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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 VG_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 VG_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 VG_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 VG_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 VG_STATIC void rb_update_bounds( rigidbody *rb )
195 {
196 box_copy( rb->bbx, rb->bbx_world );
197 m4x3_transform_aabb( rb->to_world, rb->bbx_world );
198 }
199
200 /*
201 * Commit transform to rigidbody. Updates matrices
202 */
203 VG_STATIC void rb_update_transform( rigidbody *rb )
204 {
205 q_normalize( rb->q );
206 q_m3x3( rb->q, rb->to_world );
207 v3_copy( rb->co, rb->to_world[3] );
208
209 m4x3_invert_affine( rb->to_world, rb->to_local );
210 m3x3_mul( rb->iI, rb->to_local, rb->iIw );
211 m3x3_mul( rb->to_world, rb->iIw, rb->iIw );
212
213 rb_update_bounds( rb );
214 }
215
216 /*
217 * Extrapolate rigidbody into a transform based on vg accumulator.
218 * Useful for rendering
219 */
220 VG_STATIC void rb_extrapolate( rigidbody *rb, v3f co, v4f q )
221 {
222 float substep = vg.time_fixed_extrapolate;
223 v3_muladds( rb->co, rb->v, k_rb_delta*substep, co );
224
225 if( v3_length2( rb->w ) > 0.0f ){
226 v4f rotation;
227 v3f axis;
228 v3_copy( rb->w, axis );
229
230 float mag = v3_length( axis );
231 v3_divs( axis, mag, axis );
232 q_axis_angle( rotation, axis, mag*k_rb_delta*substep );
233 q_mul( rotation, rb->q, q );
234 q_normalize( q );
235 }
236 else{
237 v4_copy( rb->q, q );
238 }
239 }
240
241 /*
242 * Initialize rigidbody and calculate masses, inertia
243 */
244 VG_STATIC void rb_init_object( rb_object *obj ){
245 float volume = 1.0f;
246 int inert = 0;
247
248 if( obj->type == k_rb_shape_box ){
249 v3f dims;
250 v3_sub( obj->rb.bbx[1], obj->rb.bbx[0], dims );
251 volume = dims[0]*dims[1]*dims[2];
252 }
253 else if( obj->type == k_rb_shape_sphere ){
254 volume = vg_sphere_volume( obj->inf.sphere.radius );
255 v3_fill( obj->rb.bbx[0], -obj->inf.sphere.radius );
256 v3_fill( obj->rb.bbx[1], obj->inf.sphere.radius );
257 }
258 else if( obj->type == k_rb_shape_capsule ){
259 float r = obj->inf.capsule.radius,
260 h = obj->inf.capsule.height;
261 volume = vg_sphere_volume( r ) + VG_PIf * r*r * (h - r*2.0f);
262
263 v3_fill( obj->rb.bbx[0], -r );
264 v3_fill( obj->rb.bbx[1], r );
265 obj->rb.bbx[0][1] = -h;
266 obj->rb.bbx[1][1] = h;
267 }
268 else if( obj->type == k_rb_shape_scene ){
269 inert = 1;
270 box_copy( obj->inf.scene.bh_scene->nodes[0].bbx, obj->rb.bbx );
271 }
272
273 if( inert ){
274 obj->rb.inv_mass = 0.0f;
275 v3_zero( obj->rb.I );
276 m3x3_zero( obj->rb.iI );
277 }
278 else{
279 float mass = 2.0f*volume;
280 obj->rb.inv_mass = 1.0f/mass;
281
282 v3f extent;
283 v3_sub( obj->rb.bbx[1], obj->rb.bbx[0], extent );
284 v3_muls( extent, 0.5f, extent );
285
286 /* local intertia tensor */
287 float scale = k_inertia_scale;
288 float ex2 = scale*extent[0]*extent[0],
289 ey2 = scale*extent[1]*extent[1],
290 ez2 = scale*extent[2]*extent[2];
291
292 obj->rb.I[0] = ((1.0f/12.0f) * mass * (ey2+ez2));
293 obj->rb.I[1] = ((1.0f/12.0f) * mass * (ex2+ez2));
294 obj->rb.I[2] = ((1.0f/12.0f) * mass * (ex2+ey2));
295
296 m3x3_identity( obj->rb.iI );
297 obj->rb.iI[0][0] = obj->rb.I[0];
298 obj->rb.iI[1][1] = obj->rb.I[1];
299 obj->rb.iI[2][2] = obj->rb.I[2];
300 m3x3_inv( obj->rb.iI, obj->rb.iI );
301 }
302
303 rb_update_transform( &obj->rb );
304 }
305
306 VG_STATIC void rb_iter( rigidbody *rb ){
307 if( !vg_validf( rb->v[0] ) ||
308 !vg_validf( rb->v[1] ) ||
309 !vg_validf( rb->v[2] ) )
310 {
311 vg_fatal_error( "NaN velocity" );
312 }
313
314 v3f gravity = { 0.0f, -9.8f, 0.0f };
315 v3_muladds( rb->v, gravity, k_rb_delta, rb->v );
316
317 /* intergrate velocity */
318 v3_muladds( rb->co, rb->v, k_rb_delta, rb->co );
319 v3_lerp( rb->w, (v3f){0.0f,0.0f,0.0f}, 0.0025f, rb->w );
320
321 /* inegrate inertia */
322 if( v3_length2( rb->w ) > 0.0f )
323 {
324 v4f rotation;
325 v3f axis;
326 v3_copy( rb->w, axis );
327
328 float mag = v3_length( axis );
329 v3_divs( axis, mag, axis );
330 q_axis_angle( rotation, axis, mag*k_rb_delta );
331 q_mul( rotation, rb->q, rb->q );
332 }
333
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 }
338
339
340 /*
341 * -----------------------------------------------------------------------------
342 * Boolean shape overlap functions
343 * -----------------------------------------------------------------------------
344 */
345
346 /*
347 * Project AABB, and triangle interval onto axis to check if they overlap
348 */
349 VG_STATIC int rb_box_triangle_interval( v3f extent, v3f axis, v3f tri[3] ){
350 float
351
352 r = extent[0] * fabsf(axis[0]) +
353 extent[1] * fabsf(axis[1]) +
354 extent[2] * fabsf(axis[2]),
355
356 p0 = v3_dot( axis, tri[0] ),
357 p1 = v3_dot( axis, tri[1] ),
358 p2 = v3_dot( axis, tri[2] ),
359
360 e = vg_maxf(-vg_maxf(p0,vg_maxf(p1,p2)), vg_minf(p0,vg_minf(p1,p2)));
361
362 if( e > r ) return 0;
363 else return 1;
364 }
365
366 /*
367 * Seperating axis test box vs triangle
368 */
369 VG_STATIC int rb_box_triangle_sat( v3f extent, v3f center,
370 m4x3f to_local, v3f tri_src[3] ){
371 v3f tri[3];
372
373 for( int i=0; i<3; i++ ){
374 m4x3_mulv( to_local, tri_src[i], tri[i] );
375 v3_sub( tri[i], center, tri[i] );
376 }
377
378 v3f f0,f1,f2,n;
379 v3_sub( tri[1], tri[0], f0 );
380 v3_sub( tri[2], tri[1], f1 );
381 v3_sub( tri[0], tri[2], f2 );
382
383
384 v3f axis[9];
385 v3_cross( (v3f){1.0f,0.0f,0.0f}, f0, axis[0] );
386 v3_cross( (v3f){1.0f,0.0f,0.0f}, f1, axis[1] );
