the box. Since there isnt a clear seperating
1148 * vector already, especially on really high aspect boxes.
1149 */
1150 float lx = v3_dot( rbb->right, delta ),
1151 ly = v3_dot( rbb->up, delta ),
1152 lz = v3_dot( rbb->forward, delta ),
1153 px = rbb->bbx[1][0] - fabsf(lx),
1154 py = rbb->bbx[1][1] - fabsf(ly),
1155 pz = rbb->bbx[1][2] - fabsf(lz);
1156
1157 if( px < py && px < pz )
1158 v3_muls( rbb->right, vg_signf(lx), ct->n );
1159 else if( py < pz )
1160 v3_muls( rbb->up, vg_signf(ly), ct->n );
1161 else
1162 v3_muls( rbb->forward, vg_signf(lz), ct->n );
1163
1164 v3_muladds( rba->co, ct->n, -r, ct->co );
1165 ct->p = r;
1166 }
1167 else
1168 {
1169 d = sqrtf(d2);
1170 v3_muls( delta, 1.0f/d, ct->n );
1171 ct->p = r-d;
1172 v3_copy( co, ct->co );
1173 }
1174
1175 ct->rba = rba;
1176 ct->rbb = rbb;
1177 return 1;
1178 }
1179
1180 return 0;
1181 }
1182
1183 static int rb_sphere_sphere( rigidbody *rba, rigidbody *rbb, rb_ct *buf )
1184 {
1185 v3f delta;
1186 v3_sub( rba->co, rbb->co, delta );
1187
1188 float d2 = v3_length2(delta),
1189 r = rba->inf.sphere.radius + rbb->inf.sphere.radius;
1190
1191 if( d2 < r*r )
1192 {
1193 float d = sqrtf(d2);
1194
1195 rb_ct *ct = buf;
1196 v3_muls( delta, 1.0f/d, ct->n );
1197
1198 v3f p0, p1;
1199 v3_muladds( rba->co, ct->n,-rba->inf.sphere.radius, p0 );
1200 v3_muladds( rbb->co, ct->n, rbb->inf.sphere.radius, p1 );
1201 v3_add( p0, p1, ct->co );
1202 v3_muls( ct->co, 0.5f, ct->co );
1203 ct->p = r-d;
1204 ct->rba = rba;
1205 ct->rbb = rbb;
1206 return 1;
1207 }
1208
1209 return 0;
1210 }
1211
1212 static int rb_sphere_triangle( rigidbody *rba, rigidbody *rbb,
1213 v3f tri[3], rb_ct *buf )
1214 {
1215 v3f delta, co;
1216
1217 closest_on_triangle( rba->co, tri, co );
1218 v3_sub( rba->co, co, delta );
1219
1220 vg_line( rba->co, co, 0xffff0000 );
1221 vg_line_pt3( rba->co, 0.1f, 0xff00ffff );
1222
1223 float d2 = v3_length2( delta ),
1224 r = rba->inf.sphere.radius;
1225
1226 if( d2 < r*r )
1227 {
1228 rb_ct *ct = buf;
1229
1230 v3f ab, ac, tn;
1231 v3_sub( tri[2], tri[0], ab );
1232 v3_sub( tri[1], tri[0], ac );
1233 v3_cross( ac, ab, tn );
1234 v3_copy( tn, ct->n );
1235 v3_normalize( ct->n );
1236
1237 float d = sqrtf(d2);
1238
1239 v3_copy( co, ct->co );
1240 ct->p = r-d;
1241 ct->rba = rba;
1242 ct->rbb = rbb;
1243 return 1;
1244 }
1245
1246 return 0;
1247 }
1248
1249 static int rb_sphere_scene( rigidbody *rba, rigidbody *rbb, rb_ct *buf )
1250 {
1251 scene *sc = rbb->inf.scene.pscene;
1252
1253 u32 geo[128];
1254 v3f tri[3];
1255 int len = bh_select( &sc->bhtris, rba->bbx_world, geo, 128 );
1256
1257 int count = 0;
1258
1259 for( int i=0; i<len; i++ )
1260 {
1261 u32 *ptri = &sc->indices[ geo[i]*3 ];
1262
1263 for( int j=0; j<3; j++ )
1264 v3_copy( sc->verts[ptri[j]].co, tri[j] );
