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bouncy balls
[carveJwlIkooP6JGAAIwe30JlM.git] / rigidbody.h
1 /*
2 * Copyright (C) 2021-2022 Mt.ZERO Software, Harry Godden - All Rights Reserved
3 */
4
5 /*
6 * Resources: Box2D - Erin Catto
7 * qu3e - Randy Gaul
8 */
9
10 #include "common.h"
11 #include "bvh.h"
12 #include "scene.h"
13
14 #include <math.h>
15
16 VG_STATIC void rb_tangent_basis( v3f n, v3f tx, v3f ty );
17 VG_STATIC bh_system bh_system_rigidbodies;
18
19 #ifndef RIGIDBODY_H
20 #define RIGIDBODY_H
21
22 /*
23 * -----------------------------------------------------------------------------
24 * (K)onstants
25 * -----------------------------------------------------------------------------
26 */
27
28 VG_STATIC const float
29 k_rb_rate = (1.0/VG_TIMESTEP_FIXED),
30 k_rb_delta = (1.0/k_rb_rate),
31 k_friction = 0.4f,
32 k_damp_linear = 0.1f, /* scale velocity 1/(1+x) */
33 k_damp_angular = 0.1f, /* scale angular 1/(1+x) */
34 k_penetration_slop = 0.01f,
35 k_inertia_scale = 8.0f,
36 k_phys_baumgarte = 0.2f,
37 k_gravity = 9.6f;
38
39 VG_STATIC float
40 k_limit_bias = 0.02f,
41 k_joint_correction = 0.01f,
42 k_joint_impulse = 1.0f,
43 k_joint_bias = 0.08f; /* positional joints */
44
45 VG_STATIC void rb_register_cvar(void)
46 {
47 vg_var_push( (struct vg_var){
48 .name = "k_limit_bias", .data = &k_limit_bias,
49 .data_type = k_var_dtype_f32, .opt_f32 = {.clamp = 0}, .persistent = 1
50 });
51
52 vg_var_push( (struct vg_var){
53 .name = "k_joint_bias", .data = &k_joint_bias,
54 .data_type = k_var_dtype_f32, .opt_f32 = {.clamp = 0}, .persistent = 1
55 });
56
57 vg_var_push( (struct vg_var){
58 .name = "k_joint_correction", .data = &k_joint_correction,
59 .data_type = k_var_dtype_f32, .opt_f32 = {.clamp = 0}, .persistent = 1
60 });
61
62 vg_var_push( (struct vg_var){
63 .name = "k_joint_impulse", .data = &k_joint_impulse,
64 .data_type = k_var_dtype_f32, .opt_f32 = {.clamp = 0}, .persistent = 1
65 });
66 }
67
68 /*
69 * -----------------------------------------------------------------------------
70 * structure definitions
71 * -----------------------------------------------------------------------------
72 */
73
74 typedef struct rigidbody rigidbody;
75 typedef struct rb_object rb_object;
76 typedef struct contact rb_ct;
77 typedef struct rb_sphere rb_sphere;
78 typedef struct rb_capsule rb_capsule;
79 typedef struct rb_scene rb_scene;
80
81 struct rb_sphere
82 {
83 float radius;
84 };
85
86 struct rb_capsule
87 {
88 float height, radius;
89 };
90
91 struct rb_scene
92 {
93 bh_tree *bh_scene;
94 };
95
96 struct rigidbody
97 {
98 v3f co, v, w;
99 v4f q;
100
101 boxf bbx, bbx_world;
102 float inv_mass;
103
104 /* inertia model and inverse world tensor */
105 v3f I;
106 m3x3f iI, iIw;
107 m4x3f to_world, to_local;
108 };
109
110 /* simple objects */
111 struct rb_object
112 {
113 rigidbody rb;
114 enum rb_shape{
115 k_rb_shape_box = 0,
116 k_rb_shape_sphere = 1,
117 k_rb_shape_capsule = 2,
118 k_rb_shape_scene = 3
119 }
120 type;
121
122 union
123 {
124 struct rb_sphere sphere;
125 struct rb_capsule capsule;
126 struct rb_scene scene;
127 }
128 inf;
129 };
130
131 VG_STATIC struct contact
132 {
133 rigidbody *rba, *rbb;
134 v3f co, n;
135 v3f t[2];
136 float p, bias, norm_impulse, tangent_impulse[2],
137 normal_mass, tangent_mass[2];
138
139 u32 element_id;
140
141 enum contact_type type;
142 }
143 rb_contact_buffer[256];
144 VG_STATIC int rb_contact_count = 0;
145
146 typedef struct rb_constr_pos rb_constr_pos;
147 typedef struct rb_constr_swingtwist rb_constr_swingtwist;
148
149 struct rb_constr_pos
150 {
151 rigidbody *rba, *rbb;
152 v3f lca, lcb;
153 };
154
155 struct rb_constr_swingtwist
156 {
157 rigidbody *rba, *rbb;
158
159 v4f conevx, conevy; /* relative to rba */
160 v3f view_offset, /* relative to rba */
161 coneva, conevxb;/* relative to rbb */
162
163 int tangent_violation, axis_violation;
164 v3f axis, tangent_axis, tangent_target, axis_target;
165
166 float conet;
167 float tangent_mass, axis_mass;
168 };
169
170 struct rb_constr_spring
171 {
172 int nothing;
173 };
174
175 /*
176 * -----------------------------------------------------------------------------
177 * Math Utils
178 * -----------------------------------------------------------------------------
179 */
180
181 VG_STATIC float sphere_volume( float radius )
182 {
183 float r3 = radius*radius*radius;
184 return (4.0f/3.0f) * VG_PIf * r3;
185 }
186
187 VG_STATIC void rb_tangent_basis( v3f n, v3f tx, v3f ty )
188 {
189 /* Compute tangent basis (box2d) */
190 if( fabsf( n[0] ) >= 0.57735027f )
191 {
192 tx[0] = n[1];
193 tx[1] = -n[0];
194 tx[2] = 0.0f;
195 }
196 else
197 {
198 tx[0] = 0.0f;
199 tx[1] = n[2];
200 tx[2] = -n[1];
201 }
202
203 v3_normalize( tx );
204 v3_cross( n, tx, ty );
205 }
206
207 /*
208 * -----------------------------------------------------------------------------
209 * Debugging
210 * -----------------------------------------------------------------------------
211 */
212
213 VG_STATIC void rb_debug_contact( rb_ct *ct )
214 {
215 v3f p1;
216 v3_muladds( ct->co, ct->n, 0.05f, p1 );
217
218 if( ct->type == k_contact_type_default )
219 {
220 vg_line_pt3( ct->co, 0.0125f, 0xff0000ff );
221 vg_line( ct->co, p1, 0xffffffff );
222 }
223 else if( ct->type == k_contact_type_edge )
224 {
225 vg_line_pt3( ct->co, 0.0125f, 0xff00ffc0 );
226 vg_line( ct->co, p1, 0xffffffff );
227 }
228 }
229
230 VG_STATIC void debug_sphere( m4x3f m, float radius, u32 colour )
231 {
232 v3f ly = { 0.0f, 0.0f, radius },
233 lx = { 0.0f, radius, 0.0f },
234 lz = { 0.0f, 0.0f, radius };
235
236 for( int i=0; i<16; i++ )
237 {
238 float t = ((float)(i+1) * (1.0f/16.0f)) * VG_PIf * 2.0f,
239 s = sinf(t),
240 c = cosf(t);
241
242 v3f py = { s*radius, 0.0f, c*radius },
243 px = { s*radius, c*radius, 0.0f },
244 pz = { 0.0f, s*radius, c*radius };
245
246 v3f p0, p1, p2, p3, p4, p5;
247 m4x3_mulv( m, py, p0 );
248 m4x3_mulv( m, ly, p1 );
249 m4x3_mulv( m, px, p2 );
250 m4x3_mulv( m, lx, p3 );
251 m4x3_mulv( m, pz, p4 );
252 m4x3_mulv( m, lz, p5 );
253
254 vg_line( p0, p1, colour == 0x00? 0xff00ff00: colour );
255 vg_line( p2, p3, colour == 0x00? 0xff0000ff: colour );
256 vg_line( p4, p5, colour == 0x00? 0xffff0000: colour );
257
258 v3_copy( py, ly );
259 v3_copy( px, lx );
260 v3_copy( pz, lz );
261 }
262 }
263
264 VG_STATIC void debug_capsule( m4x3f m, float radius, float h, u32 colour )
265 {
266 v3f ly = { 0.0f, 0.0f, radius },
267 lx = { 0.0f, radius, 0.0f },
268 lz = { 0.0f, 0.0f, radius };
269
270 float s0 = sinf(0.0f)*radius,
271 c0 = cosf(0.0f)*radius;
272
273 v3f p0, p1, up, right, forward;
274 m3x3_mulv( m, (v3f){0.0f,1.0f,0.0f}, up );
275 m3x3_mulv( m, (v3f){1.0f,0.0f,0.0f}, right );
276 m3x3_mulv( m, (v3f){0.0f,0.0f,-1.0f}, forward );
277 v3_muladds( m[3], up, -h*0.5f+radius, p0 );
278 v3_muladds( m[3], up, h*0.5f-radius, p1 );
279
280 v3f a0, a1, b0, b1;