387 v3_cross( (v3f){1.0f,0.0f,0.0f}, f2, axis[2] );
388 v3_cross( (v3f){0.0f,1.0f,0.0f}, f0, axis[3] );
389 v3_cross( (v3f){0.0f,1.0f,0.0f}, f1, axis[4] );
390 v3_cross( (v3f){0.0f,1.0f,0.0f}, f2, axis[5] );
391 v3_cross( (v3f){0.0f,0.0f,1.0f}, f0, axis[6] );
392 v3_cross( (v3f){0.0f,0.0f,1.0f}, f1, axis[7] );
393 v3_cross( (v3f){0.0f,0.0f,1.0f}, f2, axis[8] );
394
395 for( int i=0; i<9; i++ )
396 if(!rb_box_triangle_interval( extent, axis[i], tri )) return 0;
397
398 /* u0, u1, u2 */
399 if(!rb_box_triangle_interval( extent, (v3f){1.0f,0.0f,0.0f}, tri )) return 0;
400 if(!rb_box_triangle_interval( extent, (v3f){0.0f,1.0f,0.0f}, tri )) return 0;
401 if(!rb_box_triangle_interval( extent, (v3f){0.0f,0.0f,1.0f}, tri )) return 0;
402
403 /* normal */
404 v3_cross( f0, f1, n );
405 if(!rb_box_triangle_interval( extent, n, tri )) return 0;
406
407 return 1;
408 }
409
410 /*
411 * -----------------------------------------------------------------------------
412 * Manifold
413 * -----------------------------------------------------------------------------
414 */
415
416 VG_STATIC int rb_manifold_apply_filtered( rb_ct *man, int len ){
417 int k = 0;
418
419 for( int i=0; i<len; i++ ){
420 rb_ct *ct = &man[i];
421
422 if( ct->type == k_contact_type_disabled )
423 continue;
424
425 man[k ++] = man[i];
426 }
427
428 return k;
429 }
430
431 /*
432 * Merge two contacts if they are within radius(r) of eachother
433 */
434 VG_STATIC void rb_manifold_contact_weld( rb_ct *ci, rb_ct *cj, float r ){
435 if( v3_dist2( ci->co, cj->co ) < r*r ){
436 cj->type = k_contact_type_disabled;
437 ci->p = (ci->p + cj->p) * 0.5f;
438
439 v3_add( ci->co, cj->co, ci->co );
440 v3_muls( ci->co, 0.5f, ci->co );
441
442 v3f delta;
443 v3_sub( ci->rba->co, ci->co, delta );
444
445 float c0 = v3_dot( ci->n, delta ),
446 c1 = v3_dot( cj->n, delta );
447
448 if( c0 < 0.0f || c1 < 0.0f ){
449 /* error */
450 ci->type = k_contact_type_disabled;
451 }
452 else{
453 v3f n;
454 v3_muls( ci->n, c0, n );
455 v3_muladds( n, cj->n, c1, n );
456 v3_normalize( n );
457 v3_copy( n, ci->n );
458 }
459 }
460 }
461
462 /*
463 *
464 */
465 VG_STATIC void rb_manifold_filter_joint_edges( rb_ct *man, int len, float r ){
466 for( int i=0; i<len-1; i++ ){
467 rb_ct *ci = &man[i];
468 if( ci->type != k_contact_type_edge )
469 continue;
470
471 for( int j=i+1; j<len; j++ ){
472 rb_ct *cj = &man[j];
473 if( cj->type != k_contact_type_edge )
474 continue;
475
476 rb_manifold_contact_weld( ci, cj, r );
477 }
478 }
479 }
480
481 /*
482 * Resolve overlapping pairs
483 */
484 VG_STATIC void rb_manifold_filter_pairs( rb_ct *man, int len, float r ){
485 for( int i=0; i<len-1; i++ ){
486 rb_ct *ci = &man[i];
487 int similar = 0;
488
489 if( ci->type == k_contact_type_disabled ) continue;
490
491 for( int j=i+1; j<len; j++ ){
492 rb_ct *cj = &man[j];
493
494 if( cj->type == k_contact_type_disabled ) continue;
495
496 if( v3_dist2( ci->co, cj->co ) < r*r ){
497 cj->type = k_contact_type_disabled;
498 v3_add( cj->n, ci->n, ci->n );
499 ci->p += cj->p;
500 similar ++;
501 }
502 }
503
504 if( similar ){
505 float n = 1.0f/((float)similar+1.0f);
506 v3_muls( ci->n, n, ci->n );
507 ci->p *= n;
508
509 if( v3_length2(ci->n) < 0.1f*0.1f )
510 ci->type = k_contact_type_disabled;
511 else
512 v3_normalize( ci->n );
513 }
514 }
515 }
516
517 /*
518 * Remove contacts that are facing away from A
519 */
520 VG_STATIC void rb_manifold_filter_backface( rb_ct *man, int len ){
521 for( int i=0; i<len; i++ ){
522 rb_ct *ct = &man[i];
523 if( ct->type == k_contact_type_disabled )
524 continue;
525
526 v3f delta;
527 v3_sub( ct->co, ct->rba->co, delta );
528
529 if( v3_dot( delta, ct->n ) > -0.001f )
530 ct->type = k_contact_type_disabled;
531 }
532 }
533
534 /*
535 * Filter out duplicate coplanar results. Good for spheres.
536 */
537 VG_STATIC void rb_manifold_filter_coplanar( rb_ct *man, int len, float w ){
538 for( int i=0; i<len; i++ ){
539 rb_ct *ci = &man[i];
540 if( ci->type == k_contact_type_disabled ||
541 ci->type == k_contact_type_edge )
542 continue;
543
544 float d1 = v3_dot( ci->co, ci->n );
545
546 for( int j=0; j<len; j++ ){
547 if( j == i )
548 continue;
549
550 rb_ct *cj = &man[j];
551 if( cj->type == k_contact_type_disabled )
552 continue;
553
554 float d2 = v3_dot( cj->co, ci->n ),
555 d = d2-d1;
556
557 if( fabsf( d ) <= w ){
558 cj->type = k_contact_type_disabled;
559 }
560 }
561 }
562 }
563
564 /*
565 * -----------------------------------------------------------------------------
566 * Collision matrix
567 * -----------------------------------------------------------------------------
568 */
569
570 /*
571 * Contact generators
572 *
573 * These do not automatically allocate contacts, an appropriately sized
574 * buffer must be supplied. The function returns the size of the manifold
575 * which was generated.
576 *
577 * The values set on the contacts are: n, co, p, rba, rbb
578 */
579
580 /*
581 * By collecting the minimum(time) and maximum(time) pairs of points, we
582 * build a reduced and stable exact manifold.
583 *
584 * tx: time at point
585 * rx: minimum distance of these points
586 * dx: the delta between the two points
587 *
588 * pairs will only ammend these if they are creating a collision
589 */
590 typedef struct capsule_manifold capsule_manifold;
591 struct capsule_manifold{
592 float t0, t1;
593 float r0, r1;
594 v3f d0, d1;
595 };
596
597 /*
598 * Expand a line manifold with a new pair. t value is the time along segment
599 * on the oriented object which created this pair.