1265
1266 vg_line(tri[0],tri[1],0xff00ff00 );
1267 vg_line(tri[1],tri[2],0xff00ff00 );
1268 vg_line(tri[2],tri[0],0xff00ff00 );
1269
1270 buf[count].element_id = ptri[0];
1271 count += rb_sphere_triangle( rba, rbb, tri, buf+count );
1272
1273 if( count == 12 )
1274 {
1275 vg_warn( "Exceeding sphere_vs_scene capacity. Geometry too dense!\n" );
1276 return count;
1277 }
1278 }
1279
1280 return count;
1281 }
1282
1283 static int rb_box_scene( rigidbody *rba, rigidbody *rbb, rb_ct *buf )
1284 {
1285 scene *sc = rbb->inf.scene.pscene;
1286
1287 u32 geo[128];
1288 v3f tri[3];
1289 int len = bh_select( &sc->bhtris, rba->bbx_world, geo, 128 );
1290
1291 int count = 0;
1292
1293 for( int i=0; i<len; i++ )
1294 {
1295 u32 *ptri = &sc->indices[ geo[i]*3 ];
1296
1297 for( int j=0; j<3; j++ )
1298 v3_copy( sc->verts[ptri[j]].co, tri[j] );
1299
1300 if( rb_box_triangle_sat( rba, tri ) )
1301 {
1302 vg_line(tri[0],tri[1],0xff50ff00 );
1303 vg_line(tri[1],tri[2],0xff50ff00 );
1304 vg_line(tri[2],tri[0],0xff50ff00 );
1305 }
1306 else
1307 {
1308 vg_line(tri[0],tri[1],0xff0000ff );
1309 vg_line(tri[1],tri[2],0xff0000ff );
1310 vg_line(tri[2],tri[0],0xff0000ff );
1311
1312 continue;
1313 }
1314
1315 v3f v0,v1,n;
1316 v3_sub( tri[1], tri[0], v0 );
1317 v3_sub( tri[2], tri[0], v1 );
1318 v3_cross( v0, v1, n );
1319 v3_normalize( n );
1320
1321 /* find best feature */
1322 float best = v3_dot( rba->right, n );
1323 int axis = 0;
1324
1325 float cy = v3_dot( rba->up, n );
1326 if( fabsf(cy) > fabsf(best) )
1327 {
1328 best = cy;
1329 axis = 1;
1330 }
1331
1332 float cz = -v3_dot( rba->forward, n );
1333 if( fabsf(cz) > fabsf(best) )
1334 {
1335 best = cz;
1336 axis = 2;
1337 }
1338
1339 v3f manifold[4];
1340
1341 if( axis == 0 )
1342 {
1343 float px = best > 0.0f? rba->bbx[0][0]: rba->bbx[1][0];
1344 manifold[0][0] = px;
1345 manifold[0][1] = rba->bbx[0][1];
1346 manifold[0][2] = rba->bbx[0][2];
1347 manifold[1][0] = px;
1348 manifold[1][1] = rba->bbx[1][1];
1349 manifold[1][2] = rba->bbx[0][2];
1350 manifold[2][0] = px;
1351 manifold[2][1] = rba->bbx[1][1];
1352 manifold[2][2] = rba->bbx[1][2];
1353 manifold[3][0] = px;
1354 manifold[3][1] = rba->bbx[0][1];
1355 manifold[3][2] = rba->bbx[1][2];
1356 }
1357 else if( axis == 1 )
1358 {
1359 float py = best > 0.0f? rba->bbx[0][1]: rba->bbx[1][1];
1360 manifold[0][0] = rba->bbx[0][0];
1361 manifold[0][1] = py;
1362 manifold[0][2] = rba->bbx[0][2];
1363 manifold[1][0] = rba->bbx[1][0];
1364 manifold[1][1] = py;
1365 manifold[1][2] = rba->bbx[0][2];
1366 manifold[2][0] = rba->bbx[1][0];
1367 manifold[2][1] = py;
1368 manifold[2][2] = rba->bbx[1][2];
1369 manifold[3][0] = rba->bbx[0][0];
1370 manifold[3][1] = py;
1371 manifold[3][2] = rba->bbx[1][2];
1372 }
1373 else
1374 {