281 v3_muladds( p0, right, radius, a0 );
282 v3_muladds( p1, right, radius, a1 );
283 v3_muladds( p0, forward, radius, b0 );
284 v3_muladds( p1, forward, radius, b1 );
285 vg_line( a0, a1, colour );
286 vg_line( b0, b1, colour );
287
288 v3_muladds( p0, right, -radius, a0 );
289 v3_muladds( p1, right, -radius, a1 );
290 v3_muladds( p0, forward, -radius, b0 );
291 v3_muladds( p1, forward, -radius, b1 );
292 vg_line( a0, a1, colour );
293 vg_line( b0, b1, colour );
294
295 for( int i=0; i<16; i++ )
296 {
297 float t = ((float)(i+1) * (1.0f/16.0f)) * VG_PIf * 2.0f,
298 s1 = sinf(t)*radius,
299 c1 = cosf(t)*radius;
300
301 v3f e0 = { s0, 0.0f, c0 },
302 e1 = { s1, 0.0f, c1 },
303 e2 = { s0, c0, 0.0f },
304 e3 = { s1, c1, 0.0f },
305 e4 = { 0.0f, c0, s0 },
306 e5 = { 0.0f, c1, s1 };
307
308 m3x3_mulv( m, e0, e0 );
309 m3x3_mulv( m, e1, e1 );
310 m3x3_mulv( m, e2, e2 );
311 m3x3_mulv( m, e3, e3 );
312 m3x3_mulv( m, e4, e4 );
313 m3x3_mulv( m, e5, e5 );
314
315 v3_add( p0, e0, a0 );
316 v3_add( p0, e1, a1 );
317 v3_add( p1, e0, b0 );
318 v3_add( p1, e1, b1 );
319
320 vg_line( a0, a1, colour );
321 vg_line( b0, b1, colour );
322
323 if( c0 < 0.0f )
324 {
325 v3_add( p0, e2, a0 );
326 v3_add( p0, e3, a1 );
327 v3_add( p0, e4, b0 );
328 v3_add( p0, e5, b1 );
329 }
330 else
331 {
332 v3_add( p1, e2, a0 );
333 v3_add( p1, e3, a1 );
334 v3_add( p1, e4, b0 );
335 v3_add( p1, e5, b1 );
336 }
337
338 vg_line( a0, a1, colour );
339 vg_line( b0, b1, colour );
340
341 s0 = s1;
342 c0 = c1;
343 }
344 }
345
346 VG_STATIC void rb_object_debug( rb_object *obj, u32 colour )
347 {
348 if( obj->type == k_rb_shape_box ){
349 v3f *box = obj->rb.bbx;
350 vg_line_boxf_transformed( obj->rb.to_world, obj->rb.bbx, colour );
351 }
352 else if( obj->type == k_rb_shape_sphere ){
353 debug_sphere( obj->rb.to_world, obj->inf.sphere.radius, colour );
354 }
355 else if( obj->type == k_rb_shape_capsule ){
356 m4x3f m0, m1;
357 float h = obj->inf.capsule.height,
358 r = obj->inf.capsule.radius;
359
360 debug_capsule( obj->rb.to_world, r, h, colour );
361 }
362 else if( obj->type == k_rb_shape_scene ){
363 vg_line_boxf( obj->rb.bbx, colour );
364 }
365 }
366
367 /*
368 * -----------------------------------------------------------------------------
369 * Integration
370 * -----------------------------------------------------------------------------
371 */
372
373 /*
374 * Update world space bounding box based on local one
375 */
376 VG_STATIC void rb_update_bounds( rigidbody *rb )
377 {
378 box_copy( rb->bbx, rb->bbx_world );
379 m4x3_transform_aabb( rb->to_world, rb->bbx_world );
380 }
381
382 /*
383 * Commit transform to rigidbody. Updates matrices
384 */
385 VG_STATIC void rb_update_transform( rigidbody *rb )
386 {
387 q_normalize( rb->q );
388 q_m3x3( rb->q, rb->to_world );
389 v3_copy( rb->co, rb->to_world[3] );
390
391 m4x3_invert_affine( rb->to_world, rb->to_local );
392
393 #if 0
394 m3x3_mulv( rb->to_world, (v3f){1.0f,0.0f, 0.0f}, rb->right );
395 m3x3_mulv( rb->to_world, (v3f){0.0f,1.0f, 0.0f}, rb->up );
396 m3x3_mulv( rb->to_world, (v3f){0.0f,0.0f,-1.0f}, rb->forward );
397 #endif
398
399 m3x3_mul( rb->iI, rb->to_local, rb->iIw );
400 m3x3_mul( rb->to_world, rb->iIw, rb->iIw );
401
402 rb_update_bounds( rb );
403 }
404
405 /*
406 * Extrapolate rigidbody into a transform based on vg accumulator.
407 * Useful for rendering
408 */
409 VG_STATIC void rb_extrapolate( rigidbody *rb, v3f co, v4f q )
410 {
411 float substep = vg_clampf( vg.accumulator / k_rb_delta, 0.0f, 1.0f );
412
413 v3_muladds( rb->co, rb->v, k_rb_delta*substep, co );
414
415 if( v3_length2( rb->w ) > 0.0f ){
416 v4f rotation;
417 v3f axis;
418 v3_copy( rb->w, axis );
419
420 float mag = v3_length( axis );
421 v3_divs( axis, mag, axis );
422 q_axis_angle( rotation, axis, mag*k_rb_delta*substep );
423 q_mul( rotation, rb->q, q );
424 q_normalize( q );
425 }
426 else{
427 v4_copy( rb->q, q );
428 }
429 }
430
431 /*
432 * Initialize rigidbody and calculate masses, inertia
433 */
434 VG_STATIC void rb_init_object( rb_object *obj )
435 {
436 float volume = 1.0f;
437 int inert = 0;
438
439 if( obj->type == k_rb_shape_box ){
440 v3f dims;
441 v3_sub( obj->rb.bbx[1], obj->rb.bbx[0], dims );
442 volume = dims[0]*dims[1]*dims[2];
443 }
444 else if( obj->type == k_rb_shape_sphere ){
445 volume = sphere_volume( obj->inf.sphere.radius );
446 v3_fill( obj->rb.bbx[0], -obj->inf.sphere.radius );
447 v3_fill( obj->rb.bbx[1], obj->inf.sphere.radius );
448 }
449 else if( obj->type == k_rb_shape_capsule ){
450 float r = obj->inf.capsule.radius,
451 h = obj->inf.capsule.height;
452 volume = sphere_volume( r ) + VG_PIf * r*r * (h - r*2.0f);
453
454 v3_fill( obj->rb.bbx[0], -r );
455 v3_fill( obj->rb.bbx[1], r );
456 obj->rb.bbx[0][1] = -h;
457 obj->rb.bbx[1][1] = h;
458 }
459 else if( obj->type == k_rb_shape_scene ){
460 inert = 1;
461 box_copy( obj->inf.scene.bh_scene->nodes[0].bbx, obj->rb.bbx );
462 }
463
464 if( inert ){
465 obj->rb.inv_mass = 0.0f;
466 v3_zero( obj->rb.I );
467 m3x3_zero( obj->rb.iI );
468 }
469 else{
470 float mass = 2.0f*volume;
471 obj->rb.inv_mass = 1.0f/mass;
472
473 v3f extent;
474 v3_sub( obj->rb.bbx[1], obj->rb.bbx[0], extent );
475 v3_muls( extent, 0.5f, extent );
476
477 /* local intertia tensor */
478 float scale = k_inertia_scale;
479 float ex2 = scale*extent[0]*extent[0],
480 ey2 = scale*extent[1]*extent[1],
481 ez2 = scale*extent[2]*extent[2];
482
483 obj->rb.I[0] = ((1.0f/12.0f) * mass * (ey2+ez2));
484 obj->rb.I[1] = ((1.0f/12.0f) * mass * (ex2+ez2));
485 obj->rb.I[2] = ((1.0f/12.0f) * mass * (ex2+ey2));
486
487 m3x3_identity( obj->rb.iI );
488 obj->rb.iI[0][0] = obj->rb.I[0];
489 obj->rb.iI[1][1] = obj->rb.I[1];
490 obj->rb.iI[2][2] = obj->rb.I[2];
491 m3x3_inv( obj->rb.iI, obj->rb.iI );
492 }
493
494 rb_update_transform( &obj->rb );
495 }
496
497 VG_STATIC void rb_iter( rigidbody *rb )
498 {
499 if( !vg_validf( rb->v[0] ) ||
500 !vg_validf( rb->v[1] ) ||
501 !vg_validf( rb->v[2] ) )
502 {
503 vg_fatal_exit_loop( "NaN velocity" );
504 }
505
506 v3f gravity = { 0.0f, -9.8f, 0.0f };
507 v3_muladds( rb->v, gravity, k_rb_delta, rb->v );
508
509 /* intergrate velocity */
510 v3_muladds( rb->co, rb->v, k_rb_delta, rb->co );
511 v3_lerp( rb->w, (v3f){0.0f,0.0f,0.0f}, 0.0025f, rb->w );
512
513 /* inegrate inertia */
514 if( v3_length2( rb->w ) > 0.0f )
515 {
516 v4f rotation;
517 v3f axis;
518 v3_copy( rb->w, axis );
519
520 float mag = v3_length( axis );
521 v3_divs( axis, mag, axis );
522 q_axis_angle( rotation, axis, mag*k_rb_delta );
523 q_mul( rotation, rb->q, rb->q );
524 }
525
526 /* damping */
527 v3_muls( rb->v, 1.0f/(1.0f+k_rb_delta*k_damp_linear), rb->v );
528 v3_muls( rb->w, 1.0f/(1.0f+k_rb_delta*k_damp_angular), rb->w );
529 }
530
531
532 /*
533 * -----------------------------------------------------------------------------
534 * Boolean shape overlap functions
535 * -----------------------------------------------------------------------------