600 */
601 VG_STATIC void rb_capsule_manifold( v3f pa, v3f pb, float t, float r,
602 capsule_manifold *manifold ){
603 v3f delta;
604 v3_sub( pa, pb, delta );
605
606 if( v3_length2(delta) < r*r ){
607 if( t < manifold->t0 ){
608 v3_copy( delta, manifold->d0 );
609 manifold->t0 = t;
610 manifold->r0 = r;
611 }
612
613 if( t > manifold->t1 ){
614 v3_copy( delta, manifold->d1 );
615 manifold->t1 = t;
616 manifold->r1 = r;
617 }
618 }
619 }
620
621 VG_STATIC void rb_capsule_manifold_init( capsule_manifold *manifold ){
622 manifold->t0 = INFINITY;
623 manifold->t1 = -INFINITY;
624 }
625
626 VG_STATIC int rb_capsule__manifold_done( m4x3f mtx, rb_capsule *c,
627 capsule_manifold *manifold,
628 rb_ct *buf ){
629 v3f p0, p1;
630 v3_muladds( mtx[3], mtx[1], -c->height*0.5f+c->radius, p0 );
631 v3_muladds( mtx[3], mtx[1], c->height*0.5f-c->radius, p1 );
632
633 int count = 0;
634 if( manifold->t0 <= 1.0f ){
635 rb_ct *ct = buf;
636
637 v3f pa;
638 v3_muls( p0, 1.0f-manifold->t0, pa );
639 v3_muladds( pa, p1, manifold->t0, pa );
640
641 float d = v3_length( manifold->d0 );
642 v3_muls( manifold->d0, 1.0f/d, ct->n );
643 v3_muladds( pa, ct->n, -c->radius, ct->co );
644
645 ct->p = manifold->r0 - d;
646 ct->type = k_contact_type_default;
647 count ++;
648 }
649
650 if( (manifold->t1 >= 0.0f) && (manifold->t0 != manifold->t1) ){
651 rb_ct *ct = buf+count;
652
653 v3f pa;
654 v3_muls( p0, 1.0f-manifold->t1, pa );
655 v3_muladds( pa, p1, manifold->t1, pa );
656
657 float d = v3_length( manifold->d1 );
658 v3_muls( manifold->d1, 1.0f/d, ct->n );
659 v3_muladds( pa, ct->n, -c->radius, ct->co );
660
661 ct->p = manifold->r1 - d;
662 ct->type = k_contact_type_default;
663
664 count ++;
665 }
666
667 /*
668 * Debugging
669 */
670
671 if( count == 2 )
672 vg_line( buf[0].co, buf[1].co, 0xff0000ff );
673
674 return count;
675 }
676
677 VG_STATIC int rb_capsule_sphere( rb_object *obja, rb_object *objb, rb_ct *buf ){
678 rigidbody *rba = &obja->rb, *rbb = &objb->rb;
679 float h = obja->inf.capsule.height,
680 ra = obja->inf.capsule.radius,
681 rb = objb->inf.sphere.radius;
682
683 v3f p0, p1;
684 v3_muladds( rba->co, rba->to_world[1], -h*0.5f+ra, p0 );
685 v3_muladds( rba->co, rba->to_world[1], h*0.5f-ra, p1 );
686
687 v3f c, delta;
688 closest_point_segment( p0, p1, rbb->co, c );
689 v3_sub( c, rbb->co, delta );
690
691 float d2 = v3_length2(delta),
692 r = ra + rb;
693
694 if( d2 < r*r ){
695 float d = sqrtf(d2);
696
697 rb_ct *ct = buf;
698 v3_muls( delta, 1.0f/d, ct->n );
699 ct->p = r-d;
700
701 v3f p0, p1;
702 v3_muladds( c, ct->n, -ra, p0 );
703 v3_muladds( rbb->co, ct->n, rb, p1 );
704 v3_add( p0, p1, ct->co );
705 v3_muls( ct->co, 0.5f, ct->co );
706
707 ct->rba = rba;
708 ct->rbb = rbb;
709 ct->type = k_contact_type_default;
710
711 return 1;
712 }
713
714 return 0;
715 }
716
717 VG_STATIC int rb_capsule__capsule( m4x3f mtxA, rb_capsule *ca,
718 m4x3f mtxB, rb_capsule *cb, rb_ct *buf ){
719 float ha = ca->height,
720 hb = cb->height,
721 ra = ca->radius,
722 rb = cb->radius,
723 r = ra+rb;
724
725 v3f p0, p1, p2, p3;
726 v3_muladds( mtxA[3], mtxA[1], -ha*0.5f+ra, p0 );
727 v3_muladds( mtxA[3], mtxA[1], ha*0.5f-ra, p1 );
728 v3_muladds( mtxB[3], mtxB[1], -hb*0.5f+rb, p2 );
729 v3_muladds( mtxB[3], mtxB[1], hb*0.5f-rb, p3 );
730
731 capsule_manifold manifold;
732 rb_capsule_manifold_init( &manifold );
733
734 v3f pa, pb;
735 float ta, tb;
736 closest_segment_segment( p0, p1, p2, p3, &ta, &tb, pa, pb );
737 rb_capsule_manifold( pa, pb, ta, r, &manifold );
738
739 ta = closest_point_segment( p0, p1, p2, pa );
740 tb = closest_point_segment( p0, p1, p3, pb );
741 rb_capsule_manifold( pa, p2, ta, r, &manifold );
742 rb_capsule_manifold( pb, p3, tb, r, &manifold );
743
744 closest_point_segment( p2, p3, p0, pa );
745 closest_point_segment( p2, p3, p1, pb );
746 rb_capsule_manifold( p0, pa, 0.0f, r, &manifold );
747 rb_capsule_manifold( p1, pb, 1.0f, r, &manifold );
748
749 return rb_capsule__manifold_done( mtxA, ca, &manifold, buf );
750 }
751
752 VG_STATIC int rb_sphere_box( rb_object *obja, rb_object *objb, rb_ct *buf ){
753 v3f co, delta;
754 rigidbody *rba = &obja->rb, *rbb = &objb->rb;
755
756 closest_point_obb( rba->co, rbb->bbx, rbb->to_world, rbb->to_local, co );
757 v3_sub( rba->co, co, delta );
758
759 float d2 = v3_length2(delta),
760 r = obja->inf.sphere.radius;
761
762 if( d2 <= r*r ){
763 float d;
764
765 rb_ct *ct = buf;
766 if( d2 <= 0.0001f ){
767 v3_sub( rba->co, rbb->co, delta );
768
769 /*
770 * some extra testing is required to find the best axis to push the
771 * object back outside the box. Since there isnt a clear seperating
772 * vector already, especially on really high aspect boxes.
773 */
774 float lx = v3_dot( rbb->to_world[0], delta ),
775 ly = v3_dot( rbb->to_world[1], delta ),
776 lz = v3_dot( rbb->to_world[2], delta ),
777 px = rbb->bbx[1][0] - fabsf(lx),
778 py = rbb->bbx[1][1] - fabsf(ly),
779 pz = rbb->bbx[1][2] - fabsf(lz);
780
781 if( px < py && px < pz )
782 v3_muls( rbb->to_world[0], vg_signf(lx), ct->n );
783 else if( py < pz )
784 v3_muls( rbb->to_world[1], vg_signf(ly), ct->n );
785 else
786 v3_muls( rbb->to_world[2], vg_signf(lz), ct->n );
787
788 v3_muladds( rba->co, ct->n, -r, ct->co );
789 ct->p = r;
790 }
791 else{
792 d = sqrtf(d2);
793 v3_muls( delta, 1.0f/d, ct->n );
794 ct->p = r-d;
795 v3_copy( co, ct->co );
796 }
797
798 ct->rba = rba;
799 ct->rbb = rbb;
800 ct->type = k_contact_type_default;
801 return 1;
802 }
803
804 return 0;
805 }
806
807 VG_STATIC int rb_sphere_sphere( rb_object *obja, rb_object *objb, rb_ct *buf ){
808 rigidbody *rba = &obja->rb, *rbb = &objb->rb;
809 v3f delta;
810 v3_sub( rba->co, rbb->co, delta );
811