1375 float pz = best > 0.0f? rba->bbx[0][2]: rba->bbx[1][2];
1376 manifold[0][0] = rba->bbx[0][0];
1377 manifold[0][1] = rba->bbx[0][1];
1378 manifold[0][2] = pz;
1379 manifold[1][0] = rba->bbx[1][0];
1380 manifold[1][1] = rba->bbx[0][1];
1381 manifold[1][2] = pz;
1382 manifold[2][0] = rba->bbx[1][0];
1383 manifold[2][1] = rba->bbx[1][1];
1384 manifold[2][2] = pz;
1385 manifold[3][0] = rba->bbx[0][0];
1386 manifold[3][1] = rba->bbx[1][1];
1387 manifold[3][2] = pz;
1388 }
1389
1390 for( int j=0; j<4; j++ )
1391 m4x3_mulv( rba->to_world, manifold[j], manifold[j] );
1392
1393 vg_line( manifold[0], manifold[1], 0xffffffff );
1394 vg_line( manifold[1], manifold[2], 0xffffffff );
1395 vg_line( manifold[2], manifold[3], 0xffffffff );
1396 vg_line( manifold[3], manifold[0], 0xffffffff );
1397
1398 for( int j=0; j<4; j++ )
1399 {
1400 rb_ct *ct = buf+count;
1401
1402 v3_copy( manifold[j], ct->co );
1403 v3_copy( n, ct->n );
1404
1405 float l0 = v3_dot( tri[0], n ),
1406 l1 = v3_dot( manifold[j], n );
1407
1408 ct->p = (l0-l1)*0.5f;
1409 if( ct->p < 0.0f )
1410 continue;
1411
1412 ct->rba = rba;
1413 ct->rbb = rbb;
1414 count ++;
1415
1416 if( count >= 12 )
1417 return count;
1418 }
1419 }
1420 return count;
1421 }
1422
1423 static int RB_MATRIX_ERROR( rigidbody *rba, rigidbody *rbb, rb_ct *buf )
1424 {
1425 vg_error( "Collision type is unimplemented between types %d and %d\n",
1426 rba->type, rbb->type );
1427
1428 return 0;
1429 }
1430
1431 static int rb_sphere_capsule( rigidbody *rba, rigidbody *rbb, rb_ct *buf )
1432 {
1433 return rb_capsule_sphere( rbb, rba, buf );
1434 }
1435
1436 static int rb_box_capsule( rigidbody *rba, rigidbody *rbb, rb_ct *buf )
1437 {
1438 return rb_capsule_box( rbb, rba, buf );
1439 }
1440
1441 static int rb_box_sphere( rigidbody *rba, rigidbody *rbb, rb_ct *buf )
1442 {
1443 return rb_sphere_box( rbb, rba, buf );
1444 }
1445
1446 static int rb_scene_box( rigidbody *rba, rigidbody *rbb, rb_ct *buf )
1447 {
1448 return rb_box_scene( rbb, rba, buf );
1449 }
1450
1451 static int (*rb_jump_table[4][4])( rigidbody *a, rigidbody *b, rb_ct *buf ) =
1452 {
1453 /* box */ /* Sphere */ /* Capsule */ /* Mesh */
1454 { RB_MATRIX_ERROR, rb_box_sphere, rb_box_capsule, rb_box_scene },
1455 { rb_sphere_box, rb_sphere_sphere, rb_sphere_capsule, rb_sphere_scene },
1456 { rb_capsule_box, rb_capsule_sphere, rb_capsule_capsule, RB_MATRIX_ERROR },
1457 { rb_scene_box, RB_MATRIX_ERROR, RB_MATRIX_ERROR, RB_MATRIX_ERROR }
1458 };
1459
1460 static int rb_collide( rigidbody *rba, rigidbody *rbb )
1461 {
1462 int (*collider_jump)(rigidbody *rba, rigidbody *rbb, rb_ct *buf )
1463 = rb_jump_table[rba->type][rbb->type];
1464
1465 /*
1466 * 12 is the maximum manifold size we can generate, so we are forced to abort
1467 * potentially checking any more.