536 */
537
538 /*
539 * Project AABB, and triangle interval onto axis to check if they overlap
540 */
541 VG_STATIC int rb_box_triangle_interval( v3f extent, v3f axis, v3f tri[3] )
542 {
543 float
544
545 r = extent[0] * fabsf(axis[0]) +
546 extent[1] * fabsf(axis[1]) +
547 extent[2] * fabsf(axis[2]),
548
549 p0 = v3_dot( axis, tri[0] ),
550 p1 = v3_dot( axis, tri[1] ),
551 p2 = v3_dot( axis, tri[2] ),
552
553 e = vg_maxf(-vg_maxf(p0,vg_maxf(p1,p2)), vg_minf(p0,vg_minf(p1,p2)));
554
555 if( e > r ) return 0;
556 else return 1;
557 }
558
559 /*
560 * Seperating axis test box vs triangle
561 */
562 VG_STATIC int rb_box_triangle_sat( v3f extent, v3f center,
563 m4x3f to_local, v3f tri_src[3] )
564 {
565 v3f tri[3];
566
567 for( int i=0; i<3; i++ ){
568 m4x3_mulv( to_local, tri_src[i], tri[i] );
569 v3_sub( tri[i], center, tri[i] );
570 }
571
572 /* u0, u1, u2 */
573 if(!rb_box_triangle_interval( extent, (v3f){1.0f,0.0f,0.0f}, tri )) return 0;
574 if(!rb_box_triangle_interval( extent, (v3f){0.0f,1.0f,0.0f}, tri )) return 0;
575 if(!rb_box_triangle_interval( extent, (v3f){0.0f,0.0f,1.0f}, tri )) return 0;
576
577 v3f v0,v1,v2,n, e0,e1,e2;
578 v3_sub( tri[1], tri[0], v0 );
579 v3_sub( tri[2], tri[0], v1 );
580 v3_sub( tri[2], tri[1], v2 );
581 v3_normalize( v0 );
582 v3_normalize( v1 );
583 v3_normalize( v2 );
584 v3_cross( v0, v1, n );
585 v3_cross( v0, n, e0 );
586 v3_cross( n, v1, e1 );
587 v3_cross( v2, n, e2 );
588
589 /* normal */
590 if(!rb_box_triangle_interval( extent, n, tri )) return 0;
591
592 v3f axis[9];
593 v3_cross( e0, (v3f){1.0f,0.0f,0.0f}, axis[0] );
594 v3_cross( e0, (v3f){0.0f,1.0f,0.0f}, axis[1] );
595 v3_cross( e0, (v3f){0.0f,0.0f,1.0f}, axis[2] );
596 v3_cross( e1, (v3f){1.0f,0.0f,0.0f}, axis[3] );
597 v3_cross( e1, (v3f){0.0f,1.0f,0.0f}, axis[4] );
598 v3_cross( e1, (v3f){0.0f,0.0f,1.0f}, axis[5] );
599 v3_cross( e2, (v3f){1.0f,0.0f,0.0f}, axis[6] );
600 v3_cross( e2, (v3f){0.0f,1.0f,0.0f}, axis[7] );
601 v3_cross( e2, (v3f){0.0f,0.0f,1.0f}, axis[8] );
602
603 for( int i=0; i<9; i++ )
604 if(!rb_box_triangle_interval( extent, axis[i], tri )) return 0;
605
606 return 1;
607 }
608
609 /*
610 * -----------------------------------------------------------------------------
611 * Manifold
612 * -----------------------------------------------------------------------------
613 */
614
615 VG_STATIC int rb_manifold_apply_filtered( rb_ct *man, int len )
616 {
617 int k = 0;
618
619 for( int i=0; i<len; i++ ){
620 rb_ct *ct = &man[i];
621
622 if( ct->type == k_contact_type_disabled )
623 continue;
624
625 man[k ++] = man[i];
626 }
627
628 return k;
629 }
630
631 /*
632 * Merge two contacts if they are within radius(r) of eachother
633 */
634 VG_STATIC void rb_manifold_contact_weld( rb_ct *ci, rb_ct *cj, float r )
635 {
636 if( v3_dist2( ci->co, cj->co ) < r*r ){
637 cj->type = k_contact_type_disabled;
638 ci->p = (ci->p + cj->p) * 0.5f;
639
640 v3_add( ci->co, cj->co, ci->co );
641 v3_muls( ci->co, 0.5f, ci->co );
642
643 v3f delta;
644 v3_sub( ci->rba->co, ci->co, delta );
645
646 float c0 = v3_dot( ci->n, delta ),
647 c1 = v3_dot( cj->n, delta );
648
649 if( c0 < 0.0f || c1 < 0.0f ){
650 /* error */
651 ci->type = k_contact_type_disabled;
652 }
653 else{
654 v3f n;
655 v3_muls( ci->n, c0, n );
656 v3_muladds( n, cj->n, c1, n );
657 v3_normalize( n );
658 v3_copy( n, ci->n );
659 }
660 }
661 }
662
663 /*
664 *
665 */
666 VG_STATIC void rb_manifold_filter_joint_edges( rb_ct *man, int len, float r )
667 {
668 for( int i=0; i<len-1; i++ ){
669 rb_ct *ci = &man[i];
670 if( ci->type != k_contact_type_edge )
671 continue;
672
673 for( int j=i+1; j<len; j++ ){
674 rb_ct *cj = &man[j];
675 if( cj->type != k_contact_type_edge )
676 continue;
677
678 rb_manifold_contact_weld( ci, cj, r );
679 }
680 }
681 }
682
683 /*
684 * Resolve overlapping pairs
685 *
686 * TODO: Remove?
687 */
688 VG_STATIC void rb_manifold_filter_pairs( rb_ct *man, int len, float r )
689 {
690 for( int i=0; i<len-1; i++ ){
691 rb_ct *ci = &man[i];
692 int similar = 0;
693
694 if( ci->type == k_contact_type_disabled ) continue;
695
696 for( int j=i+1; j<len; j++ ){
697 rb_ct *cj = &man[j];
698
699 if( cj->type == k_contact_type_disabled ) continue;
700
701 if( v3_dist2( ci->co, cj->co ) < r*r ){
702 cj->type = k_contact_type_disabled;
703 v3_add( cj->n, ci->n, ci->n );
704 ci->p += cj->p;
705 similar ++;
706 }
707 }
708
709 if( similar ){
710 float n = 1.0f/((float)similar+1.0f);
711 v3_muls( ci->n, n, ci->n );
712 ci->p *= n;
713
714 if( v3_length2(ci->n) < 0.1f*0.1f )
715 ci->type = k_contact_type_disabled;
716 else
717 v3_normalize( ci->n );
718 }
719 }
720 }
721
722 /*
723 * Remove contacts that are facing away from A
724 */
725 VG_STATIC void rb_manifold_filter_backface( rb_ct *man, int len )
726 {
727 for( int i=0; i<len; i++ ){
728 rb_ct *ct = &man[i];
729 if( ct->type == k_contact_type_disabled )
730 continue;
731
732 v3f delta;
733 v3_sub( ct->co, ct->rba->co, delta );
734
735 if( v3_dot( delta, ct->n ) > -0.001f )
736 ct->type = k_contact_type_disabled;
737 }
738 }
739
740 /*
741 * Filter out duplicate coplanar results. Good for spheres.
742 */
743 VG_STATIC void rb_manifold_filter_coplanar( rb_ct *man, int len, float w )
744 {
745 for( int i=0; i<len; i++ ){
746 rb_ct *ci = &man[i];
747 if( ci->type == k_contact_type_disabled ||
748 ci->type == k_contact_type_edge )
749 continue;
750
751 float d1 = v3_dot( ci->co, ci->n );
752
753 for( int j=0; j<len; j++ ){
754 if( j == i )
755 continue;
756
757 rb_ct *cj = &man[j];
758 if( cj->type == k_contact_type_disabled )
759 continue;
760
761 float d2 = v3_dot( cj->co, ci->n ),
762 d = d2-d1;
763
764 if( fabsf( d ) <= w ){
765 cj->type = k_contact_type_disabled;
766 }
767 }
768 }
769 }
770
771 /*
772 * -----------------------------------------------------------------------------
773 * Collision matrix
774 * -----------------------------------------------------------------------------
775 */
776
777 /*
778 * Contact generators
779 *
780 * These do not automatically allocate contacts, an appropriately sized
781 * buffer must be supplied. The function returns the size of the manifold
782 * which was generated.
783 *
784 * The values set on the contacts are: n, co, p, rba, rbb
785 */
786
787 /*
788 * By collecting the minimum(time) and maximum(time) pairs of points, we
789 * build a reduced and stable exact manifold.
790 *
791 * tx: time at point
792 * rx: minimum distance of these points
793 * dx: the delta between the two points
794 *
795 * pairs will only ammend these if they are creating a collision
796 */
797 typedef struct capsule_manifold capsule_manifold;
798 struct capsule_manifold
799 {
800 float t0, t1;
801 float r0, r1;
802 v3f d0, d1;
803 };
804
805 /*
806 * Expand a line manifold with a new pair. t value is the time along segment
807 * on the oriented object which created this pair.