812 float d2 = v3_length2(delta),
813 r = obja->inf.sphere.radius + objb->inf.sphere.radius;
814
815 if( d2 < r*r ){
816 float d = sqrtf(d2);
817
818 rb_ct *ct = buf;
819 v3_muls( delta, 1.0f/d, ct->n );
820
821 v3f p0, p1;
822 v3_muladds( rba->co, ct->n,-obja->inf.sphere.radius, p0 );
823 v3_muladds( rbb->co, ct->n, objb->inf.sphere.radius, p1 );
824 v3_add( p0, p1, ct->co );
825 v3_muls( ct->co, 0.5f, ct->co );
826 ct->type = k_contact_type_default;
827 ct->p = r-d;
828 ct->rba = rba;
829 ct->rbb = rbb;
830 return 1;
831 }
832
833 return 0;
834 }
835
836 VG_STATIC int rb_sphere__triangle( m4x3f mtxA, rb_sphere *b,
837 v3f tri[3], rb_ct *buf ){
838 v3f delta, co;
839 enum contact_type type = closest_on_triangle_1( mtxA[3], tri, co );
840
841 v3_sub( mtxA[3], co, delta );
842
843 float d2 = v3_length2( delta ),
844 r = b->radius;
845
846 if( d2 <= r*r ){
847 rb_ct *ct = buf;
848
849 v3f ab, ac, tn;
850 v3_sub( tri[2], tri[0], ab );
851 v3_sub( tri[1], tri[0], ac );
852 v3_cross( ac, ab, tn );
853 v3_copy( tn, ct->n );
854
855 if( v3_length2( ct->n ) <= 0.00001f ){
856 vg_error( "Zero area triangle!\n" );
857 return 0;
858 }
859
860 v3_normalize( ct->n );
861
862 float d = sqrtf(d2);
863
864 v3_copy( co, ct->co );
865 ct->type = type;
866 ct->p = r-d;
867 return 1;
868 }
869
870 return 0;
871 }
872
873 VG_STATIC int rb_sphere__scene( m4x3f mtxA, rb_sphere *b,
874 m4x3f mtxB, rb_scene *s, rb_ct *buf ){
875 scene_context *sc = s->bh_scene->user;
876
877 int count = 0;
878
879 float r = b->radius + 0.1f;
880 boxf box;
881 v3_sub( mtxA[3], (v3f){ r,r,r }, box[0] );
882 v3_add( mtxA[3], (v3f){ r,r,r }, box[1] );
883
884 bh_iter it;
885 i32 idx;
886 bh_iter_init_box( 0, &it, box );
887
888 while( bh_next( s->bh_scene, &it, &idx ) ){
889 u32 *ptri = &sc->arrindices[ idx*3 ];
890 v3f tri[3];
891
892 for( int j=0; j<3; j++ )
893 v3_copy( sc->arrvertices[ptri[j]].co, tri[j] );
894
895 buf[ count ].element_id = ptri[0];
896
897 vg_line( tri[0],tri[1],0x70ff6000 );
898 vg_line( tri[1],tri[2],0x70ff6000 );
899 vg_line( tri[2],tri[0],0x70ff6000 );
900
901 int contact = rb_sphere__triangle( mtxA, b, tri, &buf[count] );
902 count += contact;
903
904 if( count == 16 ){
905 vg_warn( "Exceeding sphere_vs_scene capacity. Geometry too dense!\n" );
906 return count;
907 }
908 }
909
910 return count;
911 }
912
913 VG_STATIC int rb_box__scene( m4x3f mtxA, boxf bbx,
914 m4x3f mtxB, rb_scene *s, rb_ct *buf ){
915 scene_context *sc = s->bh_scene->user;
916 v3f tri[3];
917
918 v3f extent, center;
919 v3_sub( bbx[1], bbx[0], extent );
920 v3_muls( extent, 0.5f, extent );
921 v3_add( bbx[0], extent, center );
922
923 float r = v3_length(extent);
924 boxf world_bbx;
925 v3_fill( world_bbx[0], -r );
926 v3_fill( world_bbx[1], r );
927 for( int i=0; i<2; i++ ){
928 v3_add( center, world_bbx[i], world_bbx[i] );
929 v3_add( mtxA[3], world_bbx[i], world_bbx[i] );
930 }
931
932 m4x3f to_local;
933 m4x3_invert_affine( mtxA, to_local );
934
935 bh_iter it;
936 bh_iter_init_box( 0, &it, world_bbx );
937 int idx;
938 int count = 0;
939
940 vg_line_boxf( world_bbx, VG__RED );
941
942 while( bh_next( s->bh_scene, &it, &idx ) ){
943 u32 *ptri = &sc->arrindices[ idx*3 ];
944
945 for( int j=0; j<3; j++ )
946 v3_copy( sc->arrvertices[ptri[j]].co, tri[j] );
947
948 if( rb_box_triangle_sat( extent, center, to_local, tri ) ){
949 vg_line(tri[0],tri[1],0xff50ff00 );
950 vg_line(tri[1],tri[2],0xff50ff00 );
951 vg_line(tri[2],tri[0],0xff50ff00 );
952 }
953 else{
954 vg_line(tri[0],tri[1],0xff0000ff );
955 vg_line(tri[1],tri[2],0xff0000ff );
956 vg_line(tri[2],tri[0],0xff0000ff );
957 continue;
958 }
959
960 v3f v0,v1,n;
961 v3_sub( tri[1], tri[0], v0 );
962 v3_sub( tri[2], tri[0], v1 );
963 v3_cross( v0, v1, n );
964 v3_normalize( n );
965
966 /* find best feature */
967 float best = v3_dot( mtxA[0], n );
968 int axis = 0;
969
970 for( int i=1; i<3; i++ ){
971 float c = v3_dot( mtxA[i], n );
972
973 if( fabsf(c) > fabsf(best) ){
974 best = c;
975 axis = i;
976 }
977 }
978
979 v3f manifold[4];
980
981 if( axis == 0 ){
982 float px = best > 0.0f? bbx[0][0]: bbx[1][0];
983 manifold[0][0] = px;
984 manifold[0][1] = bbx[0][1];
985 manifold[0][2] = bbx[0][2];
986 manifold[1][0] = px;
987 manifold[1][1] = bbx[1][1];
988 manifold[1][2] = bbx[0][2];
989 manifold[2][0] = px;
990 manifold[2][1] = bbx[1][1];
991 manifold[2][2] = bbx[1][2];
992 manifold[3][0] = px;
993 manifold[3][1] = bbx[0][1];
994 manifold[3][2] = bbx[1][2];
995 }
996 else if( axis == 1 ){
997 float py = best > 0.0f? bbx[0][1]: bbx[1][1];
998 manifold[0][0] = bbx[0][0];
999 manifold[0][1] = py;
1000 manifold[0][2] = bbx[0][2];
1001 manifold[1][0] = bbx[1][0];
1002 manifold[1][1] = py;
1003 manifold[1][2] = bbx[0][2];
1004 manifold[2][0] = bbx[1][0];
1005 manifold[2][1] = py;
1006 manifold[2][2] = bbx[1][2];
1007 manifold[3][0] = bbx[0][0];
1008 manifold[3][1] = py;
1009 manifold[3][2] = bbx[1][2];
1010 }
1011 else{
1012 float pz = best > 0.0f? bbx[0][2]: bbx[1][2];
1013 manifold[0][0] = bbx[0][0];
1014 manifold[0][1] = bbx[0][1];
1015 manifold[0][2] = pz;
1016 manifold[1][0] = bbx[1][0];
1017 manifold[1][1] = bbx[0][1];
1018 manifold[1][2] = pz;
1019 manifold[2][0] = bbx[1][0];
1020 manifold[2][1] = bbx[1][1];
1021 manifold[2][2] = pz;
1022 manifold[3][0] = bbx[0][0];
1023 manifold[3][1] = bbx[1][1];
1024 manifold[3][2] = pz;
1025 }
1026
1027 for( int j=0; j<4; j++ )
1028 m4x3_mulv( mtxA, manifold[j], manifold[j] );
1029
1030 vg_line( manifold[0], manifold[1], 0xffffffff );
1031 vg_line( manifold[1], manifold[2], 0xffffffff );
1032 vg_line( manifold[2], manifold[3], 0xffffffff );
1033 vg_line( manifold[3], manifold[0], 0xffffffff );
1034
1035 for( int j=0; j<4; j++ ){
