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[carveJwlIkooP6JGAAIwe30JlM.git] / rigidbody.h
1 /*
2 * Copyright (C) 2021-2023 Mt.ZERO Software, Harry Godden - All Rights Reserved
3 */
4
5 /*
6 * Resources: Box2D - Erin Catto
7 * qu3e - Randy Gaul
8 */
9
10 #include "vg/vg_console.h"
11 #include "bvh.h"
12 #include "scene.h"
13
14 #include <math.h>
15
16 static bh_system bh_system_rigidbodies;
17
18 #ifndef RIGIDBODY_H
19 #define RIGIDBODY_H
20
21 /*
22 * -----------------------------------------------------------------------------
23 * (K)onstants
24 * -----------------------------------------------------------------------------
25 */
26
27 static const float
28 k_rb_rate = (1.0/VG_TIMESTEP_FIXED),
29 k_rb_delta = (1.0/k_rb_rate),
30 k_friction = 0.4f,
31 k_damp_linear = 0.1f, /* scale velocity 1/(1+x) */
32 k_damp_angular = 0.1f, /* scale angular 1/(1+x) */
33 k_penetration_slop = 0.01f,
34 k_inertia_scale = 8.0f,
35 k_phys_baumgarte = 0.2f,
36 k_gravity = 9.6f;
37
38 static float
39 k_limit_bias = 0.02f,
40 k_joint_correction = 0.01f,
41 k_joint_impulse = 1.0f,
42 k_joint_bias = 0.08f; /* positional joints */
43
44 static void rb_register_cvar(void){
45 VG_VAR_F32( k_limit_bias, flags=VG_VAR_CHEAT );
46 VG_VAR_F32( k_joint_bias, flags=VG_VAR_CHEAT );
47 VG_VAR_F32( k_joint_correction, flags=VG_VAR_CHEAT );
48 VG_VAR_F32( k_joint_impulse, flags=VG_VAR_CHEAT );
49 }
50
51 /*
52 * -----------------------------------------------------------------------------
53 * structure definitions
54 * -----------------------------------------------------------------------------
55 */
56
57 typedef struct rigidbody rigidbody;
58 typedef struct rb_object rb_object;
59 typedef struct contact rb_ct;
60 typedef struct rb_sphere rb_sphere;
61 typedef struct rb_capsule rb_capsule;
62 typedef struct rb_scene rb_scene;
63
64 struct rb_sphere{
65 float radius;
66 };
67
68 struct rb_capsule{
69 float height, radius;
70 };
71
72 struct rb_scene{
73 bh_tree *bh_scene;
74 };
75
76 struct rigidbody{
77 v3f co, v, w;
78 v4f q;
79
80 boxf bbx, bbx_world;
81 float inv_mass;
82
83 /* inertia model and inverse world tensor */
84 v3f I;
85 m3x3f iI, iIw;
86 m4x3f to_world, to_local;
87 };
88
89 /* simple objects */
90 struct rb_object{
91 rigidbody rb;
92 enum rb_shape{
93 k_rb_shape_box = 0,
94 k_rb_shape_sphere = 1,
95 k_rb_shape_capsule = 2,
96 k_rb_shape_scene = 3
97 }
98 type;
99
100 union{
101 struct rb_sphere sphere;
102 struct rb_capsule capsule;
103 struct rb_scene scene;
104 }
105 inf;
106 };
107
108 static struct contact{
109 rigidbody *rba, *rbb;
110 v3f co, n;
111 v3f t[2];
112 float p, bias, norm_impulse, tangent_impulse[2],
113 normal_mass, tangent_mass[2];
114
115 u32 element_id;
116
117 enum contact_type type;
118 }
119 rb_contact_buffer[256];
120 static int rb_contact_count = 0;
121
122 typedef struct rb_constr_pos rb_constr_pos;
123 typedef struct rb_constr_swingtwist rb_constr_swingtwist;
124
125 struct rb_constr_pos{
126 rigidbody *rba, *rbb;
127 v3f lca, lcb;
128 };
129
130 struct rb_constr_swingtwist{
131 rigidbody *rba, *rbb;
132
133 v4f conevx, conevy; /* relative to rba */
134 v3f view_offset, /* relative to rba */
135 coneva, conevxb;/* relative to rbb */
136
137 int tangent_violation, axis_violation;
138 v3f axis, tangent_axis, tangent_target, axis_target;
139
140 float conet;
141 float tangent_mass, axis_mass;
142 };
143
144 /*
145 * -----------------------------------------------------------------------------
146 * Debugging
147 * -----------------------------------------------------------------------------
148 */
149
150 static void rb_debug_contact( rb_ct *ct ){
151 v3f p1;
152 v3_muladds( ct->co, ct->n, 0.05f, p1 );
153
154 if( ct->type == k_contact_type_default ){
155 vg_line_point( ct->co, 0.0125f, 0xff0000ff );
156 vg_line( ct->co, p1, 0xffffffff );
157 }
158 else if( ct->type == k_contact_type_edge ){
159 vg_line_point( ct->co, 0.0125f, 0xff00ffc0 );
160 vg_line( ct->co, p1, 0xffffffff );
161 }
162 }
163
164
165 static void rb_object_debug( rb_object *obj, u32 colour ){
166 if( obj->type == k_rb_shape_box ){
167 v3f *box = obj->rb.bbx;
168 vg_line_boxf_transformed( obj->rb.to_world, obj->rb.bbx, colour );
169 }
170 else if( obj->type == k_rb_shape_sphere ){
171 vg_line_sphere( obj->rb.to_world, obj->inf.sphere.radius, colour );
172 }
173 else if( obj->type == k_rb_shape_capsule ){
174 m4x3f m0, m1;
175 float h = obj->inf.capsule.height,
176 r = obj->inf.capsule.radius;
177
178 vg_line_capsule( obj->rb.to_world, r, h, colour );
179 }
180 else if( obj->type == k_rb_shape_scene ){
181 vg_line_boxf( obj->rb.bbx, colour );
182 }
183 }
184
185 /*
186 * -----------------------------------------------------------------------------
187 * Integration
188 * -----------------------------------------------------------------------------
189 */
190
191 /*
192 * Update world space bounding box based on local one
193 */
194 static void rb_update_bounds( rigidbody *rb ){
195 box_init_inf( rb->bbx_world );
196 m4x3_expand_aabb_aabb( rb->to_world, rb->bbx_world, rb->bbx );
197 }
198
199 /*
200 * Commit transform to rigidbody. Updates matrices
201 */
202 static void rb_update_transform( rigidbody *rb )
203 {
204 q_normalize( rb->q );
205 q_m3x3( rb->q, rb->to_world );
206 v3_copy( rb->co, rb->to_world[3] );
207
208 m4x3_invert_affine( rb->to_world, rb->to_local );
209 m3x3_mul( rb->iI, rb->to_local, rb->iIw );
210 m3x3_mul( rb->to_world, rb->iIw, rb->iIw );
211
212 rb_update_bounds( rb );
213 }
214
215 /*
216 * Extrapolate rigidbody into a transform based on vg accumulator.