808 */
809 VG_STATIC void rb_capsule_manifold( v3f pa, v3f pb, float t, float r,
810 capsule_manifold *manifold )
811 {
812 v3f delta;
813 v3_sub( pa, pb, delta );
814
815 if( v3_length2(delta) < r*r ){
816 if( t < manifold->t0 ){
817 v3_copy( delta, manifold->d0 );
818 manifold->t0 = t;
819 manifold->r0 = r;
820 }
821
822 if( t > manifold->t1 ){
823 v3_copy( delta, manifold->d1 );
824 manifold->t1 = t;
825 manifold->r1 = r;
826 }
827 }
828 }
829
830 VG_STATIC void rb_capsule_manifold_init( capsule_manifold *manifold )
831 {
832 manifold->t0 = INFINITY;
833 manifold->t1 = -INFINITY;
834 }
835
836 VG_STATIC int rb_capsule__manifold_done( m4x3f mtx, rb_capsule *c,
837 capsule_manifold *manifold,
838 rb_ct *buf )
839 {
840 v3f p0, p1;
841 v3_muladds( mtx[3], mtx[1], -c->height*0.5f+c->radius, p0 );
842 v3_muladds( mtx[3], mtx[1], c->height*0.5f-c->radius, p1 );
843
844 int count = 0;
845 if( manifold->t0 <= 1.0f ){
846 rb_ct *ct = buf;
847
848 v3f pa;
849 v3_muls( p0, 1.0f-manifold->t0, pa );
850 v3_muladds( pa, p1, manifold->t0, pa );
851
852 float d = v3_length( manifold->d0 );
853 v3_muls( manifold->d0, 1.0f/d, ct->n );
854 v3_muladds( pa, ct->n, -c->radius, ct->co );
855
856 ct->p = manifold->r0 - d;
857 ct->type = k_contact_type_default;
858 count ++;
859 }
860
861 if( (manifold->t1 >= 0.0f) && (manifold->t0 != manifold->t1) ){
862 rb_ct *ct = buf+count;
863
864 v3f pa;
865 v3_muls( p0, 1.0f-manifold->t1, pa );
866 v3_muladds( pa, p1, manifold->t1, pa );
867
868 float d = v3_length( manifold->d1 );
869 v3_muls( manifold->d1, 1.0f/d, ct->n );
870 v3_muladds( pa, ct->n, -c->radius, ct->co );
871
872 ct->p = manifold->r1 - d;
873 ct->type = k_contact_type_default;
874
875 count ++;
876 }
877
878 /*
879 * Debugging
880 */
881
882 if( count == 2 )
883 vg_line( buf[0].co, buf[1].co, 0xff0000ff );
884
885 return count;
886 }
887
888 VG_STATIC int rb_capsule_sphere( rb_object *obja, rb_object *objb, rb_ct *buf )
889 {
890 rigidbody *rba = &obja->rb, *rbb = &objb->rb;
891 float h = obja->inf.capsule.height,
892 ra = obja->inf.capsule.radius,
893 rb = objb->inf.sphere.radius;
894
895 v3f p0, p1;
896 v3_muladds( rba->co, rba->to_world[1], -h*0.5f+ra, p0 );
897 v3_muladds( rba->co, rba->to_world[1], h*0.5f-ra, p1 );
898
899 v3f c, delta;
900 closest_point_segment( p0, p1, rbb->co, c );
901 v3_sub( c, rbb->co, delta );
902
903 float d2 = v3_length2(delta),
904 r = ra + rb;
905
906 if( d2 < r*r ){
907 float d = sqrtf(d2);
908
909 rb_ct *ct = buf;
910 v3_muls( delta, 1.0f/d, ct->n );
911 ct->p = r-d;
912
913 v3f p0, p1;
914 v3_muladds( c, ct->n, -ra, p0 );
915 v3_muladds( rbb->co, ct->n, rb, p1 );
916 v3_add( p0, p1, ct->co );
917 v3_muls( ct->co, 0.5f, ct->co );
918
919 ct->rba = rba;
920 ct->rbb = rbb;
921 ct->type = k_contact_type_default;
922
923 return 1;
924 }
925
926 return 0;
927 }
928
929 VG_STATIC int rb_capsule__capsule( m4x3f mtxA, rb_capsule *ca,
930 m4x3f mtxB, rb_capsule *cb, rb_ct *buf )
931 {
932 float ha = ca->height,
933 hb = cb->height,
934 ra = ca->radius,
935 rb = cb->radius,
936 r = ra+rb;
937
938 v3f p0, p1, p2, p3;
939 v3_muladds( mtxA[3], mtxA[1], -ha*0.5f+ra, p0 );
940 v3_muladds( mtxA[3], mtxA[1], ha*0.5f-ra, p1 );
941 v3_muladds( mtxB[3], mtxB[1], -hb*0.5f+rb, p2 );
942 v3_muladds( mtxB[3], mtxB[1], hb*0.5f-rb, p3 );
943
944 capsule_manifold manifold;
945 rb_capsule_manifold_init( &manifold );
946
947 v3f pa, pb;
948 float ta, tb;
949 closest_segment_segment( p0, p1, p2, p3, &ta, &tb, pa, pb );
950 rb_capsule_manifold( pa, pb, ta, r, &manifold );
951
952 ta = closest_point_segment( p0, p1, p2, pa );
953 tb = closest_point_segment( p0, p1, p3, pb );
954 rb_capsule_manifold( pa, p2, ta, r, &manifold );
955 rb_capsule_manifold( pb, p3, tb, r, &manifold );
956
957 closest_point_segment( p2, p3, p0, pa );
958 closest_point_segment( p2, p3, p1, pb );
959 rb_capsule_manifold( p0, pa, 0.0f, r, &manifold );
960 rb_capsule_manifold( p1, pb, 1.0f, r, &manifold );
961
962 return rb_capsule__manifold_done( mtxA, ca, &manifold, buf );
963 }
964
965 #if 0
966 /*
967 * Generates up to two contacts; optimised for the most stable manifold
968 */
969 VG_STATIC int rb_capsule_box( rigidbody *rba, rigidbody *rbb, rb_ct *buf )
970 {
971 float h = rba->inf.capsule.height,
972 r = rba->inf.capsule.radius;
973
974 /*
975 * Solving this in symetric local space of the cube saves us some time and a
976 * couple branches when it comes to the quad stage.
977 */
978 v3f centroid;
979 v3_add( rbb->bbx[0], rbb->bbx[1], centroid );
980 v3_muls( centroid, 0.5f, centroid );
981
982 boxf bbx;
983 v3_sub( rbb->bbx[0], centroid, bbx[0] );
984 v3_sub( rbb->bbx[1], centroid, bbx[1] );
985
986 v3f pc, p0w, p1w, p0, p1;
987 v3_muladds( rba->co, rba->up, -h*0.5f+r, p0w );
988 v3_muladds( rba->co, rba->up, h*0.5f-r, p1w );
989
990 m4x3_mulv( rbb->to_local, p0w, p0 );
991 m4x3_mulv( rbb->to_local, p1w, p1 );
992 v3_sub( p0, centroid, p0 );
993 v3_sub( p1, centroid, p1 );
994 v3_add( p0, p1, pc );
995 v3_muls( pc, 0.5f, pc );
996
997 /*
998 * Finding an appropriate quad to collide lines with
999 */
1000 v3f region;
1001 v3_div( pc, bbx[1], region );
1002
1003 v3f quad[4];
1004 if( (fabsf(region[0]) > fabsf(region[1])) &&
1005 (fabsf(region[0]) > fabsf(region[2])) )
1006 {
1007 float px = vg_signf(region[0]) * bbx[1][0];
1008 v3_copy( (v3f){ px, bbx[0][1], bbx[0][2] }, quad[0] );
1009 v3_copy( (v3f){ px, bbx[1][1], bbx[0][2] }, quad[1] );
1010 v3_copy( (v3f){ px, bbx[1][1], bbx[1][2] }, quad[2] );
1011 v3_copy( (v3f){ px, bbx[0][1], bbx[1][2] }, quad[3] );
1012 }
1013 else if( fabsf(region[1]) > fabsf(region[2]) )
1014 {
1015 float py = vg_signf(region[1]) * bbx[1][1];
1016 v3_copy( (v3f){ bbx[0][0], py, bbx[0][2] }, quad[0] );
1017 v3_copy( (v3f){ bbx[1][0], py, bbx[0][2] }, quad[1] );
1018 v3_copy( (v3f){ bbx[1][0], py, bbx[1][2] }, quad[2] );
1019 v3_copy( (v3f){ bbx[0][0], py, bbx[1][2] }, quad[3] );
1020 }
1021 else
1022 {
1023 float pz = vg_signf(region[2]) * bbx[1][2];
1024 v3_copy( (v3f){ bbx[0][0], bbx[0][1], pz }, quad[0] );
1025 v3_copy( (v3f){ bbx[1][0], bbx[0][1], pz }, quad[1] );
1026 v3_copy( (v3f){ bbx[1][0], bbx[1][1], pz }, quad[2] );
1027 v3_copy( (v3f){ bbx[0][0], bbx[1][1], pz }, quad[3] );
1028 }
1029
1030 capsule_manifold manifold;
1031 rb_capsule_manifold_init( &manifold );
1032
1033 v3f c0, c1;
1034 closest_point_aabb( p0, bbx, c0 );
1035 closest_point_aabb( p1, bbx, c1 );
1036
1037 v3f d0, d1, da;
1038 v3_sub( c0, p0, d0 );
1039 v3_sub( c1, p1, d1 );
1040 v3_sub( p1, p0, da );
1041
1042 v3_normalize(d0);
1043 v3_normalize(d1);
1044 v3_normalize(da);
1045
1046 if( v3_dot( da, d0 ) <= 0.01f )
1047 rb_capsule_manifold( p0, c0, 0.0f, r, &manifold );
1048
1049 if( v3_dot( da, d1 ) >= -0.01f )
1050 rb_capsule_manifold( p1, c1, 1.0f, r, &manifold );
1051
1052 for( int i=0; i<4; i++ )
1053 {
1054 int i0 = i,
1055 i1 = (i+1)%4;
1056
1057 v3f ca, cb;
1058 float ta, tb;
1059 closest_segment_segment( p0, p1, quad[i0], quad[i1], &ta, &tb, ca, cb );
1060 rb_capsule_manifold( ca, cb, ta, r, &manifold );
1061 }
1062
1063 /*
1064 * Create final contacts based on line manifold
1065 */
1066 m3x3_mulv( rbb->to_world, manifold.d0, manifold.d0 );
1067 m3x3_mulv( rbb->to_world, manifold.d1, manifold.d1 );
1068
1069 /*
1070 * Debugging
1071 */
1072
1073 #if 0
1074 for( int i=0; i<4; i++ )
1075 {
1076 v3f q0, q1;
1077 int i0 = i,
1078 i1 = (i+1)%4;
1079
1080 v3_add( quad[i0], centroid, q0 );
1081 v3_add( quad[i1], centroid, q1 );
1082
1083 m4x3_mulv( rbb->to_world, q0, q0 );
1084 m4x3_mulv( rbb->to_world, q1, q1 );
1085
1086 vg_line( q0, q1, 0xffffffff );
1087 }
1088 #endif
1089
1090 return rb_capsule_manifold_done( rba, rbb, &manifold, buf );
1091 }
1092 #endif
1093
1094 VG_STATIC int rb_sphere_box( rb_object *obja, rb_object *objb, rb_ct *buf )
1095 {
1096 v3f co, delta;
1097 rigidbody *rba = &obja->rb, *rbb = &objb->rb;
1098
1099 closest_point_obb( rba->co, rbb->bbx, rbb->to_world, rbb->to_local, co );
1100 v3_sub( rba->co, co, delta );
1101
1102 float d2 = v3_length2(delta),
1103 r = obja->inf.sphere.radius;
1104
1105 if( d2 <= r*r ){
1106 float d;
1107
1108 rb_ct *ct = buf;
1109 if( d2 <= 0.0001f ){
1110 v3_sub( rba->co, rbb->co, delta );
1111
1112 /*
1113 * some extra testing is required to find the best axis to push the
1114 * object back outside the box. Since there isnt a clear seperating
1115 * vector already, especially on really high aspect boxes.