1036 rb_ct *ct = buf+count;
1037
1038 v3_copy( manifold[j], ct->co );
1039 v3_copy( n, ct->n );
1040
1041 float l0 = v3_dot( tri[0], n ),
1042 l1 = v3_dot( manifold[j], n );
1043
1044 ct->p = (l0-l1)*0.5f;
1045 if( ct->p < 0.0f )
1046 continue;
1047
1048 ct->type = k_contact_type_default;
1049 count ++;
1050
1051 if( count >= 12 )
1052 return count;
1053 }
1054 }
1055 return count;
1056 }
1057
1058 VG_STATIC int rb_capsule__triangle( m4x3f mtxA, rb_capsule *c,
1059 v3f tri[3], rb_ct *buf ){
1060 v3f pc, p0w, p1w;
1061 v3_muladds( mtxA[3], mtxA[1], -c->height*0.5f+c->radius, p0w );
1062 v3_muladds( mtxA[3], mtxA[1], c->height*0.5f-c->radius, p1w );
1063
1064 capsule_manifold manifold;
1065 rb_capsule_manifold_init( &manifold );
1066
1067 v3f c0, c1;
1068 closest_on_triangle_1( p0w, tri, c0 );
1069 closest_on_triangle_1( p1w, tri, c1 );
1070
1071 v3f d0, d1, da;
1072 v3_sub( c0, p0w, d0 );
1073 v3_sub( c1, p1w, d1 );
1074 v3_sub( p1w, p0w, da );
1075
1076 v3_normalize(d0);
1077 v3_normalize(d1);
1078 v3_normalize(da);
1079
1080 if( v3_dot( da, d0 ) <= 0.01f )
1081 rb_capsule_manifold( p0w, c0, 0.0f, c->radius, &manifold );
1082
1083 if( v3_dot( da, d1 ) >= -0.01f )
1084 rb_capsule_manifold( p1w, c1, 1.0f, c->radius, &manifold );
1085
1086 for( int i=0; i<3; i++ ){
1087 int i0 = i,
1088 i1 = (i+1)%3;
1089
1090 v3f ca, cb;
1091 float ta, tb;
1092 closest_segment_segment( p0w, p1w, tri[i0], tri[i1], &ta, &tb, ca, cb );
1093 rb_capsule_manifold( ca, cb, ta, c->radius, &manifold );
1094 }
1095
1096 v3f v0, v1, n;
1097 v3_sub( tri[1], tri[0], v0 );
1098 v3_sub( tri[2], tri[0], v1 );
1099 v3_cross( v0, v1, n );
1100
1101 if( v3_length2( n ) <= 0.00001f ){
1102 vg_error( "Zero area triangle!\n" );
1103 return 0;
1104 }
1105
1106 v3_normalize( n );
1107
1108 int count = rb_capsule__manifold_done( mtxA, c, &manifold, buf );
1109 for( int i=0; i<count; i++ )
1110 v3_copy( n, buf[i].n );
1111
1112 return count;
1113 }
1114
1115 /* mtxB is defined only for tradition; it is not used currently */
1116 VG_STATIC int rb_capsule__scene( m4x3f mtxA, rb_capsule *c,
1117 m4x3f mtxB, rb_scene *s,
1118 rb_ct *buf ){
1119 int count = 0;
1120
1121 boxf bbx;
1122 v3_sub( mtxA[3], (v3f){ c->height, c->height, c->height }, bbx[0] );
1123 v3_add( mtxA[3], (v3f){ c->height, c->height, c->height }, bbx[1] );
1124
1125 scene_context *sc = s->bh_scene->user;
1126
1127 bh_iter it;
1128 bh_iter_init_box( 0, &it, bbx );
1129 i32 idx;
1130 while( bh_next( s->bh_scene, &it, &idx ) ){
1131 u32 *ptri = &sc->arrindices[ idx*3 ];
1132 v3f tri[3];
1133
1134 for( int j=0; j<3; j++ )
1135 v3_copy( sc->arrvertices[ptri[j]].co, tri[j] );
1136
1137 buf[ count ].element_id = ptri[0];
1138
1139 int contact = rb_capsule__triangle( mtxA, c, tri, &buf[count] );
1140 count += contact;
1141
1142 if( count >= 16 ){
1143 vg_warn("Exceeding capsule_vs_scene capacity. Geometry too dense!\n");
1144 return count;
1145 }
1146 }
1147
1148 return count;
1149 }
1150
1151 VG_STATIC int rb_global_has_space( void ){
1152 if( rb_contact_count + 16 > vg_list_size(rb_contact_buffer) )
1153 return 0;
1154
1155 return 1;
1156 }
1157
1158 VG_STATIC rb_ct *rb_global_buffer( void ){
1159 return &rb_contact_buffer[ rb_contact_count ];
1160 }
1161
1162 /*
1163 * -----------------------------------------------------------------------------
1164 * Dynamics
1165 * -----------------------------------------------------------------------------
1166 */
1167
1168 VG_STATIC void rb_solver_reset(void){
1169 rb_contact_count = 0;
1170 }
1171
1172 VG_STATIC rb_ct *rb_global_ct(void){
1173 return rb_contact_buffer + rb_contact_count;
1174 }
1175
1176 VG_STATIC void rb_prepare_contact( rb_ct *ct, float timestep ){
1177 ct->bias = -0.2f * (timestep*3600.0f)
1178 * vg_minf( 0.0f, -ct->p+k_penetration_slop );
1179
1180 v3_tangent_basis( ct->n, ct->t[0], ct->t[1] );
1181 ct->norm_impulse = 0.0f;
1182 ct->tangent_impulse[0] = 0.0f;
1183 ct->tangent_impulse[1] = 0.0f;
1184 }
1185
1186 /* calculate total move. manifold should belong to ONE object only */
1187 VG_STATIC void rb_depenetrate( rb_ct *manifold, int len, v3f dt ){
1188 v3_zero( dt );
1189
1190 for( int j=0; j<7; j++ )
1191 {
1192 for( int i=0; i<len; i++ )
1193 {
1194 struct contact *ct = &manifold[i];
1195
1196 float resolved_amt = v3_dot( ct->n, dt ),
1197 remaining = (ct->p-k_penetration_slop) - resolved_amt,
1198 apply = vg_maxf( remaining, 0.0f ) * 0.4f;
1199
1200 v3_muladds( dt, ct->n, apply, dt );
1201 }
1202 }
1203 }
1204
1205 /*
1206 * Initializing things like tangent vectors
1207 */
1208 VG_STATIC void rb_presolve_contacts( rb_ct *buffer, int len ){
1209 for( int i=0; i<len; i++ ){
1210 rb_ct *ct = &buffer[i];
1211 rb_prepare_contact( ct, k_rb_delta );
1212
1213 v3f ra, rb, raCn, rbCn, raCt, rbCt;
1214 v3_sub( ct->co, ct->rba->co, ra );
1215 v3_sub( ct->co, ct->rbb->co, rb );
1216 v3_cross( ra, ct->n, raCn );
1217 v3_cross( rb, ct->n, rbCn );
1218
1219 /* orient inverse inertia tensors */
1220 v3f raCnI, rbCnI;
1221 m3x3_mulv( ct->rba->iIw, raCn, raCnI );
1222 m3x3_mulv( ct->rbb->iIw, rbCn, rbCnI );
1223
1224 ct->normal_mass = ct->rba->inv_mass + ct->rbb->inv_mass;
1225 ct->normal_mass += v3_dot( raCn, raCnI );
1226 ct->normal_mass += v3_dot( rbCn, rbCnI );
1227 ct->normal_mass = 1.0f/ct->normal_mass;
1228
1229 for( int j=0; j<2; j++ ){
1230 v3f raCtI, rbCtI;
1231 v3_cross( ct->t[j], ra, raCt );
1232 v3_cross( ct->t[j], rb, rbCt );
1233 m3x3_mulv( ct->rba->iIw, raCt, raCtI );
1234 m3x3_mulv( ct->rbb->iIw, rbCt, rbCtI );
1235
1236 ct->tangent_mass[j] = ct->rba->inv_mass + ct->rbb->inv_mass;
1237 ct->tangent_mass[j] += v3_dot( raCt, raCtI );
1238 ct->tangent_mass[j] += v3_dot( rbCt, rbCtI );