217 * Useful for rendering
218 */
219 static void rb_extrapolate( rigidbody *rb, v3f co, v4f q )
220 {
221 float substep = vg.time_fixed_extrapolate;
222 v3_muladds( rb->co, rb->v, k_rb_delta*substep, co );
223
224 if( v3_length2( rb->w ) > 0.0f ){
225 v4f rotation;
226 v3f axis;
227 v3_copy( rb->w, axis );
228
229 float mag = v3_length( axis );
230 v3_divs( axis, mag, axis );
231 q_axis_angle( rotation, axis, mag*k_rb_delta*substep );
232 q_mul( rotation, rb->q, q );
233 q_normalize( q );
234 }
235 else{
236 v4_copy( rb->q, q );
237 }
238 }
239
240 /*
241 * Initialize rigidbody and calculate masses, inertia
242 */
243 static void rb_init_object( rb_object *obj ){
244 float volume = 1.0f;
245 int inert = 0;
246
247 if( obj->type == k_rb_shape_box ){
248 v3f dims;
249 v3_sub( obj->rb.bbx[1], obj->rb.bbx[0], dims );
250 volume = dims[0]*dims[1]*dims[2];
251 }
252 else if( obj->type == k_rb_shape_sphere ){
253 volume = vg_sphere_volume( obj->inf.sphere.radius );
254 v3_fill( obj->rb.bbx[0], -obj->inf.sphere.radius );
255 v3_fill( obj->rb.bbx[1], obj->inf.sphere.radius );
256 }
257 else if( obj->type == k_rb_shape_capsule ){
258 float r = obj->inf.capsule.radius,
259 h = obj->inf.capsule.height;
260 volume = vg_sphere_volume( r ) + VG_PIf * r*r * (h - r*2.0f);
261
262 v3_fill( obj->rb.bbx[0], -r );
263 v3_fill( obj->rb.bbx[1], r );
264 obj->rb.bbx[0][1] = -h;
265 obj->rb.bbx[1][1] = h;
266 }
267 else if( obj->type == k_rb_shape_scene ){
268 inert = 1;
269 box_copy( obj->inf.scene.bh_scene->nodes[0].bbx, obj->rb.bbx );
270 }
271
272 if( inert ){
273 obj->rb.inv_mass = 0.0f;
274 v3_zero( obj->rb.I );
275 m3x3_zero( obj->rb.iI );
276 }
277 else{
278 float mass = 2.0f*volume;
279 obj->rb.inv_mass = 1.0f/mass;
280
281 v3f extent;
282 v3_sub( obj->rb.bbx[1], obj->rb.bbx[0], extent );
283 v3_muls( extent, 0.5f, extent );
284
285 /* local intertia tensor */
286 float scale = k_inertia_scale;
287 float ex2 = scale*extent[0]*extent[0],
288 ey2 = scale*extent[1]*extent[1],
289 ez2 = scale*extent[2]*extent[2];
290
291 obj->rb.I[0] = ((1.0f/12.0f) * mass * (ey2+ez2));
292 obj->rb.I[1] = ((1.0f/12.0f) * mass * (ex2+ez2));
293 obj->rb.I[2] = ((1.0f/12.0f) * mass * (ex2+ey2));
294
295 m3x3_identity( obj->rb.iI );
296 obj->rb.iI[0][0] = obj->rb.I[0];
297 obj->rb.iI[1][1] = obj->rb.I[1];
298 obj->rb.iI[2][2] = obj->rb.I[2];
299 m3x3_inv( obj->rb.iI, obj->rb.iI );
300 }
301
302 rb_update_transform( &obj->rb );
303 }
304
305 static void rb_iter( rigidbody *rb ){
306 if( !vg_validf( rb->v[0] ) ||
307 !vg_validf( rb->v[1] ) ||
308 !vg_validf( rb->v[2] ) )
309 {
310 vg_fatal_error( "NaN velocity" );
311 }
312
313 v3f gravity = { 0.0f, -9.8f, 0.0f };
314 v3_muladds( rb->v, gravity, k_rb_delta, rb->v );
315
316 /* intergrate velocity */
317 v3_muladds( rb->co, rb->v, k_rb_delta, rb->co );
318 v3_lerp( rb->w, (v3f){0.0f,0.0f,0.0f}, 0.0025f, rb->w );
319
320 /* inegrate inertia */
321 if( v3_length2( rb->w ) > 0.0f )
322 {
323 v4f rotation;
324 v3f axis;
325 v3_copy( rb->w, axis );
326
327 float mag = v3_length( axis );
328 v3_divs( axis, mag, axis );
329 q_axis_angle( rotation, axis, mag*k_rb_delta );
330 q_mul( rotation, rb->q, rb->q );
331 }
332
333 #if 0
334 /* damping */
335 v3_muls( rb->v, 1.0f/(1.0f+k_rb_delta*k_damp_linear), rb->v );
336 v3_muls( rb->w, 1.0f/(1.0f+k_rb_delta*k_damp_angular), rb->w );
337 #endif
338 }
339
340
341 /*
342 * -----------------------------------------------------------------------------
343 * Boolean shape overlap functions
344 * -----------------------------------------------------------------------------
345 */
346
347 /*
348 * Project AABB, and triangle interval onto axis to check if they overlap
349 */
350 static int rb_box_triangle_interval( v3f extent, v3f axis, v3f tri[3] ){
351 float
352
353 r = extent[0] * fabsf(axis[0]) +
354 extent[1] * fabsf(axis[1]) +
355 extent[2] * fabsf(axis[2]),
356
357 p0 = v3_dot( axis, tri[0] ),
358 p1 = v3_dot( axis, tri[1] ),
359 p2 = v3_dot( axis, tri[2] ),
360
361 e = vg_maxf(-vg_maxf(p0,vg_maxf(p1,p2)), vg_minf(p0,vg_minf(p1,p2)));
362
363 if( e > r ) return 0;
364 else return 1;
365 }
366
367 /*
368 * Seperating axis test box vs triangle
369 */
370 static int rb_box_triangle_sat( v3f extent, v3f center,
371 m4x3f to_local, v3f tri_src[3] ){
372 v3f tri[3];
373
374 for( int i=0; i<3; i++ ){
375 m4x3_mulv( to_local, tri_src[i], tri[i] );
376 v3_sub( tri[i], center, tri[i] );
377 }
378
379 v3f f0,f1,f2,n;
380 v3_sub( tri[1], tri[0], f0 );
381 v3_sub( tri[2], tri[1], f1 );
382 v3_sub( tri[0], tri[2], f2 );
383
384
385 v3f axis[9];
386 v3_cross( (v3f){1.0f,0.0f,0.0f}, f0, axis[0] );
387 v3_cross( (v3f){1.0f,0.0f,0.0f}, f1, axis[1] );
388 v3_cross( (v3f){1.0f,0.0f,0.0f}, f2, axis[2] );
389 v3_cross( (v3f){0.0f,1.0f,0.0f}, f0, axis[3] );
390 v3_cross( (v3f){0.0f,1.0f,0.0f}, f1, axis[4] );
391 v3_cross( (v3f){0.0f,1.0f,0.0f}, f2, axis[5] );
392 v3_cross( (v3f){0.0f,0.0f,1.0f}, f0, axis[6] );
393 v3_cross( (v3f){0.0f,0.0f,1.0f}, f1, axis[7] );
394 v3_cross( (v3f){0.0f,0.0f,1.0f}, f2, axis[8] );
395
396 for( int i=0; i<9; i++ )
397 if(!rb_box_triangle_interval( extent, axis[i], tri )) return 0;
398
399 /* u0, u1, u2 */
400 if(!rb_box_triangle_interval( extent, (v3f){1.0f,0.0f,0.0f}, tri )) return 0;
401 if(!rb_box_triangle_interval( extent, (v3f){0.0f,1.0f,0.0f}, tri )) return 0;
402 if(!rb_box_triangle_interval( extent, (v3f){0.0f,0.0f,1.0f}, tri )) return 0;
403
404 /* normal */
405 v3_cross( f0, f1, n );
406 if(!rb_box_triangle_interval( extent, n, tri )) return 0;
407
408 return 1;
409 }
410
411 /*
412 * -----------------------------------------------------------------------------
413 * Manifold
414 * -----------------------------------------------------------------------------
415 */
416
417 static int rb_manifold_apply_filtered( rb_ct *man, int len ){
418 int k = 0;
419
420 for( int i=0; i<len; i++ ){
421 rb_ct *ct = &man[i];
422
423 if( ct->type == k_contact_type_disabled )
424 continue;
425
426 man[k ++] = man[i];
427 }
428
429 return k;
430 }
431
432 /*
433 * Merge two contacts if they are within radius(r) of eachother
434 */
435 static void rb_manifold_contact_weld( rb_ct *ci, rb_ct *cj, float r ){
436 if( v3_dist2( ci->co, cj->co ) < r*r ){
437 cj->type = k_contact_type_disabled;
438 ci->p = (ci->p + cj->p) * 0.5f;
439
440 v3_add( ci->co, cj->co, ci->co );
441 v3_muls( ci->co, 0.5f, ci->co );
442
443 v3f delta;
444 v3_sub( ci->rba->co, ci->co, delta );
445
446 float c0 = v3_dot( ci->n, delta ),
447 c1 = v3_dot( cj->n, delta );
448
449 if( c0 < 0.0f || c1 < 0.0f ){
450 /* error */
451 ci->type = k_contact_type_disabled;
452 }
453 else{
454 v3f n;
455 v3_muls( ci->n, c0, n );
456 v3_muladds( n, cj->n, c1, n );
457 v3_normalize( n );
458 v3_copy( n, ci->n );
459 }
460 }
461 }
462
463 /*
464 *
465 */
466 static void rb_manifold_filter_joint_edges( rb_ct *man, int len, float r ){
467 for( int i=0; i<len-1; i++ ){
468 rb_ct *ci = &man[i];
469 if( ci->type != k_contact_type_edge )
470 continue;
471
472 for( int j=i+1; j<len; j++ ){
473 rb_ct *cj = &man[j];
474 if( cj->type != k_contact_type_edge )
475 continue;
476
477 rb_manifold_contact_weld( ci, cj, r );
478 }
479 }
480 }
481
482 /*
483 * Resolve overlapping pairs
484 */
485 static void rb_manifold_filter_pairs( rb_ct *man, int len, float r ){
486 for( int i=0; i<len-1; i++ ){
487 rb_ct *ci = &man[i];
488 int similar = 0;
489
490 if( ci->type == k_contact_type_disabled ) continue;
491
492 for( int j=i+1; j<len; j++ ){
493 rb_ct *cj = &man[j];
494
495 if( cj->type == k_contact_type_disabled ) continue;
496
497 if( v3_dist2( ci->co, cj->co ) < r*r ){
498 cj->type = k_contact_type_disabled;
499 v3_add( cj->n, ci->n, ci->n );
500 ci->p += cj->p;
501 similar ++;
502 }
503 }
504
505 if( similar ){
506 float n = 1.0f/((float)similar+1.0f);
507 v3_muls( ci->n, n, ci->n );
508 ci->p *= n;
509
510 if( v3_length2(ci->n) < 0.1f*0.1f )
511 ci->type = k_contact_type_disabled;
512 else
513 v3_normalize( ci->n );
514 }
515 }
516 }
517
518 /*
519 * Remove contacts that are facing away from A
520 */
521 static void rb_manifold_filter_backface( rb_ct *man, int len ){
522 for( int i=0; i<len; i++ ){
523 rb_ct *ct = &man[i];
524 if( ct->type == k_contact_type_disabled )
525 continue;
526
527 v3f delta;
528 v3_sub( ct->co, ct->rba->co, delta );
529
530 if( v3_dot( delta, ct->n ) > -0.001f )
531 ct->type = k_contact_type_disabled;
532 }
533 }
534
535 /*
536 * Filter out duplicate coplanar results. Good for spheres.