1468 */
1469 if( rb_contact_count + 12 > vg_list_size(rb_contact_buffer) )
1470 {
1471 vg_warn( "Too many contacts made in global collider buffer (%d of %d\n)",
1472 rb_contact_count, vg_list_size(rb_contact_buffer) );
1473 return 0;
1474 }
1475
1476 /*
1477 * FUTURE: Replace this with a more dedicated broad phase pass
1478 */
1479 if( box_overlap( rba->bbx_world, rbb->bbx_world ) )
1480 {
1481 int count = collider_jump( rba, rbb, rb_contact_buffer+rb_contact_count);
1482 rb_contact_count += count;
1483 return count;
1484 }
1485 else
1486 return 0;
1487 }
1488
1489 /*
1490 * -----------------------------------------------------------------------------
1491 * Dynamics
1492 * -----------------------------------------------------------------------------
1493 */
1494
1495 static void rb_solver_reset(void)
1496 {
1497 rb_contact_count = 0;
1498 }
1499
1500 static rb_ct *rb_global_ct(void)
1501 {
1502 return rb_contact_buffer + rb_contact_count;
1503 }
1504
1505 /*
1506 * Initializing things like tangent vectors
1507 */
1508 static void rb_presolve_contacts( rb_ct *buffer, int len )
1509 {
1510 for( int i=0; i<len; i++ )
1511 {
1512 rb_ct *ct = &buffer[i];
1513 ct->bias = -0.2f * k_rb_rate * vg_minf( 0.0f, -ct->p+k_penetration_slop );
1514 rb_tangent_basis( ct->n, ct->t[0], ct->t[1] );
1515
1516 ct->norm_impulse = 0.0f;
1517 ct->tangent_impulse[0] = 0.0f;
1518 ct->tangent_impulse[1] = 0.0f;
1519
1520 v3f ra, rb, raCn, rbCn, raCt, rbCt;
1521 v3_sub( ct->co, ct->rba->co, ra );
1522 v3_sub( ct->co, ct->rbb->co, rb );
1523 v3_cross( ra, ct->n, raCn );
1524 v3_cross( rb, ct->n, rbCn );
1525
1526 /* orient inverse inertia tensors */
1527 v3f raCnI, rbCnI;
1528 m3x3_mulv( ct->rba->iIw, raCn, raCnI );
1529 m3x3_mulv( ct->rbb->iIw, rbCn, rbCnI );
1530
1531 ct->normal_mass = ct->rba->inv_mass + ct->rbb->inv_mass;
1532 ct->normal_mass += v3_dot( raCn, raCnI );
1533 ct->normal_mass += v3_dot( rbCn, rbCnI );
1534 ct->normal_mass = 1.0f/ct->normal_mass;
1535
1536 for( int j=0; j<2; j++ )
1537 {
1538 v3f raCtI, rbCtI;
1539 v3_cross( ct->t[j], ra, raCt );
1540 v3_cross( ct->t[j], rb, rbCt );
1541 m3x3_mulv( ct->rba->iIw, raCt, raCtI );
1542 m3x3_mulv( ct->rbb->iIw, rbCt, rbCtI );
1543
1544 ct->tangent_mass[j] = ct->rba->inv_mass + ct->rbb->inv_mass;
1545 ct->tangent_mass[j] += v3_dot( raCt, raCtI );
1546 ct->tangent_mass[j] += v3_dot( rbCt, rbCtI );
1547 ct->tangent_mass[j] = 1.0f/ct->tangent_mass[j];
1548 }
1549
1550 rb_debug_contact( ct );
1551 }
1552 }
1553
1554 /*
1555 * Creates relative contact velocity vector, and offsets between each body
1556 */
1557 static void rb_rcv( rb_ct *ct, v3f rv, v3f da, v3f db )