1239 ct->tangent_mass[j] = 1.0f/ct->tangent_mass[j];
1240 }
1241
1242 rb_debug_contact( ct );
1243 }
1244 }
1245
1246 /*
1247 * Creates relative contact velocity vector
1248 */
1249 VG_STATIC void rb_rcv( rigidbody *rba, rigidbody *rbb, v3f ra, v3f rb, v3f rv ){
1250 v3f rva, rvb;
1251 v3_cross( rba->w, ra, rva );
1252 v3_add( rba->v, rva, rva );
1253 v3_cross( rbb->w, rb, rvb );
1254 v3_add( rbb->v, rvb, rvb );
1255
1256 v3_sub( rva, rvb, rv );
1257 }
1258
1259 VG_STATIC void rb_contact_restitution( rb_ct *ct, float cr ){
1260 v3f rv, ra, rb;
1261 v3_sub( ct->co, ct->rba->co, ra );
1262 v3_sub( ct->co, ct->rbb->co, rb );
1263 rb_rcv( ct->rba, ct->rbb, ra, rb, rv );
1264
1265 float v = v3_dot( rv, ct->n );
1266
1267 if( v < -1.0f ){
1268 ct->bias += -cr * v;
1269 }
1270 }
1271
1272 /*
1273 * Apply impulse to object
1274 */
1275 VG_STATIC void rb_linear_impulse( rigidbody *rb, v3f delta, v3f impulse ){
1276 /* linear */
1277 v3_muladds( rb->v, impulse, rb->inv_mass, rb->v );
1278
1279 /* Angular velocity */
1280 v3f wa;
1281 v3_cross( delta, impulse, wa );
1282
1283 m3x3_mulv( rb->iIw, wa, wa );
1284 v3_add( rb->w, wa, rb->w );
1285 }
1286
1287 /*
1288 * One iteration to solve the contact constraint
1289 */
1290 VG_STATIC void rb_solve_contacts( rb_ct *buf, int len ){
1291 for( int i=0; i<len; i++ ){
1292 struct contact *ct = &buf[i];
1293
1294 v3f rv, ra, rb;
1295 v3_sub( ct->co, ct->rba->co, ra );
1296 v3_sub( ct->co, ct->rbb->co, rb );
1297 rb_rcv( ct->rba, ct->rbb, ra, rb, rv );
1298
1299 /* Friction */
1300 for( int j=0; j<2; j++ ){
1301 float f = k_friction * ct->norm_impulse,
1302 vt = v3_dot( rv, ct->t[j] ),
1303 lambda = ct->tangent_mass[j] * -vt;
1304
1305 float temp = ct->tangent_impulse[j];
1306 ct->tangent_impulse[j] = vg_clampf( temp + lambda, -f, f );
1307 lambda = ct->tangent_impulse[j] - temp;
1308
1309 v3f impulse;
1310 v3_muls( ct->t[j], lambda, impulse );
1311 rb_linear_impulse( ct->rba, ra, impulse );
1312
1313 v3_muls( ct->t[j], -lambda, impulse );
1314 rb_linear_impulse( ct->rbb, rb, impulse );
1315 }
1316
1317 /* Normal */
1318 rb_rcv( ct->rba, ct->rbb, ra, rb, rv );
1319 float vn = v3_dot( rv, ct->n ),
1320 lambda = ct->normal_mass * (-vn + ct->bias);
1321
1322 float temp = ct->norm_impulse;
1323 ct->norm_impulse = vg_maxf( temp + lambda, 0.0f );
1324 lambda = ct->norm_impulse - temp;
1325
1326 v3f impulse;
1327 v3_muls( ct->n, lambda, impulse );
1328 rb_linear_impulse( ct->rba, ra, impulse );
1329
1330 v3_muls( ct->n, -lambda, impulse );
1331 rb_linear_impulse( ct->rbb, rb, impulse );
1332 }
1333 }
1334
1335 /*
1336 * -----------------------------------------------------------------------------
1337 * Constraints
1338 * -----------------------------------------------------------------------------
1339 */
1340
1341 VG_STATIC void rb_debug_position_constraints( rb_constr_pos *buffer, int len ){
1342 for( int i=0; i<len; i++ ){
1343 rb_constr_pos *constr = &buffer[i];
1344 rigidbody *rba = constr->rba, *rbb = constr->rbb;
1345
1346 v3f wca, wcb;
1347 m3x3_mulv( rba->to_world, constr->lca, wca );
1348 m3x3_mulv( rbb->to_world, constr->lcb, wcb );
1349
1350 v3f p0, p1;
1351 v3_add( wca, rba->co, p0 );
1352 v3_add( wcb, rbb->co, p1 );
1353 vg_line_point( p0, 0.0025f, 0xff000000 );
1354 vg_line_point( p1, 0.0025f, 0xffffffff );
1355 vg_line2( p0, p1, 0xff000000, 0xffffffff );
1356 }
1357 }
1358
1359 VG_STATIC void rb_presolve_swingtwist_constraints( rb_constr_swingtwist *buf,
1360 int len ){
1361 float size = 0.12f;
1362
1363 for( int i=0; i<len; i++ ){
1364 rb_constr_swingtwist *st = &buf[ i ];
1365
1366 v3f vx, vy, va, vxb, axis, center;
1367
1368 m3x3_mulv( st->rba->to_world, st->conevx, vx );
1369 m3x3_mulv( st->rbb->to_world, st->conevxb, vxb );
1370 m3x3_mulv( st->rba->to_world, st->conevy, vy );
1371 m3x3_mulv( st->rbb->to_world, st->coneva, va );
1372 m4x3_mulv( st->rba->to_world, st->view_offset, center );
1373 v3_cross( vy, vx, axis );
1374
1375 /* Constraint violated ? */
1376 float fx = v3_dot( vx, va ), /* projection world */
1377 fy = v3_dot( vy, va ),
1378 fn = v3_dot( va, axis ),
1379
1380 rx = st->conevx[3], /* elipse radii */
1381 ry = st->conevy[3],
1382
1383 lx = fx/rx, /* projection local (fn==lz) */
1384 ly = fy/ry;
1385
1386 st->tangent_violation = ((lx*lx + ly*ly) > fn*fn) || (fn <= 0.0f);
1387 if( st->tangent_violation ){
1388 /* Calculate a good position and the axis to solve on */
1389 v2f closest, tangent,
1390 p = { fx/fabsf(fn), fy/fabsf(fn) };
1391
1392 closest_point_elipse( p, (v2f){rx,ry}, closest );
1393 tangent[0] = -closest[1] / (ry*ry);
1394 tangent[1] = closest[0] / (rx*rx);
1395 v2_normalize( tangent );
1396
1397 v3f v0, v1;
1398 v3_muladds( axis, vx, closest[0], v0 );
1399 v3_muladds( v0, vy, closest[1], v0 );
1400 v3_normalize( v0 );
1401
1402 v3_muls( vx, tangent[0], v1 );
1403 v3_muladds( v1, vy, tangent[1], v1 );
1404
1405 v3_copy( v0, st->tangent_target );
1406 v3_copy( v1, st->tangent_axis );
1407
1408 /* calculate mass */
1409 v3f aIw, bIw;
1410 m3x3_mulv( st->rba->iIw, st->tangent_axis, aIw );
1411 m3x3_mulv( st->rbb->iIw, st->tangent_axis, bIw );
1412 st->tangent_mass = 1.0f / (v3_dot( st->tangent_axis, aIw ) +
1413 v3_dot( st->tangent_axis, bIw ));
1414
1415 float angle = v3_dot( va, st->tangent_target );
1416 }
1417
1418 v3f refaxis;
1419 v3_cross( vy, va, refaxis ); /* our default rotation */
1420 v3_normalize( refaxis );
1421
1422 float angle = v3_dot( refaxis, vxb );
1423 st->axis_violation = fabsf(angle) < st->conet;
1424
1425 if( st->axis_violation ){
1426 v3f dir_test;
1427 v3_cross( refaxis, vxb, dir_test );
1428
1429 if( v3_dot(dir_test, va) < 0.0f )