1116 */
1117 float lx = v3_dot( rbb->to_world[0], delta ),
1118 ly = v3_dot( rbb->to_world[1], delta ),
1119 lz = v3_dot( rbb->to_world[2], delta ),
1120 px = rbb->bbx[1][0] - fabsf(lx),
1121 py = rbb->bbx[1][1] - fabsf(ly),
1122 pz = rbb->bbx[1][2] - fabsf(lz);
1123
1124 if( px < py && px < pz )
1125 v3_muls( rbb->to_world[0], vg_signf(lx), ct->n );
1126 else if( py < pz )
1127 v3_muls( rbb->to_world[1], vg_signf(ly), ct->n );
1128 else
1129 v3_muls( rbb->to_world[2], vg_signf(lz), ct->n );
1130
1131 v3_muladds( rba->co, ct->n, -r, ct->co );
1132 ct->p = r;
1133 }
1134 else{
1135 d = sqrtf(d2);
1136 v3_muls( delta, 1.0f/d, ct->n );
1137 ct->p = r-d;
1138 v3_copy( co, ct->co );
1139 }
1140
1141 ct->rba = rba;
1142 ct->rbb = rbb;
1143 ct->type = k_contact_type_default;
1144 return 1;
1145 }
1146
1147 return 0;
1148 }
1149
1150 VG_STATIC int rb_sphere_sphere( rb_object *obja, rb_object *objb, rb_ct *buf )
1151 {
1152 rigidbody *rba = &obja->rb, *rbb = &objb->rb;
1153 v3f delta;
1154 v3_sub( rba->co, rbb->co, delta );
1155
1156 float d2 = v3_length2(delta),
1157 r = obja->inf.sphere.radius + objb->inf.sphere.radius;
1158
1159 if( d2 < r*r ){
1160 float d = sqrtf(d2);
1161
1162 rb_ct *ct = buf;
1163 v3_muls( delta, 1.0f/d, ct->n );
1164
1165 v3f p0, p1;
1166 v3_muladds( rba->co, ct->n,-obja->inf.sphere.radius, p0 );
1167 v3_muladds( rbb->co, ct->n, objb->inf.sphere.radius, p1 );
1168 v3_add( p0, p1, ct->co );
1169 v3_muls( ct->co, 0.5f, ct->co );
1170 ct->type = k_contact_type_default;
1171 ct->p = r-d;
1172 ct->rba = rba;
1173 ct->rbb = rbb;
1174 return 1;
1175 }
1176
1177 return 0;
1178 }
1179
1180 //#define RIGIDBODY_DYNAMIC_MESH_EDGES
1181
1182 #if 0
1183 __attribute__ ((deprecated))
1184 VG_STATIC int rb_sphere_triangle( rigidbody *rba, rigidbody *rbb,
1185 v3f tri[3], rb_ct *buf )
1186 {
1187 v3f delta, co;
1188
1189 #ifdef RIGIDBODY_DYNAMIC_MESH_EDGES
1190 closest_on_triangle_1( rba->co, tri, co );
1191 #else
1192 enum contact_type type = closest_on_triangle_1( rba->co, tri, co );
1193 #endif
1194
1195 v3_sub( rba->co, co, delta );
1196
1197 float d2 = v3_length2( delta ),
1198 r = rba->inf.sphere.radius;
1199
1200 if( d2 < r*r )
1201 {
1202 rb_ct *ct = buf;
1203
1204 v3f ab, ac, tn;
1205 v3_sub( tri[2], tri[0], ab );
1206 v3_sub( tri[1], tri[0], ac );
1207 v3_cross( ac, ab, tn );
1208 v3_copy( tn, ct->n );
1209
1210 if( v3_length2( ct->n ) <= 0.00001f )
1211 {
1212 vg_error( "Zero area triangle!\n" );
1213 return 0;
1214 }
1215
1216 v3_normalize( ct->n );
1217
1218 float d = sqrtf(d2);
1219
1220 v3_copy( co, ct->co );
1221 ct->type = type;
1222 ct->p = r-d;
1223 ct->rba = rba;
1224 ct->rbb = rbb;
1225 return 1;
1226 }
1227
1228 return 0;
1229 }
1230 #endif
1231
1232 VG_STATIC int rb_sphere__triangle( m4x3f mtxA, rb_sphere *b,
1233 v3f tri[3], rb_ct *buf )
1234 {
1235 v3f delta, co;
1236 enum contact_type type = closest_on_triangle_1( mtxA[3], tri, co );
1237
1238 v3_sub( mtxA[3], co, delta );
1239
1240 float d2 = v3_length2( delta ),
1241 r = b->radius;
1242
1243 if( d2 <= r*r ){
1244 rb_ct *ct = buf;
1245
1246 v3f ab, ac, tn;
1247 v3_sub( tri[2], tri[0], ab );
1248 v3_sub( tri[1], tri[0], ac );
1249 v3_cross( ac, ab, tn );
1250 v3_copy( tn, ct->n );
1251
1252 if( v3_length2( ct->n ) <= 0.00001f ){
1253 vg_error( "Zero area triangle!\n" );
1254 return 0;
1255 }
1256
1257 v3_normalize( ct->n );
1258
1259 float d = sqrtf(d2);
1260
1261 v3_copy( co, ct->co );
1262 ct->type = type;
1263 ct->p = r-d;
1264 return 1;
1265 }
1266
1267 return 0;
1268 }
1269
1270 VG_STATIC int rb_sphere__scene( m4x3f mtxA, rb_sphere *b,
1271 m4x3f mtxB, rb_scene *s, rb_ct *buf )
1272 {
1273 scene *sc = s->bh_scene->user;
1274
1275 bh_iter it;
1276 bh_iter_init( 0, &it );
1277 int idx;
1278
1279 int count = 0;
1280
1281 float r = b->radius + 0.1f;
1282 boxf box;
1283 v3_sub( mtxA[3], (v3f){ r,r,r }, box[0] );
1284 v3_add( mtxA[3], (v3f){ r,r,r }, box[1] );
1285
1286 while( bh_next( s->bh_scene, &it, box, &idx ) ){
1287 u32 *ptri = &sc->arrindices[ idx*3 ];
1288 v3f tri[3];
1289
1290 for( int j=0; j<3; j++ )
1291 v3_copy( sc->arrvertices[ptri[j]].co, tri[j] );
1292
1293 buf[ count ].element_id = ptri[0];
1294
1295 vg_line( tri[0],tri[1],0x70ff6000 );
1296 vg_line( tri[1],tri[2],0x70ff6000 );
1297 vg_line( tri[2],tri[0],0x70ff6000 );
1298
1299 int contact = rb_sphere__triangle( mtxA, b, tri, &buf[count] );
1300 count += contact;
1301
1302 if( count == 16 ){
1303 vg_warn( "Exceeding sphere_vs_scene capacity. Geometry too dense!\n" );
1304 return count;
1305 }
1306 }
1307
1308 return count;
1309 }
1310
1311 VG_STATIC int rb_box__scene( m4x3f mtxA, boxf bbx,
1312 m4x3f mtxB, rb_scene *s, rb_ct *buf )
1313 {
1314 scene *sc = s->bh_scene->user;
1315 v3f tri[3];
1316
1317 v3f extent, center;
1318 v3_sub( bbx[1], bbx[0], extent );
1319 v3_muls( extent, 0.5f, extent );
1320 v3_add( bbx[0], extent, center );
1321
1322 float r = v3_length(extent);
1323 boxf world_bbx;
1324 v3_fill( world_bbx[0], -r );
1325 v3_fill( world_bbx[1], r );
1326 for( int i=0; i<2; i++ ){
1327 v3_add( center, world_bbx[i], world_bbx[i] );
1328 v3_add( mtxA[3], world_bbx[i], world_bbx[i] );
1329 }
1330
1331 m4x3f to_local;
1332 m4x3_invert_affine( mtxA, to_local );
1333
1334 bh_iter it;
1335 bh_iter_init( 0, &it );
1336 int idx;
1337 int count = 0;
1338
1339 vg_line_boxf( world_bbx, VG__RED );
1340
1341 while( bh_next( s->bh_scene, &it, world_bbx, &idx ) ){
1342 u32 *ptri = &sc->arrindices[ idx*3 ];
1343
1344 for( int j=0; j<3; j++ )
1345 v3_copy( sc->arrvertices[ptri[j]].co, tri[j] );
1346
1347 if( rb_box_triangle_sat( extent, center, to_local, tri ) ){
1348 vg_line(tri[0],tri[1],0xff50ff00 );
1349 vg_line(tri[1],tri[2],0xff50ff00 );
1350 vg_line(tri[2],tri[0],0xff50ff00 );
1351 }
1352 else{
1353 vg_line(tri[0],tri[1],0xff0000ff );
1354 vg_line(tri[1],tri[2],0xff0000ff );
1355 vg_line(tri[2],tri[0],0xff0000ff );
1356 continue;
1357 }
1358
1359 v3f v0,v1,n;
1360 v3_sub( tri[1], tri[0], v0 );
1361 v3_sub( tri[2], tri[0], v1 );
1362 v3_cross( v0, v1, n );
1363 v3_normalize( n );
1364
1365 /* find best feature */
1366 float best = v3_dot( mtxA[0], n );
1367 int axis = 0;
1368
1369 for( int i=1; i<3; i++ ){
1370 float c = v3_dot( mtxA[i], n );
1371
1372 if( fabsf(c) > fabsf(best) ){
1373 best = c;
1374 axis = i;
1375 }
1376 }
1377
1378 v3f manifold[4];
1379
1380 if( axis == 0 ){
1381 float px = best > 0.0f? bbx[0][0]: bbx[1][0];
1382 manifold[0][0] = px;
1383 manifold[0][1] = bbx[0][1];
1384 manifold[0][2] = bbx[0][2];
1385 manifold[1][0] = px;
1386 manifold[1][1] = bbx[1][1];
1387 manifold[1][2] = bbx[0][2];
1388 manifold[2][0] = px;
1389 manifold[2][1] = bbx[1][1];
1390 manifold[2][2] = bbx[1][2];
1391 manifold[3][0] = px;
1392 manifold[3][1] = bbx[0][1];
1393 manifold[3][2] = bbx[1][2];
1394 }
1395 else if( axis == 1 ){
1396 float py = best > 0.0f? bbx[0][1]: bbx[1][1];
1397 manifold[0][0] = bbx[0][0];
1398 manifold[0][1] = py;
1399 manifold[0][2] = bbx[0][2];
1400 manifold[1][0] = bbx[1][0];