537 */
538 static void rb_manifold_filter_coplanar( rb_ct *man, int len, float w ){
539 for( int i=0; i<len; i++ ){
540 rb_ct *ci = &man[i];
541 if( ci->type == k_contact_type_disabled ||
542 ci->type == k_contact_type_edge )
543 continue;
544
545 float d1 = v3_dot( ci->co, ci->n );
546
547 for( int j=0; j<len; j++ ){
548 if( j == i )
549 continue;
550
551 rb_ct *cj = &man[j];
552 if( cj->type == k_contact_type_disabled )
553 continue;
554
555 float d2 = v3_dot( cj->co, ci->n ),
556 d = d2-d1;
557
558 if( fabsf( d ) <= w ){
559 cj->type = k_contact_type_disabled;
560 }
561 }
562 }
563 }
564
565 /*
566 * -----------------------------------------------------------------------------
567 * Collision matrix
568 * -----------------------------------------------------------------------------
569 */
570
571 /*
572 * Contact generators
573 *
574 * These do not automatically allocate contacts, an appropriately sized
575 * buffer must be supplied. The function returns the size of the manifold
576 * which was generated.
577 *
578 * The values set on the contacts are: n, co, p, rba, rbb
579 */
580
581 /*
582 * By collecting the minimum(time) and maximum(time) pairs of points, we
583 * build a reduced and stable exact manifold.
584 *
585 * tx: time at point
586 * rx: minimum distance of these points
587 * dx: the delta between the two points
588 *
589 * pairs will only ammend these if they are creating a collision
590 */
591 typedef struct capsule_manifold capsule_manifold;
592 struct capsule_manifold{
593 float t0, t1;
594 float r0, r1;
595 v3f d0, d1;
596 };
597
598 /*
599 * Expand a line manifold with a new pair. t value is the time along segment
600 * on the oriented object which created this pair.
601 */
602 static void rb_capsule_manifold( v3f pa, v3f pb, float t, float r,
603 capsule_manifold *manifold ){
604 v3f delta;
605 v3_sub( pa, pb, delta );
606
607 if( v3_length2(delta) < r*r ){
608 if( t < manifold->t0 ){
609 v3_copy( delta, manifold->d0 );
610 manifold->t0 = t;
611 manifold->r0 = r;
612 }
613
614 if( t > manifold->t1 ){
615 v3_copy( delta, manifold->d1 );
616 manifold->t1 = t;
617 manifold->r1 = r;
618 }
619 }
620 }
621
622 static void rb_capsule_manifold_init( capsule_manifold *manifold ){
623 manifold->t0 = INFINITY;
624 manifold->t1 = -INFINITY;
625 }
626
627 static int rb_capsule__manifold_done( m4x3f mtx, rb_capsule *c,
628 capsule_manifold *manifold,
629 rb_ct *buf ){
630 v3f p0, p1;
631 v3_muladds( mtx[3], mtx[1], -c->height*0.5f+c->radius, p0 );
632 v3_muladds( mtx[3], mtx[1], c->height*0.5f-c->radius, p1 );
633
634 int count = 0;
635 if( manifold->t0 <= 1.0f ){
636 rb_ct *ct = buf;
637
638 v3f pa;
639 v3_muls( p0, 1.0f-manifold->t0, pa );
640 v3_muladds( pa, p1, manifold->t0, pa );
641
642 float d = v3_length( manifold->d0 );
643 v3_muls( manifold->d0, 1.0f/d, ct->n );
644 v3_muladds( pa, ct->n, -c->radius, ct->co );
645
646 ct->p = manifold->r0 - d;
647 ct->type = k_contact_type_default;
648 count ++;
649 }
650
651 if( (manifold->t1 >= 0.0f) && (manifold->t0 != manifold->t1) ){
652 rb_ct *ct = buf+count;
653
654 v3f pa;
655 v3_muls( p0, 1.0f-manifold->t1, pa );
656 v3_muladds( pa, p1, manifold->t1, pa );
657
658 float d = v3_length( manifold->d1 );
659 v3_muls( manifold->d1, 1.0f/d, ct->n );
660 v3_muladds( pa, ct->n, -c->radius, ct->co );
661
662 ct->p = manifold->r1 - d;
663 ct->type = k_contact_type_default;
664
665 count ++;
666 }
667
668 /*
669 * Debugging
670 */
671
672 if( count == 2 )
673 vg_line( buf[0].co, buf[1].co, 0xff0000ff );
674
675 return count;
676 }
677
678 static int rb_capsule_sphere( rb_object *obja, rb_object *objb, rb_ct *buf ){
679 rigidbody *rba = &obja->rb, *rbb = &objb->rb;
680 float h = obja->inf.capsule.height,
681 ra = obja->inf.capsule.radius,
682 rb = objb->inf.sphere.radius;
683
684 v3f p0, p1;
685 v3_muladds( rba->co, rba->to_world[1], -h*0.5f+ra, p0 );
686 v3_muladds( rba->co, rba->to_world[1], h*0.5f-ra, p1 );
687
688 v3f c, delta;
689 closest_point_segment( p0, p1, rbb->co, c );
690 v3_sub( c, rbb->co, delta );
691
692 float d2 = v3_length2(delta),
693 r = ra + rb;
694
695 if( d2 < r*r ){
696 float d = sqrtf(d2);
697
698 rb_ct *ct = buf;
699 v3_muls( delta, 1.0f/d, ct->n );
700 ct->p = r-d;
701
702 v3f p0, p1;
703 v3_muladds( c, ct->n, -ra, p0 );
704 v3_muladds( rbb->co, ct->n, rb, p1 );
705 v3_add( p0, p1, ct->co );
706 v3_muls( ct->co, 0.5f, ct->co );
707
708 ct->rba = rba;
709 ct->rbb = rbb;
710 ct->type = k_contact_type_default;
711
712 return 1;
713 }
714
715 return 0;
716 }
717
718 static int rb_capsule__capsule( m4x3f mtxA, rb_capsule *ca,
719 m4x3f mtxB, rb_capsule *cb, rb_ct *buf ){
720 float ha = ca->height,
721 hb = cb->height,
722 ra = ca->radius,
723 rb = cb->radius,
724 r = ra+rb;
725
726 v3f p0, p1, p2, p3;
727 v3_muladds( mtxA[3], mtxA[1], -ha*0.5f+ra, p0 );
728 v3_muladds( mtxA[3], mtxA[1], ha*0.5f-ra, p1 );
729 v3_muladds( mtxB[3], mtxB[1], -hb*0.5f+rb, p2 );
730 v3_muladds( mtxB[3], mtxB[1], hb*0.5f-rb, p3 );
731
732 capsule_manifold manifold;
733 rb_capsule_manifold_init( &manifold );
734
735 v3f pa, pb;
736 float ta, tb;
737 closest_segment_segment( p0, p1, p2, p3, &ta, &tb, pa, pb );
738 rb_capsule_manifold( pa, pb, ta, r, &manifold );
739
740 ta = closest_point_segment( p0, p1, p2, pa );
741 tb = closest_point_segment( p0, p1, p3, pb );
742 rb_capsule_manifold( pa, p2, ta, r, &manifold );
743 rb_capsule_manifold( pb, p3, tb, r, &manifold );
744
745 closest_point_segment( p2, p3, p0, pa );
746 closest_point_segment( p2, p3, p1, pb );
747 rb_capsule_manifold( p0, pa, 0.0f, r, &manifold );
748 rb_capsule_manifold( p1, pb, 1.0f, r, &manifold );
749
750 return rb_capsule__manifold_done( mtxA, ca, &manifold, buf );
751 }
752
753 static int rb_sphere_box( rb_object *obja, rb_object *objb, rb_ct *buf ){
754 v3f co, delta;
755 rigidbody *rba = &obja->rb, *rbb = &objb->rb;
756
757 closest_point_obb( rba->co, rbb->bbx, rbb->to_world, rbb->to_local, co );
758 v3_sub( rba->co, co, delta );
759
760 float d2 = v3_length2(delta),
761 r = obja->inf.sphere.radius;
762
763 if( d2 <= r*r ){
764 float d;
765
766 rb_ct *ct = buf;
767 if( d2 <= 0.0001f ){
768 v3_sub( rba->co, rbb->co, delta );
769
770 /*
771 * some extra testing is required to find the best axis to push the
772 * object back outside the box. Since there isnt a clear seperating
773 * vector already, especially on really high aspect boxes.