1430 st->axis_violation = -st->axis_violation;
1431
1432 float newang = (float)st->axis_violation * acosf(st->conet-0.0001f);
1433
1434 v3f refaxis_up;
1435 v3_cross( va, refaxis, refaxis_up );
1436 v3_muls( refaxis_up, sinf(newang), st->axis_target );
1437 v3_muladds( st->axis_target, refaxis, -cosf(newang), st->axis_target );
1438
1439 /* calculate mass */
1440 v3_copy( va, st->axis );
1441 v3f aIw, bIw;
1442 m3x3_mulv( st->rba->iIw, st->axis, aIw );
1443 m3x3_mulv( st->rbb->iIw, st->axis, bIw );
1444 st->axis_mass = 1.0f / (v3_dot( st->axis, aIw ) +
1445 v3_dot( st->axis, bIw ));
1446 }
1447 }
1448 }
1449
1450 VG_STATIC void rb_debug_swingtwist_constraints( rb_constr_swingtwist *buf,
1451 int len ){
1452 float size = 0.12f;
1453
1454 for( int i=0; i<len; i++ ){
1455 rb_constr_swingtwist *st = &buf[ i ];
1456
1457 v3f vx, vxb, vy, va, axis, center;
1458
1459 m3x3_mulv( st->rba->to_world, st->conevx, vx );
1460 m3x3_mulv( st->rbb->to_world, st->conevxb, vxb );
1461 m3x3_mulv( st->rba->to_world, st->conevy, vy );
1462 m3x3_mulv( st->rbb->to_world, st->coneva, va );
1463 m4x3_mulv( st->rba->to_world, st->view_offset, center );
1464 v3_cross( vy, vx, axis );
1465
1466 float rx = st->conevx[3], /* elipse radii */
1467 ry = st->conevy[3];
1468
1469 v3f p0, p1;
1470 v3_muladds( center, va, size, p1 );
1471 vg_line( center, p1, 0xffffffff );
1472 vg_line_point( p1, 0.00025f, 0xffffffff );
1473
1474 if( st->tangent_violation ){
1475 v3_muladds( center, st->tangent_target, size, p0 );
1476
1477 vg_line( center, p0, 0xff00ff00 );
1478 vg_line_point( p0, 0.00025f, 0xff00ff00 );
1479 vg_line( p1, p0, 0xff000000 );
1480 }
1481
1482 for( int x=0; x<32; x++ ){
1483 float t0 = ((float)x * (1.0f/32.0f)) * VG_TAUf,
1484 t1 = (((float)x+1.0f) * (1.0f/32.0f)) * VG_TAUf,
1485 c0 = cosf( t0 ),
1486 s0 = sinf( t0 ),
1487 c1 = cosf( t1 ),
1488 s1 = sinf( t1 );
1489
1490 v3f v0, v1;
1491 v3_muladds( axis, vx, c0*rx, v0 );
1492 v3_muladds( v0, vy, s0*ry, v0 );
1493 v3_muladds( axis, vx, c1*rx, v1 );
1494 v3_muladds( v1, vy, s1*ry, v1 );
1495
1496 v3_normalize( v0 );
1497 v3_normalize( v1 );
1498
1499 v3_muladds( center, v0, size, p0 );
1500 v3_muladds( center, v1, size, p1 );
1501
1502 u32 col0r = fabsf(c0) * 255.0f,
1503 col0g = fabsf(s0) * 255.0f,
1504 col1r = fabsf(c1) * 255.0f,
1505 col1g = fabsf(s1) * 255.0f,
1506 col = st->tangent_violation? 0xff0000ff: 0xff000000,
1507 col0 = col | (col0r<<16) | (col0g << 8),
1508 col1 = col | (col1r<<16) | (col1g << 8);
1509
1510 vg_line2( center, p0, VG__NONE, col0 );
1511 vg_line2( p0, p1, col0, col1 );
1512 }
1513
1514 /* Draw twist */
1515 v3_muladds( center, va, size, p0 );
1516 v3_muladds( p0, vxb, size, p1 );
1517
1518 vg_line( p0, p1, 0xff0000ff );
1519
1520 if( st->axis_violation ){
1521 v3_muladds( p0, st->axis_target, size*1.25f, p1 );
1522 vg_line( p0, p1, 0xffffff00 );
1523 vg_line_point( p1, 0.0025f, 0xffffff80 );
1524 }
1525
1526 v3f refaxis;
1527 v3_cross( vy, va, refaxis ); /* our default rotation */
1528 v3_normalize( refaxis );
1529 v3f refaxis_up;
1530 v3_cross( va, refaxis, refaxis_up );
1531 float newang = acosf(st->conet-0.0001f);
1532
1533 v3_muladds( p0, refaxis_up, sinf(newang)*size, p1 );
1534 v3_muladds( p1, refaxis, -cosf(newang)*size, p1 );
1535 vg_line( p0, p1, 0xff000000 );
1536
1537 v3_muladds( p0, refaxis_up, sinf(-newang)*size, p1 );
1538 v3_muladds( p1, refaxis, -cosf(-newang)*size, p1 );
1539 vg_line( p0, p1, 0xff404040 );
1540 }
1541 }
1542
1543 /*
1544 * Solve a list of positional constraints
1545 */
1546 VG_STATIC void rb_solve_position_constraints( rb_constr_pos *buf, int len ){
1547 for( int i=0; i<len; i++ ){
1548 rb_constr_pos *constr = &buf[i];
1549 rigidbody *rba = constr->rba, *rbb = constr->rbb;
1550
1551 v3f wa, wb;
1552 m3x3_mulv( rba->to_world, constr->lca, wa );
1553 m3x3_mulv( rbb->to_world, constr->lcb, wb );
1554
1555 m3x3f ssra, ssrat, ssrb, ssrbt;
1556
1557 m3x3_skew_symetric( ssrat, wa );
1558 m3x3_skew_symetric( ssrbt, wb );
1559 m3x3_transpose( ssrat, ssra );
1560 m3x3_transpose( ssrbt, ssrb );
1561
1562 v3f b, b_wa, b_wb, b_a, b_b;
1563 m3x3_mulv( ssra, rba->w, b_wa );
1564 m3x3_mulv( ssrb, rbb->w, b_wb );
1565 v3_add( rba->v, b_wa, b );
1566 v3_sub( b, rbb->v, b );
1567 v3_sub( b, b_wb, b );
1568 v3_muls( b, -1.0f, b );
1569
1570 m3x3f invMa, invMb;
1571 m3x3_diagonal( invMa, rba->inv_mass );
1572 m3x3_diagonal( invMb, rbb->inv_mass );
1573
1574 m3x3f ia, ib;
1575 m3x3_mul( ssra, rba->iIw, ia );
1576 m3x3_mul( ia, ssrat, ia );
1577 m3x3_mul( ssrb, rbb->iIw, ib );
1578 m3x3_mul( ib, ssrbt, ib );
1579
1580 m3x3f cma, cmb;
1581 m3x3_add( invMa, ia, cma );
1582 m3x3_add( invMb, ib, cmb );
1583
1584 m3x3f A;
1585 m3x3_add( cma, cmb, A );
1586
1587 /* Solve Ax = b ( A^-1*b = x ) */
1588 v3f impulse;
1589 m3x3f invA;
1590 m3x3_inv( A, invA );
1591 m3x3_mulv( invA, b, impulse );
1592
1593 v3f delta_va, delta_wa, delta_vb, delta_wb;
1594 m3x3f iwa, iwb;
1595 m3x3_mul( rba->iIw, ssrat, iwa );
1596 m3x3_mul( rbb->iIw, ssrbt, iwb );
1597
1598 m3x3_mulv( invMa, impulse, delta_va );
1599 m3x3_mulv( invMb, impulse, delta_vb );
1600 m3x3_mulv( iwa, impulse, delta_wa );
1601 m3x3_mulv( iwb, impulse, delta_wb );
1602
1603 v3_add( rba->v, delta_va, rba->v );
1604 v3_add( rba->w, delta_wa, rba->w );
1605 v3_sub( rbb->v, delta_vb, rbb->v );
1606 v3_sub( rbb->w, delta_wb, rbb->w );
1607 }
1608 }
1609
1610 VG_STATIC void rb_solve_swingtwist_constraints( rb_constr_swingtwist *buf,
1611 int len ){
1612 float size = 0.12f;
1613
1614 for( int i=0; i<len; i++ ){
1615 rb_constr_swingtwist *st = &buf[ i ];
1616
1617 if( !st->axis_violation )
1618 continue;
1619
1620 float rv = v3_dot( st->axis, st->rbb->w ) -