1401 manifold[1][1] = py;
1402 manifold[1][2] = bbx[0][2];
1403 manifold[2][0] = bbx[1][0];
1404 manifold[2][1] = py;
1405 manifold[2][2] = bbx[1][2];
1406 manifold[3][0] = bbx[0][0];
1407 manifold[3][1] = py;
1408 manifold[3][2] = bbx[1][2];
1409 }
1410 else{
1411 float pz = best > 0.0f? bbx[0][2]: bbx[1][2];
1412 manifold[0][0] = bbx[0][0];
1413 manifold[0][1] = bbx[0][1];
1414 manifold[0][2] = pz;
1415 manifold[1][0] = bbx[1][0];
1416 manifold[1][1] = bbx[0][1];
1417 manifold[1][2] = pz;
1418 manifold[2][0] = bbx[1][0];
1419 manifold[2][1] = bbx[1][1];
1420 manifold[2][2] = pz;
1421 manifold[3][0] = bbx[0][0];
1422 manifold[3][1] = bbx[1][1];
1423 manifold[3][2] = pz;
1424 }
1425
1426 for( int j=0; j<4; j++ )
1427 m4x3_mulv( mtxA, manifold[j], manifold[j] );
1428
1429 vg_line( manifold[0], manifold[1], 0xffffffff );
1430 vg_line( manifold[1], manifold[2], 0xffffffff );
1431 vg_line( manifold[2], manifold[3], 0xffffffff );
1432 vg_line( manifold[3], manifold[0], 0xffffffff );
1433
1434 for( int j=0; j<4; j++ ){
1435 rb_ct *ct = buf+count;
1436
1437 v3_copy( manifold[j], ct->co );
1438 v3_copy( n, ct->n );
1439
1440 float l0 = v3_dot( tri[0], n ),
1441 l1 = v3_dot( manifold[j], n );
1442
1443 ct->p = (l0-l1)*0.5f;
1444 if( ct->p < 0.0f )
1445 continue;
1446
1447 ct->type = k_contact_type_default;
1448 count ++;
1449
1450 if( count >= 12 )
1451 return count;
1452 }
1453 }
1454 return count;
1455 }
1456
1457 VG_STATIC int rb_capsule__triangle( m4x3f mtxA, rb_capsule *c,
1458 v3f tri[3], rb_ct *buf )
1459 {
1460 v3f pc, p0w, p1w;
1461 v3_muladds( mtxA[3], mtxA[1], -c->height*0.5f+c->radius, p0w );
1462 v3_muladds( mtxA[3], mtxA[1], c->height*0.5f-c->radius, p1w );
1463
1464 capsule_manifold manifold;
1465 rb_capsule_manifold_init( &manifold );
1466
1467 v3f c0, c1;
1468 closest_on_triangle_1( p0w, tri, c0 );
1469 closest_on_triangle_1( p1w, tri, c1 );
1470
1471 v3f d0, d1, da;
1472 v3_sub( c0, p0w, d0 );
1473 v3_sub( c1, p1w, d1 );
1474 v3_sub( p1w, p0w, da );
1475
1476 v3_normalize(d0);
1477 v3_normalize(d1);
1478 v3_normalize(da);
1479
1480 if( v3_dot( da, d0 ) <= 0.01f )
1481 rb_capsule_manifold( p0w, c0, 0.0f, c->radius, &manifold );
1482
1483 if( v3_dot( da, d1 ) >= -0.01f )
1484 rb_capsule_manifold( p1w, c1, 1.0f, c->radius, &manifold );
1485
1486 for( int i=0; i<3; i++ ){
1487 int i0 = i,
1488 i1 = (i+1)%3;
1489
1490 v3f ca, cb;
1491 float ta, tb;
1492 closest_segment_segment( p0w, p1w, tri[i0], tri[i1], &ta, &tb, ca, cb );
1493 rb_capsule_manifold( ca, cb, ta, c->radius, &manifold );
1494 }
1495
1496 v3f v0, v1, n;
1497 v3_sub( tri[1], tri[0], v0 );
1498 v3_sub( tri[2], tri[0], v1 );
1499 v3_cross( v0, v1, n );
1500 v3_normalize( n );
1501
1502 int count = rb_capsule__manifold_done( mtxA, c, &manifold, buf );
1503 for( int i=0; i<count; i++ )
1504 v3_copy( n, buf[i].n );
1505
1506 return count;
1507 }
1508
1509 /* mtxB is defined only for tradition; it is not used currently */
1510 VG_STATIC int rb_capsule__scene( m4x3f mtxA, rb_capsule *c,
1511 m4x3f mtxB, rb_scene *s,
1512 rb_ct *buf )
1513 {
1514 bh_iter it;
1515 bh_iter_init( 0, &it );
1516 int idx;
1517 int count = 0;
1518
1519 boxf bbx;
1520 v3_sub( mtxA[3], (v3f){ c->height, c->height, c->height }, bbx[0] );
1521 v3_add( mtxA[3], (v3f){ c->height, c->height, c->height }, bbx[1] );
1522
1523 scene *sc = s->bh_scene->user;
1524
1525 while( bh_next( s->bh_scene, &it, bbx, &idx ) ){
1526 u32 *ptri = &sc->arrindices[ idx*3 ];
1527 v3f tri[3];
1528
1529 for( int j=0; j<3; j++ )
1530 v3_copy( sc->arrvertices[ptri[j]].co, tri[j] );
1531
1532 buf[ count ].element_id = ptri[0];
1533
1534 int contact = rb_capsule__triangle( mtxA, c, tri, &buf[count] );
1535 count += contact;
1536
1537 if( count >= 16 ){
1538 vg_warn("Exceeding capsule_vs_scene capacity. Geometry too dense!\n");
1539 return count;
1540 }
1541 }
1542
1543 return count;
1544 }
1545
1546 VG_STATIC int rb_global_has_space( void )
1547 {
1548 if( rb_contact_count + 16 > vg_list_size(rb_contact_buffer) )
1549 return 0;
1550
1551 return 1;
1552 }
1553
1554 VG_STATIC rb_ct *rb_global_buffer( void )
1555 {
1556 return &rb_contact_buffer[ rb_contact_count ];
1557 }
1558
1559 /*
1560 * -----------------------------------------------------------------------------
1561 * Dynamics
1562 * -----------------------------------------------------------------------------
1563 */
1564
1565 VG_STATIC void rb_solver_reset(void)
1566 {
1567 rb_contact_count = 0;
1568 }
1569
1570 VG_STATIC rb_ct *rb_global_ct(void)
1571 {
1572 return rb_contact_buffer + rb_contact_count;
1573 }
1574
1575 VG_STATIC void rb_prepare_contact( rb_ct *ct, float timestep )
1576 {
1577 ct->bias = -0.2f * (timestep*3600.0f)
1578 * vg_minf( 0.0f, -ct->p+k_penetration_slop );
1579
1580 rb_tangent_basis( ct->n, ct->t[0], ct->t[1] );
1581 ct->norm_impulse = 0.0f;
1582 ct->tangent_impulse[0] = 0.0f;
1583 ct->tangent_impulse[1] = 0.0f;
1584 }
1585
1586 /* calculate total move. manifold should belong to ONE object only */
1587 VG_STATIC void rb_depenetrate( rb_ct *manifold, int len, v3f dt )
1588 {
1589 v3_zero( dt );
1590
1591 for( int j=0; j<7; j++ )
1592 {
1593 for( int i=0; i<len; i++ )
1594 {
1595 struct contact *ct = &manifold[i];
1596
1597 float resolved_amt = v3_dot( ct->n, dt ),
1598 remaining = (ct->p-k_penetration_slop) - resolved_amt,
1599 apply = vg_maxf( remaining, 0.0f ) * 0.4f;
1600
1601 v3_muladds( dt, ct->n, apply, dt );
1602 }
1603 }
1604 }
1605
1606 /*
1607 * Initializing things like tangent vectors
1608 */
1609 VG_STATIC void rb_presolve_contacts( rb_ct *buffer, int len )
1610 {
1611 for( int i=0; i<len; i++ ){
1612 rb_ct *ct = &buffer[i];
1613 rb_prepare_contact( ct, k_rb_delta );
1614
1615 v3f ra, rb, raCn, rbCn, raCt, rbCt;
1616 v3_sub( ct->co, ct->rba->co, ra );
1617 v3_sub( ct->co, ct->rbb->co, rb );
1618 v3_cross( ra, ct->n, raCn );
1619 v3_cross( rb, ct->n, rbCn );
1620
1621 /* orient inverse inertia tensors */
1622 v3f raCnI, rbCnI;
1623 m3x3_mulv( ct->rba->iIw, raCn, raCnI );
1624 m3x3_mulv( ct->rbb->iIw, rbCn, rbCnI );
1625
1626 ct->normal_mass = ct->rba->inv_mass + ct->rbb->inv_mass;
1627 ct->normal_mass += v3_dot( raCn, raCnI );
1628 ct->normal_mass += v3_dot( rbCn, rbCnI );
1629 ct->normal_mass = 1.0f/ct->normal_mass;
1630
1631 for( int j=0; j<2; j++ ){
1632 v3f raCtI, rbCtI;
1633 v3_cross( ct->t[j], ra, raCt );
1634 v3_cross( ct->t[j], rb, rbCt );
1635 m3x3_mulv( ct->rba->iIw, raCt, raCtI );
1636 m3x3_mulv( ct->rbb->iIw, rbCt, rbCtI );
1637
1638 ct->tangent_mass[j] = ct->rba->inv_mass + ct->rbb->inv_mass;
1639 ct->tangent_mass[j] += v3_dot( raCt, raCtI );
1640 ct->tangent_mass[j] += v3_dot( rbCt, rbCtI );
1641 ct->tangent_mass[j] = 1.0f/ct->tangent_mass[j];
1642 }
1643
1644 rb_debug_contact( ct );
1645 }
1646 }
1647
1648 /*
1649 * Creates relative contact velocity vector
1650 */
1651 VG_STATIC void rb_rcv( rigidbody *rba, rigidbody *rbb, v3f ra, v3f rb, v3f rv )
1652 {
1653 v3f rva, rvb;
1654 v3_cross( rba->w, ra, rva );