774 */
775 float lx = v3_dot( rbb->to_world[0], delta ),
776 ly = v3_dot( rbb->to_world[1], delta ),
777 lz = v3_dot( rbb->to_world[2], delta ),
778 px = rbb->bbx[1][0] - fabsf(lx),
779 py = rbb->bbx[1][1] - fabsf(ly),
780 pz = rbb->bbx[1][2] - fabsf(lz);
781
782 if( px < py && px < pz )
783 v3_muls( rbb->to_world[0], vg_signf(lx), ct->n );
784 else if( py < pz )
785 v3_muls( rbb->to_world[1], vg_signf(ly), ct->n );
786 else
787 v3_muls( rbb->to_world[2], vg_signf(lz), ct->n );
788
789 v3_muladds( rba->co, ct->n, -r, ct->co );
790 ct->p = r;
791 }
792 else{
793 d = sqrtf(d2);
794 v3_muls( delta, 1.0f/d, ct->n );
795 ct->p = r-d;
796 v3_copy( co, ct->co );
797 }
798
799 ct->rba = rba;
800 ct->rbb = rbb;
801 ct->type = k_contact_type_default;
802 return 1;
803 }
804
805 return 0;
806 }
807
808 static int rb_sphere_sphere( rb_object *obja, rb_object *objb, rb_ct *buf ){
809 rigidbody *rba = &obja->rb, *rbb = &objb->rb;
810 v3f delta;
811 v3_sub( rba->co, rbb->co, delta );
812
813 float d2 = v3_length2(delta),
814 r = obja->inf.sphere.radius + objb->inf.sphere.radius;
815
816 if( d2 < r*r ){
817 float d = sqrtf(d2);
818
819 rb_ct *ct = buf;
820 v3_muls( delta, 1.0f/d, ct->n );
821
822 v3f p0, p1;
823 v3_muladds( rba->co, ct->n,-obja->inf.sphere.radius, p0 );
824 v3_muladds( rbb->co, ct->n, objb->inf.sphere.radius, p1 );
825 v3_add( p0, p1, ct->co );
826 v3_muls( ct->co, 0.5f, ct->co );
827 ct->type = k_contact_type_default;
828 ct->p = r-d;
829 ct->rba = rba;
830 ct->rbb = rbb;
831 return 1;
832 }
833
834 return 0;
835 }
836
837 static int rb_sphere__triangle( m4x3f mtxA, rb_sphere *b,
838 v3f tri[3], rb_ct *buf ){
839 v3f delta, co;
840 enum contact_type type = closest_on_triangle_1( mtxA[3], tri, co );
841
842 v3_sub( mtxA[3], co, delta );
843
844 float d2 = v3_length2( delta ),
845 r = b->radius;
846
847 if( d2 <= r*r ){
848 rb_ct *ct = buf;
849
850 v3f ab, ac, tn;
851 v3_sub( tri[2], tri[0], ab );
852 v3_sub( tri[1], tri[0], ac );
853 v3_cross( ac, ab, tn );
854 v3_copy( tn, ct->n );
855
856 if( v3_length2( ct->n ) <= 0.00001f ){
857 #ifdef RIGIDBODY_CRY_ABOUT_EVERYTHING
858 vg_error( "Zero area triangle!\n" );
859 #endif
860 return 0;
861 }
862
863 v3_normalize( ct->n );
864
865 float d = sqrtf(d2);
866
867 v3_copy( co, ct->co );
868 ct->type = type;
869 ct->p = r-d;
870 return 1;
871 }
872
873 return 0;
874 }
875
876 static int rb_sphere__scene( m4x3f mtxA, rb_sphere *b,
877 m4x3f mtxB, rb_scene *s, rb_ct *buf,
878 u16 ignore ){
879 scene_context *sc = s->bh_scene->user;
880
881 int count = 0;
882
883 float r = b->radius + 0.1f;
884 boxf box;
885 v3_sub( mtxA[3], (v3f){ r,r,r }, box[0] );
886 v3_add( mtxA[3], (v3f){ r,r,r }, box[1] );
887
888 bh_iter it;
889 i32 idx;
890 bh_iter_init_box( 0, &it, box );
891
892 while( bh_next( s->bh_scene, &it, &idx ) ){
893 u32 *ptri = &sc->arrindices[ idx*3 ];
894 v3f tri[3];
895
896 if( sc->arrvertices[ptri[0]].flags & ignore ) continue;
897
898 for( int j=0; j<3; j++ )
899 v3_copy( sc->arrvertices[ptri[j]].co, tri[j] );
900
901 buf[ count ].element_id = ptri[0];
902
903 vg_line( tri[0],tri[1],0x70ff6000 );
904 vg_line( tri[1],tri[2],0x70ff6000 );
905 vg_line( tri[2],tri[0],0x70ff6000 );
906
907 int contact = rb_sphere__triangle( mtxA, b, tri, &buf[count] );
908 count += contact;
909
910 if( count == 16 ){
911 vg_warn( "Exceeding sphere_vs_scene capacity. Geometry too dense!\n" );
912 return count;
913 }
914 }
915
916 return count;
917 }
918
919 static int rb_box__scene( m4x3f mtxA, boxf bbx,
920 m4x3f mtxB, rb_scene *s, rb_ct *buf, u16 ignore ){
921 scene_context *sc = s->bh_scene->user;
922 v3f tri[3];
923
924 v3f extent, center;
925 v3_sub( bbx[1], bbx[0], extent );
926 v3_muls( extent, 0.5f, extent );
927 v3_add( bbx[0], extent, center );
928
929 float r = v3_length(extent);
930 boxf world_bbx;
931 v3_fill( world_bbx[0], -r );
932 v3_fill( world_bbx[1], r );
933 for( int i=0; i<2; i++ ){
934 v3_add( center, world_bbx[i], world_bbx[i] );
935 v3_add( mtxA[3], world_bbx[i], world_bbx[i] );
936 }
937
938 m4x3f to_local;
939 m4x3_invert_affine( mtxA, to_local );
940
941 bh_iter it;
942 bh_iter_init_box( 0, &it, world_bbx );
943 int idx;
944 int count = 0;
945
946 vg_line_boxf( world_bbx, VG__RED );
947
948 while( bh_next( s->bh_scene, &it, &idx ) ){
949 u32 *ptri = &sc->arrindices[ idx*3 ];
950 if( sc->arrvertices[ptri[0]].flags & ignore ) continue;
951
952 for( int j=0; j<3; j++ )
953 v3_copy( sc->arrvertices[ptri[j]].co, tri[j] );
954
955 if( rb_box_triangle_sat( extent, center, to_local, tri ) ){
956 vg_line(tri[0],tri[1],0xff50ff00 );
957 vg_line(tri[1],tri[2],0xff50ff00 );
958 vg_line(tri[2],tri[0],0xff50ff00 );
959 }
960 else{
961 vg_line(tri[0],tri[1],0xff0000ff );
962 vg_line(tri[1],tri[2],0xff0000ff );
963 vg_line(tri[2],tri[0],0xff0000ff );
964 continue;
965 }
966
967 v3f v0,v1,n;
968 v3_sub( tri[1], tri[0], v0 );
969 v3_sub( tri[2], tri[0], v1 );
970 v3_cross( v0, v1, n );
971
972 if( v3_length2( n ) <= 0.00001f ){
973 #ifdef RIGIDBODY_CRY_ABOUT_EVERYTHING
974 vg_error( "Zero area triangle!\n" );
975 #endif
976 return 0;
977 }
978
979 v3_normalize( n );
980
981 /* find best feature */
982 float best = v3_dot( mtxA[0], n );
983 int axis = 0;
984
985 for( int i=1; i<3; i++ ){
986 float c = v3_dot( mtxA[i], n );
987
988 if( fabsf(c) > fabsf(best) ){
989 best = c;
990 axis = i;
991 }
992 }
993
994 v3f manifold[4];
995
996 if( axis == 0 ){
997 float px = best > 0.0f? bbx[0][0]: bbx[1][0];
998 manifold[0][0] = px;
999 manifold[0][1] = bbx[0][1];
1000 manifold[0][2] = bbx[0][2];
1001 manifold[1][0] = px;
1002 manifold[1][1] = bbx[1][1];
1003 manifold[1][2] = bbx[0][2];
1004 manifold[2][0] = px;
1005 manifold[2][1] = bbx[1][1];
1006 manifold[2][2] = bbx[1][2];
1007 manifold[3][0] = px;
1008 manifold[3][1] = bbx[0][1];
1009 manifold[3][2] = bbx[1][2];
1010 }
1011 else if( axis == 1 ){
1012 float py = best > 0.0f? bbx[0][1]: bbx[1][1];
1013 manifold[0][0] = bbx[0][0];
1014 manifold[0][1] = py;
1015 manifold[0][2] = bbx[0][2];
1016 manifold[1][0] = bbx[1][0];
1017 manifold[1][1] = py;
1018 manifold[1][2] = bbx[0][2];
1019 manifold[2][0] = bbx[1][0];