1558 {
1559 rigidbody *rba = ct->rba,
1560 *rbb = ct->rbb;
1561
1562 v3_sub( ct->co, rba->co, da );
1563 v3_sub( ct->co, rbb->co, db );
1564
1565 v3f rva, rvb;
1566 v3_cross( rba->w, da, rva );
1567 v3_add( rba->v, rva, rva );
1568 v3_cross( rbb->w, db, rvb );
1569 v3_add( rbb->v, rvb, rvb );
1570
1571 v3_sub( rva, rvb, rv );
1572 }
1573
1574 /*
1575 * Apply impulse to object
1576 */
1577 static void rb_linear_impulse( rigidbody *rb, v3f delta, v3f impulse )
1578 {
1579 /* linear */
1580 v3_muladds( rb->v, impulse, rb->inv_mass, rb->v );
1581
1582 /* Angular velocity */
1583 v3f wa;
1584 v3_cross( delta, impulse, wa );
1585
1586 m3x3_mulv( rb->iIw, wa, wa );
1587 v3_add( rb->w, wa, rb->w );
1588 }
1589
1590 /*
1591 * One iteration to solve the contact constraint
1592 */
1593 static void rb_solve_contacts( rb_ct *buf, int len )
1594 {
1595 for( int i=0; i<len; i++ )
1596 {
1597 struct contact *ct = &buf[i];
1598 rigidbody *rb = ct->rba;
1599
1600 v3f rv, da, db;
1601 rb_rcv( ct, rv, da, db );
1602
1603 /* Friction */
1604 for( int j=0; j<2; j++ )
1605 {
1606 float f = k_friction * ct->norm_impulse,
1607 vt = v3_dot( rv, ct->t[j] ),
1608 lambda = ct->tangent_mass[j] * -vt;
1609
1610 float temp = ct->tangent_impulse[j];
1611 ct->tangent_impulse[j] = vg_clampf( temp + lambda, -f, f );
1612 lambda = ct->tangent_impulse[j] - temp;
1613
1614 v3f impulse;
1615 v3_muls( ct->t[j], lambda, impulse );
1616 rb_linear_impulse( ct->rba, da, impulse );
1617
1618 v3_muls( ct->t[j], -lambda, impulse );
1619 rb_linear_impulse( ct->rbb, db, impulse );
1620 }
1621
1622 /* Normal */
1623 rb_rcv( ct, rv, da, db );
1624 float vn = v3_dot( rv, ct->n ),
1625 lambda = ct->normal_mass * (-vn + ct->bias);
1626
1627 float temp = ct->norm_impulse;
1628 ct->norm_impulse = vg_maxf( temp + lambda, 0.0f );
1629 lambda = ct->norm_impulse - temp;
1630
1631 v3f impulse;
1632 v3_muls( ct->n, lambda, impulse );
1633 rb_linear_impulse( ct->rba, da, impulse );
1634
1635 v3_muls( ct->n, -lambda, impulse );
1636 rb_linear_impulse( ct->rbb, db, impulse );
1637 }
1638 }
1639
1640 /*
1641 * -----------------------------------------------------------------------------
1642 * Constraints
1643 * -----------------------------------------------------------------------------
1644 */
1645
1646 static void draw_angle_limit( v3f c, v3f major, v3f minor,
1647 float amin, float amax, float measured,
1648 u32 colour )
1649 {
1650 float f = 0.05f;
1651 v3f ay, ax;
1652 v3_muls( major, f, ay );
1653 v3_muls( minor, f, ax );
1654
1655 for( int x=0; x<16; x++ )
1656 {
1657 float t0 = (float)x / 16.0f,