1655 v3_add( rba->v, rva, rva );
1656 v3_cross( rbb->w, rb, rvb );
1657 v3_add( rbb->v, rvb, rvb );
1658
1659 v3_sub( rva, rvb, rv );
1660 }
1661
1662 VG_STATIC void rb_contact_restitution( rb_ct *ct, float cr )
1663 {
1664 v3f rv, ra, rb;
1665 v3_sub( ct->co, ct->rba->co, ra );
1666 v3_sub( ct->co, ct->rbb->co, rb );
1667 rb_rcv( ct->rba, ct->rbb, ra, rb, rv );
1668
1669 float v = v3_dot( rv, ct->n );
1670
1671 if( v < -1.0f ){
1672 ct->bias += -cr * v;
1673 }
1674 }
1675
1676 /*
1677 * Apply impulse to object
1678 */
1679 VG_STATIC void rb_linear_impulse( rigidbody *rb, v3f delta, v3f impulse )
1680 {
1681 /* linear */
1682 v3_muladds( rb->v, impulse, rb->inv_mass, rb->v );
1683
1684 /* Angular velocity */
1685 v3f wa;
1686 v3_cross( delta, impulse, wa );
1687
1688 m3x3_mulv( rb->iIw, wa, wa );
1689 v3_add( rb->w, wa, rb->w );
1690 }
1691
1692 /*
1693 * One iteration to solve the contact constraint
1694 */
1695 VG_STATIC void rb_solve_contacts( rb_ct *buf, int len )
1696 {
1697 for( int i=0; i<len; i++ ){
1698 struct contact *ct = &buf[i];
1699
1700 v3f rv, ra, rb;
1701 v3_sub( ct->co, ct->rba->co, ra );
1702 v3_sub( ct->co, ct->rbb->co, rb );
1703 rb_rcv( ct->rba, ct->rbb, ra, rb, rv );
1704
1705 /* Friction */
1706 for( int j=0; j<2; j++ ){
1707 float f = k_friction * ct->norm_impulse,
1708 vt = v3_dot( rv, ct->t[j] ),
1709 lambda = ct->tangent_mass[j] * -vt;
1710
1711 float temp = ct->tangent_impulse[j];
1712 ct->tangent_impulse[j] = vg_clampf( temp + lambda, -f, f );
1713 lambda = ct->tangent_impulse[j] - temp;
1714
1715 v3f impulse;
1716 v3_muls( ct->t[j], lambda, impulse );
1717 rb_linear_impulse( ct->rba, ra, impulse );
1718
1719 v3_muls( ct->t[j], -lambda, impulse );
1720 rb_linear_impulse( ct->rbb, rb, impulse );
1721 }
1722
1723 /* Normal */
1724 rb_rcv( ct->rba, ct->rbb, ra, rb, rv );
1725 float vn = v3_dot( rv, ct->n ),
1726 lambda = ct->normal_mass * (-vn + ct->bias);
1727
1728 float temp = ct->norm_impulse;
1729 ct->norm_impulse = vg_maxf( temp + lambda, 0.0f );
1730 lambda = ct->norm_impulse - temp;
1731
1732 v3f impulse;
1733 v3_muls( ct->n, lambda, impulse );
1734 rb_linear_impulse( ct->rba, ra, impulse );
1735
1736 v3_muls( ct->n, -lambda, impulse );
1737 rb_linear_impulse( ct->rbb, rb, impulse );
1738 }
1739 }
1740
1741 /*
1742 * -----------------------------------------------------------------------------
1743 * Constraints
1744 * -----------------------------------------------------------------------------
1745 */
1746
1747 VG_STATIC void rb_debug_position_constraints( rb_constr_pos *buffer, int len )
1748 {
1749 for( int i=0; i<len; i++ ){
1750 rb_constr_pos *constr = &buffer[i];
1751 rigidbody *rba = constr->rba, *rbb = constr->rbb;
1752
1753 v3f wca, wcb;
1754 m3x3_mulv( rba->to_world, constr->lca, wca );
1755 m3x3_mulv( rbb->to_world, constr->lcb, wcb );
1756
1757 v3f p0, p1;
1758 v3_add( wca, rba->co, p0 );
1759 v3_add( wcb, rbb->co, p1 );
1760 vg_line_pt3( p0, 0.0025f, 0xff000000 );
1761 vg_line_pt3( p1, 0.0025f, 0xffffffff );
1762 vg_line2( p0, p1, 0xff000000, 0xffffffff );
1763 }
1764 }
1765
1766 VG_STATIC void rb_presolve_swingtwist_constraints( rb_constr_swingtwist *buf,
1767 int len )
1768 {
1769 float size = 0.12f;
1770
1771 for( int i=0; i<len; i++ ){
1772 rb_constr_swingtwist *st = &buf[ i ];
1773
1774 v3f vx, vy, va, vxb, axis, center;
1775
1776 m3x3_mulv( st->rba->to_world, st->conevx, vx );
1777 m3x3_mulv( st->rbb->to_world, st->conevxb, vxb );
1778 m3x3_mulv( st->rba->to_world, st->conevy, vy );
1779 m3x3_mulv( st->rbb->to_world, st->coneva, va );
1780 m4x3_mulv( st->rba->to_world, st->view_offset, center );
1781 v3_cross( vy, vx, axis );
1782
1783 /* Constraint violated ? */
1784 float fx = v3_dot( vx, va ), /* projection world */
1785 fy = v3_dot( vy, va ),
1786 fn = v3_dot( va, axis ),
1787
1788 rx = st->conevx[3], /* elipse radii */
1789 ry = st->conevy[3],
1790
1791 lx = fx/rx, /* projection local (fn==lz) */
1792 ly = fy/ry;
1793
1794 st->tangent_violation = ((lx*lx + ly*ly) > fn*fn) || (fn <= 0.0f);
1795 if( st->tangent_violation ){
1796 /* Calculate a good position and the axis to solve on */
1797 v2f closest, tangent,
1798 p = { fx/fabsf(fn), fy/fabsf(fn) };
1799
1800 closest_point_elipse( p, (v2f){rx,ry}, closest );
1801 tangent[0] = -closest[1] / (ry*ry);
1802 tangent[1] = closest[0] / (rx*rx);
1803 v2_normalize( tangent );
1804
1805 v3f v0, v1;
1806 v3_muladds( axis, vx, closest[0], v0 );
1807 v3_muladds( v0, vy, closest[1], v0 );
1808 v3_normalize( v0 );
1809
1810 v3_muls( vx, tangent[0], v1 );
1811 v3_muladds( v1, vy, tangent[1], v1 );
1812
1813 v3_copy( v0, st->tangent_target );
1814 v3_copy( v1, st->tangent_axis );
1815
1816 /* calculate mass */
1817 v3f aIw, bIw;
1818 m3x3_mulv( st->rba->iIw, st->tangent_axis, aIw );
1819 m3x3_mulv( st->rbb->iIw, st->tangent_axis, bIw );
1820 st->tangent_mass = 1.0f / (v3_dot( st->tangent_axis, aIw ) +
1821 v3_dot( st->tangent_axis, bIw ));
1822
1823 float angle = v3_dot( va, st->tangent_target );
1824 }
1825
1826 v3f refaxis;
1827 v3_cross( vy, va, refaxis ); /* our default rotation */
1828 v3_normalize( refaxis );
1829
1830 float angle = v3_dot( refaxis, vxb );
1831 st->axis_violation = fabsf(angle) < st->conet;
1832
1833 if( st->axis_violation ){
1834 v3f dir_test;
1835 v3_cross( refaxis, vxb, dir_test );
1836
1837 if( v3_dot(dir_test, va) < 0.0f )
1838 st->axis_violation = -st->axis_violation;
1839
1840 float newang = (float)st->axis_violation * acosf(st->conet-0.0001f);
1841
1842 v3f refaxis_up;
1843 v3_cross( va, refaxis, refaxis_up );
1844 v3_muls( refaxis_up, sinf(newang), st->axis_target );
1845 v3_muladds( st->axis_target, refaxis, -cosf(newang), st->axis_target );
1846
1847 /* calculate mass */
1848 v3_copy( va, st->axis );
1849 v3f aIw, bIw;
1850 m3x3_mulv( st->rba->iIw, st->axis, aIw );
1851 m3x3_mulv( st->rbb->iIw, st->axis, bIw );
1852 st->axis_mass = 1.0f / (v3_dot( st->axis, aIw ) +
1853 v3_dot( st->axis, bIw ));
1854 }
1855 }
1856 }
1857
1858 VG_STATIC void rb_debug_swingtwist_constraints( rb_constr_swingtwist *buf,
1859 int len )
1860 {
1861 float size = 0.12f;
1862
1863 for( int i=0; i<len; i++ ){
1864 rb_constr_swingtwist *st = &buf[ i ];
1865
1866 v3f vx, vxb, vy, va, axis, center;
1867
1868 m3x3_mulv( st->rba->to_world, st->conevx, vx );
1869 m3x3_mulv( st->rbb->to_world, st->conevxb, vxb );
1870 m3x3_mulv( st->rba->to_world, st->conevy, vy );
1871 m3x3_mulv( st->rbb->to_world, st->coneva, va );
1872 m4x3_mulv( st->rba->to_world, st->view_offset, center );
1873 v3_cross( vy, vx, axis );
1874
1875 float rx = st->conevx[3], /* elipse radii */
1876 ry = st->conevy[3];
1877
1878 v3f p0, p1;
1879 v3_muladds( center, va, size, p1 );
1880 vg_line( center, p1, 0xffffffff );
1881 vg_line_pt3( p1, 0.00025f, 0xffffffff );
1882
1883 if( st->tangent_violation ){
1884 v3_muladds( center, st->tangent_target, size, p0 );
1885
1886 vg_line( center, p0, 0xff00ff00 );
1887 vg_line_pt3( p0, 0.00025f, 0xff00ff00 );