1020 manifold[2][1] = py;
1021 manifold[2][2] = bbx[1][2];
1022 manifold[3][0] = bbx[0][0];
1023 manifold[3][1] = py;
1024 manifold[3][2] = bbx[1][2];
1025 }
1026 else{
1027 float pz = best > 0.0f? bbx[0][2]: bbx[1][2];
1028 manifold[0][0] = bbx[0][0];
1029 manifold[0][1] = bbx[0][1];
1030 manifold[0][2] = pz;
1031 manifold[1][0] = bbx[1][0];
1032 manifold[1][1] = bbx[0][1];
1033 manifold[1][2] = pz;
1034 manifold[2][0] = bbx[1][0];
1035 manifold[2][1] = bbx[1][1];
1036 manifold[2][2] = pz;
1037 manifold[3][0] = bbx[0][0];
1038 manifold[3][1] = bbx[1][1];
1039 manifold[3][2] = pz;
1040 }
1041
1042 for( int j=0; j<4; j++ )
1043 m4x3_mulv( mtxA, manifold[j], manifold[j] );
1044
1045 vg_line( manifold[0], manifold[1], 0xffffffff );
1046 vg_line( manifold[1], manifold[2], 0xffffffff );
1047 vg_line( manifold[2], manifold[3], 0xffffffff );
1048 vg_line( manifold[3], manifold[0], 0xffffffff );
1049
1050 for( int j=0; j<4; j++ ){
1051 rb_ct *ct = buf+count;
1052
1053 v3_copy( manifold[j], ct->co );
1054 v3_copy( n, ct->n );
1055
1056 float l0 = v3_dot( tri[0], n ),
1057 l1 = v3_dot( manifold[j], n );
1058
1059 ct->p = (l0-l1)*0.5f;
1060 if( ct->p < 0.0f )
1061 continue;
1062
1063 ct->type = k_contact_type_default;
1064 count ++;
1065
1066 if( count >= 12 )
1067 return count;
1068 }
1069 }
1070 return count;
1071 }
1072
1073 static int rb_capsule__triangle( m4x3f mtxA, rb_capsule *c,
1074 v3f tri[3], rb_ct *buf ){
1075 v3f pc, p0w, p1w;
1076 v3_muladds( mtxA[3], mtxA[1], -c->height*0.5f+c->radius, p0w );
1077 v3_muladds( mtxA[3], mtxA[1], c->height*0.5f-c->radius, p1w );
1078
1079 capsule_manifold manifold;
1080 rb_capsule_manifold_init( &manifold );
1081
1082 v3f v0, v1, n;
1083 v3_sub( tri[1], tri[0], v0 );
1084 v3_sub( tri[2], tri[0], v1 );
1085 v3_cross( v0, v1, n );
1086
1087 if( v3_length2( n ) <= 0.00001f ){
1088 #ifdef RIGIDBODY_CRY_ABOUT_EVERYTHING
1089 vg_error( "Zero area triangle!\n" );
1090 #endif
1091 return 0;
1092 }
1093
1094 v3_normalize( n );
1095
1096 #if 1
1097 /* deep penetration recovery. for when we clip through the triangles. so its
1098 * not very 'correct' */
1099 f32 dist;
1100 if( ray_tri( tri, p0w, mtxA[1], &dist, 1 ) ){
1101 f32 l = c->height - c->radius*2.0f;
1102 if( (dist >= 0.0f) && (dist < l) ){
1103 v3f co;
1104 v3_muladds( p0w, mtxA[1], dist, co );
1105 vg_line_point( co, 0.02f, 0xffffff00 );
1106
1107 v3f d0, d1;
1108 v3_sub( p0w, co, d0 );
1109 v3_sub( p1w, co, d1 );
1110
1111 f32 p = vg_minf( v3_dot( n, d0 ), v3_dot( n, d1 ) ) - c->radius;
1112
1113 rb_ct *ct = buf;
1114 ct->p = -p;
1115 ct->type = k_contact_type_default;
1116 v3_copy( n, ct->n );
1117 v3_muladds( co, n, p, ct->co );
1118
1119 return 1;
1120 }
1121 }
1122 #endif
1123
1124 v3f c0, c1;
1125 closest_on_triangle_1( p0w, tri, c0 );
1126 closest_on_triangle_1( p1w, tri, c1 );
1127
1128 v3f d0, d1, da;
1129 v3_sub( c0, p0w, d0 );
1130 v3_sub( c1, p1w, d1 );
1131 v3_sub( p1w, p0w, da );
1132
1133 v3_normalize(d0);
1134 v3_normalize(d1);
1135 v3_normalize(da);
1136
1137 /* the two balls at the ends */
1138 if( v3_dot( da, d0 ) <= 0.01f )
1139 rb_capsule_manifold( p0w, c0, 0.0f, c->radius, &manifold );
1140 if( v3_dot( da, d1 ) >= -0.01f )
1141 rb_capsule_manifold( p1w, c1, 1.0f, c->radius, &manifold );
1142
1143 /* the edges to edges */
1144 for( int i=0; i<3; i++ ){
1145 int i0 = i,
1146 i1 = (i+1)%3;
1147
1148 v3f ca, cb;
1149 float ta, tb;
1150 closest_segment_segment( p0w, p1w, tri[i0], tri[i1], &ta, &tb, ca, cb );
1151 rb_capsule_manifold( ca, cb, ta, c->radius, &manifold );
1152 }
1153
1154 int count = rb_capsule__manifold_done( mtxA, c, &manifold, buf );
1155 for( int i=0; i<count; i++ )
1156 v3_copy( n, buf[i].n );
1157
1158 return count;
1159 }
1160
1161 /* mtxB is defined only for tradition; it is not used currently */
1162 static int rb_capsule__scene( m4x3f mtxA, rb_capsule *c,
1163 m4x3f mtxB, rb_scene *s,
1164 rb_ct *buf, u16 ignore ){
1165 int count = 0;
1166
1167 boxf bbx;
1168 v3_sub( mtxA[3], (v3f){ c->height, c->height, c->height }, bbx[0] );
1169 v3_add( mtxA[3], (v3f){ c->height, c->height, c->height }, bbx[1] );
1170
1171 scene_context *sc = s->bh_scene->user;
1172
1173 bh_iter it;
1174 bh_iter_init_box( 0, &it, bbx );
1175 i32 idx;
1176 while( bh_next( s->bh_scene, &it, &idx ) ){
1177 u32 *ptri = &sc->arrindices[ idx*3 ];
1178 if( sc->arrvertices[ptri[0]].flags & ignore ) continue;
1179
1180 v3f tri[3];
1181 for( int j=0; j<3; j++ )
1182 v3_copy( sc->arrvertices[ptri[j]].co, tri[j] );
1183
1184 buf[ count ].element_id = ptri[0];
1185
1186 int contact = rb_capsule__triangle( mtxA, c, tri, &buf[count] );
1187 count += contact;
1188
1189 if( count >= 16 ){
1190 vg_warn("Exceeding capsule_vs_scene capacity. Geometry too dense!\n");
1191 return count;
1192 }
1193 }
1194
1195 return count;
1196 }
1197
1198 static int rb_global_has_space( void ){
1199 if( rb_contact_count + 16 > vg_list_size(rb_contact_buffer) )
1200 return 0;
1201
1202 return 1;
1203 }
1204
1205 static rb_ct *rb_global_buffer( void ){
1206 return &rb_contact_buffer[ rb_contact_count ];
1207 }
1208
1209 /*
1210 * -----------------------------------------------------------------------------
1211 * Dynamics
1212 * -----------------------------------------------------------------------------
1213 */
1214
1215 static void rb_solver_reset(void){
1216 rb_contact_count = 0;
1217 }
1218
1219 static rb_ct *rb_global_ct(void){
1220 return rb_contact_buffer + rb_contact_count;
1221 }
1222
1223 static void rb_prepare_contact( rb_ct *ct, float timestep ){
1224 ct->bias = -0.2f * (timestep*3600.0f)
1225 * vg_minf( 0.0f, -ct->p+k_penetration_slop );
1226
1227 v3_tangent_basis( ct->n, ct->t[0], ct->t[1] );
1228 ct->norm_impulse = 0.0f;
1229 ct->tangent_impulse[0] = 0.0f;
1230 ct->tangent_impulse[1] = 0.0f;
1231 }
1232
1233 /* calculate total move. manifold should belong to ONE object only */
1234 static void rb_depenetrate( rb_ct *manifold, int len, v3f dt ){
1235 v3_zero( dt );
1236
1237 for( int j=0; j<7; j++ )
1238 {
1239 for( int i=0; i<len; i++ )
1240 {
1241 struct contact *ct = &manifold[i];
1242
1243 float resolved_amt = v3_dot( ct->n, dt ),