1621 v3_dot( st->axis, st->rba->w );
1622
1623 if( rv * (float)st->axis_violation > 0.0f )
1624 continue;
1625
1626 v3f impulse, wa, wb;
1627 v3_muls( st->axis, rv*st->axis_mass, impulse );
1628 m3x3_mulv( st->rba->iIw, impulse, wa );
1629 v3_add( st->rba->w, wa, st->rba->w );
1630
1631 v3_muls( impulse, -1.0f, impulse );
1632 m3x3_mulv( st->rbb->iIw, impulse, wb );
1633 v3_add( st->rbb->w, wb, st->rbb->w );
1634
1635 float rv2 = v3_dot( st->axis, st->rbb->w ) -
1636 v3_dot( st->axis, st->rba->w );
1637 }
1638
1639 for( int i=0; i<len; i++ ){
1640 rb_constr_swingtwist *st = &buf[ i ];
1641
1642 if( !st->tangent_violation )
1643 continue;
1644
1645 float rv = v3_dot( st->tangent_axis, st->rbb->w ) -
1646 v3_dot( st->tangent_axis, st->rba->w );
1647
1648 if( rv > 0.0f )
1649 continue;
1650
1651 v3f impulse, wa, wb;
1652 v3_muls( st->tangent_axis, rv*st->tangent_mass, impulse );
1653 m3x3_mulv( st->rba->iIw, impulse, wa );
1654 v3_add( st->rba->w, wa, st->rba->w );
1655
1656 v3_muls( impulse, -1.0f, impulse );
1657 m3x3_mulv( st->rbb->iIw, impulse, wb );
1658 v3_add( st->rbb->w, wb, st->rbb->w );
1659
1660 float rv2 = v3_dot( st->tangent_axis, st->rbb->w ) -
1661 v3_dot( st->tangent_axis, st->rba->w );
1662 }
1663 }
1664
1665 VG_STATIC void rb_solve_constr_angle( rigidbody *rba, rigidbody *rbb,
1666 v3f ra, v3f rb ){
1667 m3x3f ssra, ssrb, ssrat, ssrbt;
1668 m3x3f cma, cmb;
1669
1670 m3x3_skew_symetric( ssrat, ra );
1671 m3x3_skew_symetric( ssrbt, rb );
1672 m3x3_transpose( ssrat, ssra );
1673 m3x3_transpose( ssrbt, ssrb );
1674
1675 m3x3_mul( ssra, rba->iIw, cma );
1676 m3x3_mul( cma, ssrat, cma );
1677 m3x3_mul( ssrb, rbb->iIw, cmb );
1678 m3x3_mul( cmb, ssrbt, cmb );
1679
1680 m3x3f A, invA;
1681 m3x3_add( cma, cmb, A );
1682 m3x3_inv( A, invA );
1683
1684 v3f b_wa, b_wb, b;
1685 m3x3_mulv( ssra, rba->w, b_wa );
1686 m3x3_mulv( ssrb, rbb->w, b_wb );
1687 v3_add( b_wa, b_wb, b );
1688 v3_negate( b, b );
1689
1690 v3f impulse;
1691 m3x3_mulv( invA, b, impulse );
1692
1693 v3f delta_wa, delta_wb;
1694 m3x3f iwa, iwb;
1695 m3x3_mul( rba->iIw, ssrat, iwa );
1696 m3x3_mul( rbb->iIw, ssrbt, iwb );
1697 m3x3_mulv( iwa, impulse, delta_wa );
1698 m3x3_mulv( iwb, impulse, delta_wb );
1699 v3_add( rba->w, delta_wa, rba->w );
1700 v3_sub( rbb->w, delta_wb, rbb->w );
1701 }
1702
1703 /*
1704 * Correct position constraint drift errors
1705 * [ 0.0 <= amt <= 1.0 ]: the correction amount
1706 */
1707 VG_STATIC void rb_correct_position_constraints( rb_constr_pos *buf, int len,
1708 float amt ){
1709 for( int i=0; i<len; i++ ){
1710 rb_constr_pos *constr = &buf[i];
1711 rigidbody *rba = constr->rba, *rbb = constr->rbb;
1712
1713 v3f p0, p1, d;
1714 m3x3_mulv( rba->to_world, constr->lca, p0 );
1715 m3x3_mulv( rbb->to_world, constr->lcb, p1 );
1716 v3_add( rba->co, p0, p0 );
1717 v3_add( rbb->co, p1, p1 );
1718 v3_sub( p1, p0, d );
1719
1720 v3_muladds( rbb->co, d, -1.0f * amt, rbb->co );
1721 rb_update_transform( rbb );
1722 }
1723 }
1724
1725 VG_STATIC void rb_correct_swingtwist_constraints( rb_constr_swingtwist *buf,
1726 int len, float amt ){
1727 for( int i=0; i<len; i++ ){
1728 rb_constr_swingtwist *st = &buf[i];
1729
1730 if( !st->tangent_violation )
1731 continue;
1732
1733 v3f va;
1734 m3x3_mulv( st->rbb->to_world, st->coneva, va );
1735
1736 float angle = v3_dot( va, st->tangent_target );
1737
1738 if( fabsf(angle) < 0.9999f ){
1739 v3f axis;
1740 v3_cross( va, st->tangent_target, axis );
1741
1742 v4f correction;
1743 q_axis_angle( correction, axis, acosf(angle) * amt );
1744 q_mul( correction, st->rbb->q, st->rbb->q );
1745 rb_update_transform( st->rbb );
1746 }
1747 }
1748
1749 for( int i=0; i<len; i++ ){
1750 rb_constr_swingtwist *st = &buf[i];
1751
1752 if( !st->axis_violation )
1753 continue;
1754
1755 v3f vxb;
1756 m3x3_mulv( st->rbb->to_world, st->conevxb, vxb );
1757
1758 float angle = v3_dot( vxb, st->axis_target );
1759
1760 if( fabsf(angle) < 0.9999f ){
1761 v3f axis;
1762 v3_cross( vxb, st->axis_target, axis );
1763
1764 v4f correction;
1765 q_axis_angle( correction, axis, acosf(angle) * amt );
1766 q_mul( correction, st->rbb->q, st->rbb->q );
1767 rb_update_transform( st->rbb );
1768 }
1769 }
1770 }
1771
1772 VG_STATIC void rb_correct_contact_constraints( rb_ct *buf, int len, float amt ){
1773 for( int i=0; i<len; i++ ){
1774 rb_ct *ct = &buf[i];
1775 rigidbody *rba = ct->rba,
1776 *rbb = ct->rbb;
1777
1778 float mass_total = 1.0f / (rba->inv_mass + rbb->inv_mass);
1779
1780 v3_muladds( rba->co, ct->n, -mass_total * rba->inv_mass, rba->co );
1781 v3_muladds( rbb->co, ct->n, mass_total * rbb->inv_mass, rbb->co );
1782 }
1783 }
1784
1785
1786 /*
1787 * Effectors
1788 */
1789
1790 VG_STATIC void rb_effect_simple_bouyency( rigidbody *ra, v4f plane,
1791 float amt, float drag ){
1792 /* float */
1793 float depth = v3_dot( plane, ra->co ) - plane[3],
1794 lambda = vg_clampf( -depth, 0.0f, 1.0f ) * amt;
1795
1796 v3_muladds( ra->v, plane, lambda * k_rb_delta, ra->v );
1797
1798 if( depth < 0.0f )
1799 v3_muls( ra->v, 1.0f-(drag*k_rb_delta), ra->v );
1800 }
1801
1802 /* apply a spring&dampener force to match ra(worldspace) on rigidbody, to
1803 * rt(worldspace)
1804 */
1805 VG_STATIC void rb_effect_spring_target_vector( rigidbody *rba, v3f ra, v3f rt,
1806 float spring, float dampening,
1807 float timestep ){
1808 float d = v3_dot( rt, ra );
1809 float a = acosf( vg_clampf( d, -1.0f, 1.0f ) );
1810
1811 v3f axis;
1812 v3_cross( rt, ra, axis );
1813
1814 float Fs = -a * spring,
1815 Fd = -v3_dot( rba->w, axis ) * dampening;
1816
1817 v3_muladds( rba->w, axis, (Fs+Fd) * timestep, rba->w );
1818 }
1819
1820 #endif /* RIGIDBODY_H */
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