1658 t1 = (float)(x+1) / 16.0f,
1659 a0 = vg_lerpf( amin, amax, t0 ),
1660 a1 = vg_lerpf( amin, amax, t1 );
1661
1662 v3f p0, p1;
1663 v3_muladds( c, ay, cosf(a0), p0 );
1664 v3_muladds( p0, ax, sinf(a0), p0 );
1665 v3_muladds( c, ay, cosf(a1), p1 );
1666 v3_muladds( p1, ax, sinf(a1), p1 );
1667
1668 vg_line( p0, p1, colour );
1669
1670 if( x == 0 )
1671 vg_line( c, p0, colour );
1672 if( x == 15 )
1673 vg_line( c, p1, colour );
1674 }
1675
1676 v3f p2;
1677 v3_muladds( c, ay, cosf(measured)*1.2f, p2 );
1678 v3_muladds( p2, ax, sinf(measured)*1.2f, p2 );
1679 vg_line( c, p2, colour );
1680 }
1681
1682 static void rb_debug_constraint_limits( rigidbody *ra, rigidbody *rb, v3f lca,
1683 v3f limits[2] )
1684 {
1685 v3f ax, ay, az, bx, by, bz;
1686 m3x3_mulv( ra->to_world, (v3f){1.0f,0.0f,0.0f}, ax );
1687 m3x3_mulv( ra->to_world, (v3f){0.0f,1.0f,0.0f}, ay );
1688 m3x3_mulv( ra->to_world, (v3f){0.0f,0.0f,1.0f}, az );
1689 m3x3_mulv( rb->to_world, (v3f){1.0f,0.0f,0.0f}, bx );
1690 m3x3_mulv( rb->to_world, (v3f){0.0f,1.0f,0.0f}, by );
1691 m3x3_mulv( rb->to_world, (v3f){0.0f,0.0f,1.0f}, bz );
1692
1693 v2f px, py, pz;
1694 px[0] = v3_dot( ay, by );
1695 px[1] = v3_dot( az, by );
1696
1697 py[0] = v3_dot( az, bz );
1698 py[1] = v3_dot( ax, bz );
1699
1700 pz[0] = v3_dot( ax, bx );
1701 pz[1] = v3_dot( ay, bx );
1702
1703 float r0 = atan2f( px[1], px[0] ),
1704 r1 = atan2f( py[1], py[0] ),
1705 r2 = atan2f( pz[1], pz[0] );
1706
1707 v3f c;
1708 m4x3_mulv( ra->to_world, lca, c );
1709 draw_angle_limit( c, ay, az, limits[0][0], limits[1][0], r0, 0xff0000ff );
1710 draw_angle_limit( c, az, ax, limits[0][1], limits[1][1], r1, 0xff00ff00 );
1711 draw_angle_limit( c, ax, ay, limits[0][2], limits[1][2], r2, 0xffff0000 );
1712 }
1713
1714 static void rb_limit_cure( rigidbody *ra, rigidbody *rb, v3f axis, float d )
1715 {
1716 if( d != 0.0f )
1717 {
1718 float avx = v3_dot( ra->w, axis ) - v3_dot( rb->w, axis );
1719 float joint_mass = rb->inv_mass + ra->inv_mass;
1720 joint_mass = 1.0f/joint_mass;
1721
1722 float bias = (k_limit_bias * k_rb_rate) * d,
1723 lambda = -(avx + bias) * joint_mass;
1724
1725 /* Angular velocity */
1726 v3f wa, wb;
1727 v3_muls( axis, lambda * ra->inv_mass, wa );
1728 v3_muls( axis, -lambda * rb->inv_mass, wb );
1729
1730 v3_add( ra->w, wa, ra->w );
1731 v3_add( rb->w, wb, rb->w );
1732 }
1733 }
1734
1735 static void rb_constraint_limits( rigidbody *ra, v3f lca,
1736 rigidbody *rb, v3f lcb, v3f limits[2] )
1737 {
1738 v3f ax, ay, az, bx, by, bz;
1739 m3x3_mulv( ra->to_world, (v3f){1.0f,0.0f,0.0f}, ax );
1740 m3x3_mulv( ra->to_world, (v3f){0.0f,1.0f,0.0f}, ay );