1244 remaining = (ct->p-k_penetration_slop) - resolved_amt,
1245 apply = vg_maxf( remaining, 0.0f ) * 0.4f;
1246
1247 v3_muladds( dt, ct->n, apply, dt );
1248 }
1249 }
1250 }
1251
1252 /*
1253 * Initializing things like tangent vectors
1254 */
1255 static void rb_presolve_contacts( rb_ct *buffer, int len ){
1256 for( int i=0; i<len; i++ ){
1257 rb_ct *ct = &buffer[i];
1258 rb_prepare_contact( ct, k_rb_delta );
1259
1260 v3f ra, rb, raCn, rbCn, raCt, rbCt;
1261 v3_sub( ct->co, ct->rba->co, ra );
1262 v3_sub( ct->co, ct->rbb->co, rb );
1263 v3_cross( ra, ct->n, raCn );
1264 v3_cross( rb, ct->n, rbCn );
1265
1266 /* orient inverse inertia tensors */
1267 v3f raCnI, rbCnI;
1268 m3x3_mulv( ct->rba->iIw, raCn, raCnI );
1269 m3x3_mulv( ct->rbb->iIw, rbCn, rbCnI );
1270
1271 ct->normal_mass = ct->rba->inv_mass + ct->rbb->inv_mass;
1272 ct->normal_mass += v3_dot( raCn, raCnI );
1273 ct->normal_mass += v3_dot( rbCn, rbCnI );
1274 ct->normal_mass = 1.0f/ct->normal_mass;
1275
1276 for( int j=0; j<2; j++ ){
1277 v3f raCtI, rbCtI;
1278 v3_cross( ct->t[j], ra, raCt );
1279 v3_cross( ct->t[j], rb, rbCt );
1280 m3x3_mulv( ct->rba->iIw, raCt, raCtI );
1281 m3x3_mulv( ct->rbb->iIw, rbCt, rbCtI );
1282
1283 ct->tangent_mass[j] = ct->rba->inv_mass + ct->rbb->inv_mass;
1284 ct->tangent_mass[j] += v3_dot( raCt, raCtI );
1285 ct->tangent_mass[j] += v3_dot( rbCt, rbCtI );
1286 ct->tangent_mass[j] = 1.0f/ct->tangent_mass[j];
1287 }
1288
1289 rb_debug_contact( ct );
1290 }
1291 }
1292
1293 /*
1294 * Creates relative contact velocity vector
1295 */
1296 static void rb_rcv( rigidbody *rba, rigidbody *rbb, v3f ra, v3f rb, v3f rv ){
1297 v3f rva, rvb;
1298 v3_cross( rba->w, ra, rva );
1299 v3_add( rba->v, rva, rva );
1300 v3_cross( rbb->w, rb, rvb );
1301 v3_add( rbb->v, rvb, rvb );
1302
1303 v3_sub( rva, rvb, rv );
1304 }
1305
1306 static void rb_contact_restitution( rb_ct *ct, float cr ){
1307 v3f rv, ra, rb;
1308 v3_sub( ct->co, ct->rba->co, ra );
1309 v3_sub( ct->co, ct->rbb->co, rb );
1310 rb_rcv( ct->rba, ct->rbb, ra, rb, rv );
1311
1312 float v = v3_dot( rv, ct->n );
1313
1314 if( v < -1.0f ){
1315 ct->bias += -cr * v;
1316 }
1317 }
1318
1319 /*
1320 * Apply impulse to object
1321 */
1322 static void rb_linear_impulse( rigidbody *rb, v3f delta, v3f impulse ){
1323 /* linear */
1324 v3_muladds( rb->v, impulse, rb->inv_mass, rb->v );
1325
1326 /* Angular velocity */
1327 v3f wa;
1328 v3_cross( delta, impulse, wa );
1329
1330 m3x3_mulv( rb->iIw, wa, wa );
1331 v3_add( rb->w, wa, rb->w );
1332 }
1333
1334 /*
1335 * One iteration to solve the contact constraint
1336 */
1337 static void rb_solve_contacts( rb_ct *buf, int len ){
1338 for( int i=0; i<len; i++ ){
1339 struct contact *ct = &buf[i];
1340
1341 v3f rv, ra, rb;
1342 v3_sub( ct->co, ct->rba->co, ra );
1343 v3_sub( ct->co, ct->rbb->co, rb );
1344 rb_rcv( ct->rba, ct->rbb, ra, rb, rv );
1345
1346 /* Friction */
1347 for( int j=0; j<2; j++ ){
1348 float f = k_friction * ct->norm_impulse,
1349 vt = v3_dot( rv, ct->t[j] ),
1350 lambda = ct->tangent_mass[j] * -vt;
1351
1352 float temp = ct->tangent_impulse[j];
1353 ct->tangent_impulse[j] = vg_clampf( temp + lambda, -f, f );
1354 lambda = ct->tangent_impulse[j] - temp;
1355
1356 v3f impulse;
1357 v3_muls( ct->t[j], lambda, impulse );
1358 rb_linear_impulse( ct->rba, ra, impulse );
1359
1360 v3_muls( ct->t[j], -lambda, impulse );
1361 rb_linear_impulse( ct->rbb, rb, impulse );
1362 }
1363
1364 /* Normal */
1365 rb_rcv( ct->rba, ct->rbb, ra, rb, rv );
1366 float vn = v3_dot( rv, ct->n ),
1367 lambda = ct->normal_mass * (-vn + ct->bias);
1368
1369 float temp = ct->norm_impulse;
1370 ct->norm_impulse = vg_maxf( temp + lambda, 0.0f );
1371 lambda = ct->norm_impulse - temp;
1372
1373 v3f impulse;
1374 v3_muls( ct->n, lambda, impulse );
1375 rb_linear_impulse( ct->rba, ra, impulse );
1376
1377 v3_muls( ct->n, -lambda, impulse );
1378 rb_linear_impulse( ct->rbb, rb, impulse );
1379 }
1380 }
1381
1382 /*
1383 * -----------------------------------------------------------------------------
1384 * Constraints
1385 * -----------------------------------------------------------------------------
1386 */
1387
1388 static void rb_debug_position_constraints( rb_constr_pos *buffer, int len ){
1389 for( int i=0; i<len; i++ ){
1390 rb_constr_pos *constr = &buffer[i];
1391 rigidbody *rba = constr->rba, *rbb = constr->rbb;
1392
1393 v3f wca, wcb;
1394 m3x3_mulv( rba->to_world, constr->lca, wca );
1395 m3x3_mulv( rbb->to_world, constr->lcb, wcb );
1396
1397 v3f p0, p1;
1398 v3_add( wca, rba->co, p0 );
1399 v3_add( wcb, rbb->co, p1 );
1400 vg_line_point( p0, 0.0025f, 0xff000000 );
1401 vg_line_point( p1, 0.0025f, 0xffffffff );
1402 vg_line2( p0, p1, 0xff000000, 0xffffffff );
1403 }
1404 }
1405
1406 static void rb_presolve_swingtwist_constraints( rb_constr_swingtwist *buf,
1407 int len ){
1408 float size = 0.12f;
1409
1410 for( int i=0; i<len; i++ ){
1411 rb_constr_swingtwist *st = &buf[ i ];
1412
1413 v3f vx, vy, va, vxb, axis, center;
1414
1415 m3x3_mulv( st->rba->to_world, st->conevx, vx );
1416 m3x3_mulv( st->rbb->to_world, st->conevxb, vxb );
1417 m3x3_mulv( st->rba->to_world, st->conevy, vy );
1418 m3x3_mulv( st->rbb->to_world, st->coneva, va );
1419 m4x3_mulv( st->rba->to_world, st->view_offset, center );
1420 v3_cross( vy, vx, axis );
1421
1422 /* Constraint violated ? */
1423 float fx = v3_dot( vx, va ), /* projection world */
1424 fy = v3_dot( vy, va ),
1425 fn = v3_dot( va, axis ),
1426
1427 rx = st->conevx[3], /* elipse radii */
1428 ry = st->conevy[3],
1429
1430 lx = fx/rx, /* projection local (fn==lz) */
1431 ly = fy/ry;
1432
1433 st->tangent_violation = ((lx*lx + ly*ly) > fn*fn) || (fn <= 0.0f);
1434 if( st->tangent_violation ){
1435 /* Calculate a good position and the axis to solve on */
1436 v2f closest, tangent,
1437 p = { fx/fabsf(fn), fy/fabsf(fn) };
1438
1439 closest_point_elipse( p, (v2f){rx,ry}, closest );
1440 tangent[0] = -closest[1] / (ry*ry);
1441 tangent[1] = closest[0] / (rx*rx);
1442 v2_normalize( tangent );
1443
1444 v3f v0, v1;
1445 v3_muladds( axis, vx, closest[0], v0 );
1446 v3_muladds( v0, vy, closest[1], v0 );
1447 v3_normalize( v0 );
1448
1449 v3_muls( vx, tangent[0], v1 );
1450 v3_muladds( v1, vy, tangent[1], v1 );
1451
1452 v3_copy( v0, st->tangent_target );
1453 v3_copy( v1, st->tangent_axis );
1454
1455 /* calculate mass */
1456 v3f aIw, bIw;
1457 m3x3_mulv( st->rba->iIw, st->tangent_axis, aIw );
1458 m3x3_mulv( st->rbb->iIw, st->tangent_axis, bIw );
1459 st->tangent_mass = 1.0f / (v3_dot( st->tangent_axis, aIw ) +
1460 v3_dot( st->tangent_axis, bIw ));
1461
1462 float angle = v3_dot( va, st->tangent_target );
1463 }
1464
1465 v3f refaxis;
1466 v3_cross( vy, va, refaxis ); /* our default rotation */
1467 v3_normalize( refaxis );
1468
1469 float angle = v3_dot( refaxis, vxb );
1470 st->axis_violation = fabsf(angle) < st->conet;
1471
1472 if( st->axis_violation ){
1473 v3f dir_test;
1474 v3_cross( refaxis, vxb, dir_test );
1475
1476 if( v3_dot(dir_test, va) < 0.0f )
1477 st->axis_violation = -st->axis_violation;
1478
1479 float newang = (float)st->axis_violation * acosf(st->conet-0.0001f);
1480
1481 v3f refaxis_up;
1482 v3_cross( va, refaxis, refaxis_up );
1483 v3_muls( refaxis_up, sinf(newang), st->axis_target );
1484 v3_muladds( st->axis_target, refaxis, -cosf(newang), st->axis_target );
1485
1486 /* calculate mass */
1487 v3_copy( va, st->axis );
1488 v3f aIw, bIw;
1489 m3x3_mulv( st->rba->iIw, st->axis, aIw );
1490 m3x3_mulv( st->rbb->iIw, st->axis, bIw );
1491 st->axis_mass = 1.0f / (v3_dot( st->axis, aIw ) +
1492 v3_dot( st->axis, bIw ));
1493 }
1494 }
1495 }
1496
1497 static void rb_debug_swingtwist_constraints( rb_constr_swingtwist *buf,
1498 int len ){
1499 float size = 0.12f;
1500
1501 for( int i=0; i<len; i++ ){
1502 rb_constr_swingtwist *st = &buf[ i ];
1503
1504 v3f vx, vxb, vy, va, axis, center;
1505
1506 m3x3_mulv( st->rba->to_world, st->conevx, vx );
1507 m3x3_mulv( st->rbb->to_world, st->conevxb, vxb );
1508 m3x3_mulv( st->rba->to_world, st->conevy, vy );
1509 m3x3_mulv( st->rbb->to_world, st->coneva, va );
1510 m4x3_mulv( st->rba->to_world, st->view_offset, center );
1511 v3_cross( vy, vx, axis );
1512
1513 float rx = st->conevx[3], /* elipse radii */
1514 ry = st->conevy[3];
1515
1516 v3f p0, p1;
1517 v3_muladds( center, va, size, p1 );
1518 vg_line( center, p1, 0xffffffff );
1519 vg_line_point( p1, 0.00025f, 0xffffffff );
1520
1521 if( st->tangent_violation ){
1522 v3_muladds( center, st->tangent_target, size, p0 );
1523
1524 vg_line( center, p0, 0xff00ff00 );
1525 vg_line_point( p0, 0.00025f, 0xff00ff00 );
1526 vg_line( p1, p0, 0xff000000 );
1527 }
1528
1529 for( int x=0; x<32; x++ ){
1530 float t0 = ((float)x * (1.0f/32.0f)) * VG_TAUf,
1531 t1 = (((float)x+1.0f) * (1.0f/32.0f)) * VG_TAUf,
1532 c0 = cosf( t0 ),
1533 s0 = sinf( t0 ),
1534 c1 = cosf( t1 ),
1535 s1 = sinf( t1 );
1536
1537 v3f v0, v1;
1538 v3_muladds( axis, vx, c0*rx, v0 );
1539 v3_muladds( v0, vy, s0*ry, v0 );
1540 v3_muladds( axis, vx, c1*rx, v1 );
1541 v3_muladds( v1, vy, s1*ry, v1 );
1542
1543 v3_normalize( v0 );
1544 v3_normalize( v1 );
1545
1546 v3_muladds( center, v0, size, p0 );
1547 v3_muladds( center, v1, size, p1 );
1548
1549 u32 col0r = fabsf(c0) * 255.0f,
1550 col0g = fabsf(s0) * 255.0f,
1551 col1r = fabsf(c1) * 255.0f,
1552 col1g = fabsf(s1) * 255.0f,
1553 col = st->tangent_violation? 0xff0000ff: 0xff000000,
1554 col0 = col | (col0r<<16) | (col0g << 8),
1555 col1 = col | (col1r<<16) | (col1g << 8);
1556
1557 vg_line2( center, p0, VG__NONE, col0 );
1558 vg_line2( p0, p1, col0, col1 );
1559 }
1560
1561 /* Draw twist */
1562 v3_muladds( center, va, size, p0 );
1563 v3_muladds( p0, vxb, size, p1 );
1564
1565 vg_line( p0, p1, 0xff0000ff );
1566
1567 if( st->axis_violation ){
1568 v3_muladds( p0, st->axis_target, size*1.25f, p1 );
1569 vg_line( p0, p1, 0xffffff00 );
1570 vg_line_point( p1, 0.0025f, 0xffffff80 );
1571 }
1572
1573 v3f refaxis;
1574 v3_cross( vy, va, refaxis ); /* our default rotation */
1575 v3_normalize( refaxis );
1576 v3f refaxis_up;
1577 v3_cross( va, refaxis, refaxis_up );
1578 float newang = acosf(st->conet-0.0001f);
1579
1580 v3_muladds( p0, refaxis_up, sinf(newang)*size, p1 );
1581 v3_muladds( p1, refaxis, -cosf(newang)*size, p1 );
1582 vg_line( p0, p1, 0xff000000 );
1583
1584 v3_muladds( p0, refaxis_up, sinf(-newang)*size, p1 );
1585 v3_muladds( p1, refaxis, -cosf(-newang)*size, p1 );
1586 vg_line( p0, p1, 0xff404040 );
1587 }
1588 }
1589
1590 /*
1591 * Solve a list of positional constraints
1592 */
1593 static void rb_solve_position_constraints( rb_constr_pos *buf, int len ){
1594 for( int i=0; i<len; i++ ){
1595 rb_constr_pos *constr = &buf[i];
1596 rigidbody *rba = constr->rba, *rbb = constr->rbb;
1597
1598 v3f wa, wb;
1599 m3x3_mulv( rba->to_world, constr->lca, wa );
1600 m3x3_mulv( rbb->to_world, constr->lcb, wb );
1601
1602 m3x3f ssra, ssrat, ssrb, ssrbt;
1603
1604 m3x3_skew_symetric( ssrat, wa );
1605 m3x3_skew_symetric( ssrbt, wb );
1606 m3x3_transpose( ssrat, ssra );
1607 m3x3_transpose( ssrbt, ssrb );
1608
1609 v3f b, b_wa, b_wb, b_a, b_b;
1610 m3x3_mulv( ssra, rba->w, b_wa );
1611 m3x3_mulv( ssrb, rbb->w, b_wb );
1612 v3_add( rba->v, b_wa, b );
1613 v3_sub( b, rbb->v, b );
1614 v3_sub( b, b_wb, b );
1615 v3_muls( b, -1.0f, b );
1616
1617 m3x3f invMa, invMb;
1618 m3x3_diagonal( invMa, rba->inv_mass );
1619 m3x3_diagonal( invMb, rbb->inv_mass );
1620
1621 m3x3f ia, ib;
1622 m3x3_mul( ssra, rba->iIw, ia );
1623 m3x3_mul( ia, ssrat, ia );
1624 m3x3_mul( ssrb, rbb->iIw, ib );
1625 m3x3_mul( ib, ssrbt, ib );
1626
1627 m3x3f cma, cmb;
1628 m3x3_add( invMa, ia, cma );
1629 m3x3_add( invMb, ib, cmb );
1630
1631 m3x3f A;
1632 m3x3_add( cma, cmb, A );
1633
1634 /* Solve Ax = b ( A^-1*b = x ) */
1635 v3f impulse;
1636 m3x3f invA;
1637 m3x3_inv( A, invA );
1638 m3x3_mulv( invA, b, impulse );
1639
1640 v3f delta_va, delta_wa, delta_vb, delta_wb;
1641 m3x3f iwa, iwb;
1642 m3x3_mul( rba->iIw, ssrat, iwa );
1643 m3x3_mul( rbb->iIw, ssrbt, iwb );
1644
1645 m3x3_mulv( invMa, impulse, delta_va );
1646 m3x3_mulv( invMb, impulse, delta_vb );
1647 m3x3_mulv( iwa, impulse, delta_wa );
1648 m3x3_mulv( iwb, impulse, delta_wb );
1649
1650 v3_add( rba->v, delta_va, rba->v );