1741 m3x3_mulv( ra->to_world, (v3f){0.0f,0.0f,1.0f}, az );
1742 m3x3_mulv( rb->to_world, (v3f){1.0f,0.0f,0.0f}, bx );
1743 m3x3_mulv( rb->to_world, (v3f){0.0f,1.0f,0.0f}, by );
1744 m3x3_mulv( rb->to_world, (v3f){0.0f,0.0f,1.0f}, bz );
1745
1746 v2f px, py, pz;
1747 px[0] = v3_dot( ay, by );
1748 px[1] = v3_dot( az, by );
1749
1750 py[0] = v3_dot( az, bz );
1751 py[1] = v3_dot( ax, bz );
1752
1753 pz[0] = v3_dot( ax, bx );
1754 pz[1] = v3_dot( ay, bx );
1755
1756 float r0 = atan2f( px[1], px[0] ),
1757 r1 = atan2f( py[1], py[0] ),
1758 r2 = atan2f( pz[1], pz[0] );
1759
1760 /* calculate angle deltas */
1761 float dx = 0.0f, dy = 0.0f, dz = 0.0f;
1762
1763 if( r0 < limits[0][0] ) dx = limits[0][0] - r0;
1764 if( r0 > limits[1][0] ) dx = limits[1][0] - r0;
1765 if( r1 < limits[0][1] ) dy = limits[0][1] - r1;
1766 if( r1 > limits[1][1] ) dy = limits[1][1] - r1;
1767 if( r2 < limits[0][2] ) dz = limits[0][2] - r2;
1768 if( r2 > limits[1][2] ) dz = limits[1][2] - r2;
1769
1770 v3f wca, wcb;
1771 m3x3_mulv( ra->to_world, lca, wca );
1772 m3x3_mulv( rb->to_world, lcb, wcb );
1773
1774 rb_limit_cure( ra, rb, ax, dx );
1775 rb_limit_cure( ra, rb, ay, dy );
1776 rb_limit_cure( ra, rb, az, dz );
1777 }
1778
1779 static void rb_debug_constraint_position( rigidbody *ra, v3f lca,
1780 rigidbody *rb, v3f lcb )
1781 {
1782 v3f wca, wcb;
1783 m3x3_mulv( ra->to_world, lca, wca );
1784 m3x3_mulv( rb->to_world, lcb, wcb );
1785
1786 v3f p0, p1;
1787 v3_add( wca, ra->co, p0 );
1788 v3_add( wcb, rb->co, p1 );
1789 vg_line_pt3( p0, 0.005f, 0xffffff00 );
1790 vg_line_pt3( p1, 0.005f, 0xffffff00 );
1791 vg_line( p0, p1, 0xffffff00 );
1792 }
1793
1794 static void rb_constraint_position( rigidbody *ra, v3f lca,
1795 rigidbody *rb, v3f lcb )
1796 {
1797 /* C = (COa + Ra*LCa) - (COb + Rb*LCb) = 0 */
1798 v3f wca, wcb;
1799 m3x3_mulv( ra->to_world, lca, wca );
1800 m3x3_mulv( rb->to_world, lcb, wcb );
1801
1802 v3f rcv;
1803 v3_sub( ra->v, rb->v, rcv );
1804
1805 v3f rcv_Ra, rcv_Rb;
1806 v3_cross( ra->w, wca, rcv_Ra );
1807 v3_cross( rb->w, wcb, rcv_Rb );
1808 v3_add( rcv_Ra, rcv, rcv );
1809 v3_sub( rcv, rcv_Rb, rcv );
1810
1811 v3f delta;
1812 v3f p0, p1;
1813 v3_add( wca, ra->co, p0 );
1814 v3_add( wcb, rb->co, p1 );
1815 v3_sub( p1, p0, delta );
1816
1817 float dist2 = v3_length2( delta );
1818
1819 if( dist2 > 0.00001f )
1820 {
1821 float dist = sqrtf(dist2);
1822 v3_muls( delta, 1.0f/dist, delta );
1823
1824 float joint_mass = rb->inv_mass + ra->inv_mass;
1825
1826 v3f raCn, rbCn, raCt, rbCt;
1827 v3_cross( wca, delta, raCn );
1828 v3_cross( wcb, delta, rbCn );
1829
1830 /* orient inverse inertia tensors */