1651 v3_add( rba->w, delta_wa, rba->w );
1652 v3_sub( rbb->v, delta_vb, rbb->v );
1653 v3_sub( rbb->w, delta_wb, rbb->w );
1654 }
1655 }
1656
1657 static void rb_solve_swingtwist_constraints( rb_constr_swingtwist *buf,
1658 int len ){
1659 float size = 0.12f;
1660
1661 for( int i=0; i<len; i++ ){
1662 rb_constr_swingtwist *st = &buf[ i ];
1663
1664 if( !st->axis_violation )
1665 continue;
1666
1667 float rv = v3_dot( st->axis, st->rbb->w ) -
1668 v3_dot( st->axis, st->rba->w );
1669
1670 if( rv * (float)st->axis_violation > 0.0f )
1671 continue;
1672
1673 v3f impulse, wa, wb;
1674 v3_muls( st->axis, rv*st->axis_mass, impulse );
1675 m3x3_mulv( st->rba->iIw, impulse, wa );
1676 v3_add( st->rba->w, wa, st->rba->w );
1677
1678 v3_muls( impulse, -1.0f, impulse );
1679 m3x3_mulv( st->rbb->iIw, impulse, wb );
1680 v3_add( st->rbb->w, wb, st->rbb->w );
1681
1682 float rv2 = v3_dot( st->axis, st->rbb->w ) -
1683 v3_dot( st->axis, st->rba->w );
1684 }
1685
1686 for( int i=0; i<len; i++ ){
1687 rb_constr_swingtwist *st = &buf[ i ];
1688
1689 if( !st->tangent_violation )
1690 continue;
1691
1692 float rv = v3_dot( st->tangent_axis, st->rbb->w ) -
1693 v3_dot( st->tangent_axis, st->rba->w );
1694
1695 if( rv > 0.0f )
1696 continue;
1697
1698 v3f impulse, wa, wb;
1699 v3_muls( st->tangent_axis, rv*st->tangent_mass, impulse );
1700 m3x3_mulv( st->rba->iIw, impulse, wa );
1701 v3_add( st->rba->w, wa, st->rba->w );
1702
1703 v3_muls( impulse, -1.0f, impulse );
1704 m3x3_mulv( st->rbb->iIw, impulse, wb );
1705 v3_add( st->rbb->w, wb, st->rbb->w );
1706
1707 float rv2 = v3_dot( st->tangent_axis, st->rbb->w ) -
1708 v3_dot( st->tangent_axis, st->rba->w );
1709 }
1710 }
1711
1712 static void rb_solve_constr_angle( rigidbody *rba, rigidbody *rbb,
1713 v3f ra, v3f rb ){
1714 m3x3f ssra, ssrb, ssrat, ssrbt;
1715 m3x3f cma, cmb;
1716
1717 m3x3_skew_symetric( ssrat, ra );
1718 m3x3_skew_symetric( ssrbt, rb );
1719 m3x3_transpose( ssrat, ssra );
1720 m3x3_transpose( ssrbt, ssrb );
1721
1722 m3x3_mul( ssra, rba->iIw, cma );
1723 m3x3_mul( cma, ssrat, cma );
1724 m3x3_mul( ssrb, rbb->iIw, cmb );
1725 m3x3_mul( cmb, ssrbt, cmb );
1726
1727 m3x3f A, invA;
1728 m3x3_add( cma, cmb, A );
1729 m3x3_inv( A, invA );
1730
1731 v3f b_wa, b_wb, b;
1732 m3x3_mulv( ssra, rba->w, b_wa );
1733 m3x3_mulv( ssrb, rbb->w, b_wb );
1734 v3_add( b_wa, b_wb, b );
1735 v3_negate( b, b );
1736
1737 v3f impulse;
1738 m3x3_mulv( invA, b, impulse );
1739
1740 v3f delta_wa, delta_wb;
1741 m3x3f iwa, iwb;
1742 m3x3_mul( rba->iIw, ssrat, iwa );
1743 m3x3_mul( rbb->iIw, ssrbt, iwb );
1744 m3x3_mulv( iwa, impulse, delta_wa );
1745 m3x3_mulv( iwb, impulse, delta_wb );
1746 v3_add( rba->w, delta_wa, rba->w );
1747 v3_sub( rbb->w, delta_wb, rbb->w );
1748 }
1749
1750 /*
1751 * Correct position constraint drift errors
1752 * [ 0.0 <= amt <= 1.0 ]: the correction amount
1753 */
1754 static void rb_correct_position_constraints( rb_constr_pos *buf, int len,
1755 float amt ){
1756 for( int i=0; i<len; i++ ){
1757 rb_constr_pos *constr = &buf[i];
1758 rigidbody *rba = constr->rba, *rbb = constr->rbb;
1759
1760 v3f p0, p1, d;
1761 m3x3_mulv( rba->to_world, constr->lca, p0 );
1762 m3x3_mulv( rbb->to_world, constr->lcb, p1 );
1763 v3_add( rba->co, p0, p0 );
1764 v3_add( rbb->co, p1, p1 );
1765 v3_sub( p1, p0, d );
1766
1767 v3_muladds( rbb->co, d, -1.0f * amt, rbb->co );
1768 rb_update_transform( rbb );
1769 }
1770 }
1771
1772 static void rb_correct_swingtwist_constraints( rb_constr_swingtwist *buf,
1773 int len, float amt ){
1774 for( int i=0; i<len; i++ ){
1775 rb_constr_swingtwist *st = &buf[i];
1776
1777 if( !st->tangent_violation )
1778 continue;
1779
1780 v3f va;
1781 m3x3_mulv( st->rbb->to_world, st->coneva, va );
1782
1783 float angle = v3_dot( va, st->tangent_target );
1784
1785 if( fabsf(angle) < 0.9999f ){
1786 v3f axis;
1787 v3_cross( va, st->tangent_target, axis );
1788
1789 v4f correction;
1790 q_axis_angle( correction, axis, acosf(angle) * amt );
1791 q_mul( correction, st->rbb->q, st->rbb->q );
1792 rb_update_transform( st->rbb );
1793 }
1794 }
1795
1796 for( int i=0; i<len; i++ ){
1797 rb_constr_swingtwist *st = &buf[i];
1798
1799 if( !st->axis_violation )
1800 continue;
1801
1802 v3f vxb;
1803 m3x3_mulv( st->rbb->to_world, st->conevxb, vxb );
1804
1805 float angle = v3_dot( vxb, st->axis_target );
1806
1807 if( fabsf(angle) < 0.9999f ){
1808 v3f axis;
1809 v3_cross( vxb, st->axis_target, axis );
1810
1811 v4f correction;
1812 q_axis_angle( correction, axis, acosf(angle) * amt );
1813 q_mul( correction, st->rbb->q, st->rbb->q );
1814 rb_update_transform( st->rbb );
1815 }
1816 }
1817 }
1818
1819 static void rb_correct_contact_constraints( rb_ct *buf, int len, float amt ){
1820 for( int i=0; i<len; i++ ){
1821 rb_ct *ct = &buf[i];
1822 rigidbody *rba = ct->rba,
1823 *rbb = ct->rbb;
1824
1825 f32 mass_total = 1.0f / (rba->inv_mass + rbb->inv_mass),
1826 d = ct->p*mass_total*amt;
1827
1828 v3_muladds( rba->co, ct->n, -d * rba->inv_mass, rba->co );
1829 v3_muladds( rbb->co, ct->n, d * rbb->inv_mass, rbb->co );
1830 }
1831 }
1832
1833
1834 /*
1835 * Effectors
1836 */
1837
1838 static void rb_effect_simple_bouyency( rigidbody *ra, v4f plane,
1839 float amt, float drag ){
1840 /* float */
1841 float depth = v3_dot( plane, ra->co ) - plane[3],
1842 lambda = vg_clampf( -depth, 0.0f, 1.0f ) * amt;
1843
1844 v3_muladds( ra->v, plane, lambda * k_rb_delta, ra->v );
1845
1846 if( depth < 0.0f )
1847 v3_muls( ra->v, 1.0f-(drag*k_rb_delta), ra->v );
1848 }
1849
1850 /* apply a spring&dampener force to match ra(worldspace) on rigidbody, to
1851 * rt(worldspace)
1852 */
1853 static void rb_effect_spring_target_vector( rigidbody *rba, v3f ra, v3f rt,
1854 float spring, float dampening,
1855 float timestep ){
1856 float d = v3_dot( rt, ra );
1857 float a = acosf( vg_clampf( d, -1.0f, 1.0f ) );
1858
1859 v3f axis;
1860 v3_cross( rt, ra, axis );
1861
1862 float Fs = -a * spring,
1863 Fd = -v3_dot( rba->w, axis ) * dampening;
1864
1865 v3_muladds( rba->w, axis, (Fs+Fd) * timestep, rba->w );
1866 }
1867
1868 #endif /* RIGIDBODY_H */
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