1831 v3f raCnI, rbCnI;
1832 m3x3_mulv( ra->iIw, raCn, raCnI );
1833 m3x3_mulv( rb->iIw, rbCn, rbCnI );
1834 joint_mass += v3_dot( raCn, raCnI );
1835 joint_mass += v3_dot( rbCn, rbCnI );
1836 joint_mass = 1.0f/joint_mass;
1837
1838 float vd = v3_dot( rcv, delta ),
1839 bias = -(k_joint_bias * k_rb_rate) * dist,
1840 lambda = -(vd + bias) * joint_mass;
1841
1842 v3f impulse;
1843 v3_muls( delta, lambda, impulse );
1844 rb_linear_impulse( ra, wca, impulse );
1845 v3_muls( delta, -lambda, impulse );
1846 rb_linear_impulse( rb, wcb, impulse );
1847
1848 /* 'fake' snap */
1849 v3_muladds( ra->co, delta, dist * k_joint_correction, ra->co );
1850 v3_muladds( rb->co, delta, -dist * k_joint_correction, rb->co );
1851 }
1852 }
1853
1854 /*
1855 * Effectors
1856 */
1857
1858 static void rb_effect_simple_bouyency( rigidbody *ra, v4f plane,
1859 float amt, float drag )
1860 {
1861 /* float */
1862 float depth = v3_dot( plane, ra->co ) - plane[3],
1863 lambda = vg_clampf( -depth, 0.0f, 1.0f ) * amt;
1864
1865 v3_muladds( ra->v, plane, lambda * ktimestep, ra->v );
1866
1867 if( depth < 0.0f )
1868 v3_muls( ra->v, 1.0f-(drag*ktimestep), ra->v );
1869 }
1870
1871 /*
1872 * -----------------------------------------------------------------------------
1873 * BVH implementation, this is ONLY for static rigidbodies, its to slow for
1874 * realtime use.
1875 * -----------------------------------------------------------------------------
1876 */
1877
1878 static void rb_bh_expand_bound( void *user, boxf bound, u32 item_index )
1879 {
1880 rigidbody *rb = &((rigidbody *)user)[ item_index ];
1881 box_concat( bound, rb->bbx_world );
1882 }
1883
1884 static float rb_bh_centroid( void *user, u32 item_index, int axis )
1885 {
1886 rigidbody *rb = &((rigidbody *)user)[ item_index ];
1887 return (rb->bbx_world[axis][0] + rb->bbx_world[1][axis]) * 0.5f;
1888 }
1889
1890 static void rb_bh_swap( void *user, u32 ia, u32 ib )
1891 {
1892 rigidbody temp, *rba, *rbb;
1893 rba = &((rigidbody *)user)[ ia ];
1894 rbb = &((rigidbody *)user)[ ib ];
1895
1896 temp = *rba;
1897 *rba = *rbb;
1898 *rbb = temp;
1899 }
1900
1901 static void rb_bh_debug( void *user, u32 item_index )
1902 {
1903 rigidbody *rb = &((rigidbody *)user)[ item_index ];
1904 rb_debug( rb, 0xff00ffff );
1905 }
1906
1907 static bh_system bh_system_rigidbodies =
1908 {
1909 .expand_bound = rb_bh_expand_bound,
1910 .item_centroid = rb_bh_centroid,
1911 .item_swap = rb_bh_swap,
1912 .item_debug = rb_bh_debug,
1913 .cast_ray = NULL
1914 };
1915
1916 #endif /* RIGIDBODY_H */
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