1888 vg_line( p1, p0, 0xff000000 );
1889 }
1890
1891 for( int x=0; x<32; x++ ){
1892 float t0 = ((float)x * (1.0f/32.0f)) * VG_TAUf,
1893 t1 = (((float)x+1.0f) * (1.0f/32.0f)) * VG_TAUf,
1894 c0 = cosf( t0 ),
1895 s0 = sinf( t0 ),
1896 c1 = cosf( t1 ),
1897 s1 = sinf( t1 );
1898
1899 v3f v0, v1;
1900 v3_muladds( axis, vx, c0*rx, v0 );
1901 v3_muladds( v0, vy, s0*ry, v0 );
1902 v3_muladds( axis, vx, c1*rx, v1 );
1903 v3_muladds( v1, vy, s1*ry, v1 );
1904
1905 v3_normalize( v0 );
1906 v3_normalize( v1 );
1907
1908 v3_muladds( center, v0, size, p0 );
1909 v3_muladds( center, v1, size, p1 );
1910
1911 u32 col0r = fabsf(c0) * 255.0f,
1912 col0g = fabsf(s0) * 255.0f,
1913 col1r = fabsf(c1) * 255.0f,
1914 col1g = fabsf(s1) * 255.0f,
1915 col = st->tangent_violation? 0xff0000ff: 0xff000000,
1916 col0 = col | (col0r<<16) | (col0g << 8),
1917 col1 = col | (col1r<<16) | (col1g << 8);
1918
1919 vg_line2( center, p0, VG__NONE, col0 );
1920 vg_line2( p0, p1, col0, col1 );
1921 }
1922
1923 /* Draw twist */
1924 v3_muladds( center, va, size, p0 );
1925 v3_muladds( p0, vxb, size, p1 );
1926
1927 vg_line( p0, p1, 0xff0000ff );
1928
1929 if( st->axis_violation ){
1930 v3_muladds( p0, st->axis_target, size*1.25f, p1 );
1931 vg_line( p0, p1, 0xffffff00 );
1932 vg_line_pt3( p1, 0.0025f, 0xffffff80 );
1933 }
1934
1935 v3f refaxis;
1936 v3_cross( vy, va, refaxis ); /* our default rotation */
1937 v3_normalize( refaxis );
1938 v3f refaxis_up;
1939 v3_cross( va, refaxis, refaxis_up );
1940 float newang = acosf(st->conet-0.0001f);
1941
1942 v3_muladds( p0, refaxis_up, sinf(newang)*size, p1 );
1943 v3_muladds( p1, refaxis, -cosf(newang)*size, p1 );
1944 vg_line( p0, p1, 0xff000000 );
1945
1946 v3_muladds( p0, refaxis_up, sinf(-newang)*size, p1 );
1947 v3_muladds( p1, refaxis, -cosf(-newang)*size, p1 );
1948 vg_line( p0, p1, 0xff404040 );
1949 }
1950 }
1951
1952 /*
1953 * Solve a list of positional constraints
1954 */
1955 VG_STATIC void rb_solve_position_constraints( rb_constr_pos *buf, int len )
1956 {
1957 for( int i=0; i<len; i++ ){
1958 rb_constr_pos *constr = &buf[i];
1959 rigidbody *rba = constr->rba, *rbb = constr->rbb;
1960
1961 v3f wa, wb;
1962 m3x3_mulv( rba->to_world, constr->lca, wa );
1963 m3x3_mulv( rbb->to_world, constr->lcb, wb );
1964
1965 m3x3f ssra, ssrat, ssrb, ssrbt;
1966
1967 m3x3_skew_symetric( ssrat, wa );
1968 m3x3_skew_symetric( ssrbt, wb );
1969 m3x3_transpose( ssrat, ssra );
1970 m3x3_transpose( ssrbt, ssrb );
1971
1972 v3f b, b_wa, b_wb, b_a, b_b;
1973 m3x3_mulv( ssra, rba->w, b_wa );
1974 m3x3_mulv( ssrb, rbb->w, b_wb );
1975 v3_add( rba->v, b_wa, b );
1976 v3_sub( b, rbb->v, b );
1977 v3_sub( b, b_wb, b );
1978 v3_muls( b, -1.0f, b );
1979
1980 m3x3f invMa, invMb;
1981 m3x3_diagonal( invMa, rba->inv_mass );
1982 m3x3_diagonal( invMb, rbb->inv_mass );
1983
1984 m3x3f ia, ib;
1985 m3x3_mul( ssra, rba->iIw, ia );
1986 m3x3_mul( ia, ssrat, ia );
1987 m3x3_mul( ssrb, rbb->iIw, ib );
1988 m3x3_mul( ib, ssrbt, ib );
1989
1990 m3x3f cma, cmb;
1991 m3x3_add( invMa, ia, cma );
1992 m3x3_add( invMb, ib, cmb );
1993
1994 m3x3f A;
1995 m3x3_add( cma, cmb, A );
1996
1997 /* Solve Ax = b ( A^-1*b = x ) */
1998 v3f impulse;
1999 m3x3f invA;
2000 m3x3_inv( A, invA );
2001 m3x3_mulv( invA, b, impulse );
2002
2003 v3f delta_va, delta_wa, delta_vb, delta_wb;
2004 m3x3f iwa, iwb;
2005 m3x3_mul( rba->iIw, ssrat, iwa );
2006 m3x3_mul( rbb->iIw, ssrbt, iwb );
2007
2008 m3x3_mulv( invMa, impulse, delta_va );
2009 m3x3_mulv( invMb, impulse, delta_vb );
2010 m3x3_mulv( iwa, impulse, delta_wa );
2011 m3x3_mulv( iwb, impulse, delta_wb );
2012
2013 v3_add( rba->v, delta_va, rba->v );
2014 v3_add( rba->w, delta_wa, rba->w );
2015 v3_sub( rbb->v, delta_vb, rbb->v );
2016 v3_sub( rbb->w, delta_wb, rbb->w );
2017 }
2018 }
2019
2020 VG_STATIC void rb_solve_swingtwist_constraints( rb_constr_swingtwist *buf,
2021 int len )
2022 {
2023 float size = 0.12f;
2024
2025 for( int i=0; i<len; i++ ){
2026 rb_constr_swingtwist *st = &buf[ i ];
2027
2028 if( !st->axis_violation )
2029 continue;
2030
2031 float rv = v3_dot( st->axis, st->rbb->w ) -
2032 v3_dot( st->axis, st->rba->w );
2033
2034 if( rv * (float)st->axis_violation > 0.0f )
2035 continue;
2036
2037 v3f impulse, wa, wb;
2038 v3_muls( st->axis, rv*st->axis_mass, impulse );
2039 m3x3_mulv( st->rba->iIw, impulse, wa );
2040 v3_add( st->rba->w, wa, st->rba->w );
2041
2042 v3_muls( impulse, -1.0f, impulse );
2043 m3x3_mulv( st->rbb->iIw, impulse, wb );
2044 v3_add( st->rbb->w, wb, st->rbb->w );
2045
2046 float rv2 = v3_dot( st->axis, st->rbb->w ) -
2047 v3_dot( st->axis, st->rba->w );
2048 }
2049
2050 for( int i=0; i<len; i++ ){
2051 rb_constr_swingtwist *st = &buf[ i ];
2052
2053 if( !st->tangent_violation )
2054 continue;
2055
2056 float rv = v3_dot( st->tangent_axis, st->rbb->w ) -
2057 v3_dot( st->tangent_axis, st->rba->w );
2058
2059 if( rv > 0.0f )
2060 continue;
2061
2062 v3f impulse, wa, wb;
2063 v3_muls( st->tangent_axis, rv*st->tangent_mass, impulse );
2064 m3x3_mulv( st->rba->iIw, impulse, wa );
2065 v3_add( st->rba->w, wa, st->rba->w );
2066
2067 v3_muls( impulse, -1.0f, impulse );
2068 m3x3_mulv( st->rbb->iIw, impulse, wb );
2069 v3_add( st->rbb->w, wb, st->rbb->w );
2070
2071 float rv2 = v3_dot( st->tangent_axis, st->rbb->w ) -
2072 v3_dot( st->tangent_axis, st->rba->w );
2073 }
2074 }
2075
2076 VG_STATIC void rb_solve_constr_angle( rigidbody *rba, rigidbody *rbb,
2077 v3f ra, v3f rb )
2078 {
2079 m3x3f ssra, ssrb, ssrat, ssrbt;
2080 m3x3f cma, cmb;
2081
2082 m3x3_skew_symetric( ssrat, ra );
2083 m3x3_skew_symetric( ssrbt, rb );
2084 m3x3_transpose( ssrat, ssra );
2085 m3x3_transpose( ssrbt, ssrb );
2086
2087 m3x3_mul( ssra, rba->iIw, cma );
2088 m3x3_mul( cma, ssrat, cma );
2089 m3x3_mul( ssrb, rbb->iIw, cmb );
2090 m3x3_mul( cmb, ssrbt, cmb );
2091
2092 m3x3f A, invA;
2093 m3x3_add( cma, cmb, A );
2094 m3x3_inv( A, invA );
2095
2096 v3f b_wa, b_wb, b;
2097 m3x3_mulv( ssra, rba->w, b_wa );
2098 m3x3_mulv( ssrb, rbb->w, b_wb );
2099 v3_add( b_wa, b_wb, b );
2100 v3_negate( b, b );
2101
2102 v3f impulse;
2103 m3x3_mulv( invA, b, impulse );
2104
2105 v3f delta_wa, delta_wb;
2106 m3x3f iwa, iwb;
2107 m3x3_mul( rba->iIw, ssrat, iwa );
2108 m3x3_mul( rbb->iIw, ssrbt, iwb );
2109 m3x3_mulv( iwa, impulse, delta_wa );
2110 m3x3_mulv( iwb, impulse, delta_wb );
2111 v3_add( rba->w, delta_wa, rba->w );
2112 v3_sub( rbb->w, delta_wb, rbb->w );
2113 }
2114
2115 /*
2116 * Correct position constraint drift errors
2117 * [ 0.0 <= amt <= 1.0 ]: the correction amount
2118 */
2119 VG_STATIC void rb_correct_position_constraints( rb_constr_pos *buf, int len,
2120 float amt )
2121 {
2122 for( int i=0; i<len; i++ ){
2123 rb_constr_pos *constr = &buf[i];
2124 rigidbody *rba = constr->rba, *rbb = constr->rbb;
2125
2126 v3f p0, p1, d;
2127 m3x3_mulv( rba->to_world, constr->lca, p0 );
2128 m3x3_mulv( rbb->to_world, constr->lcb, p1 );
2129 v3_add( rba->co, p0, p0 );
2130 v3_add( rbb->co, p1, p1 );
2131 v3_sub( p1, p0, d );
2132
2133 v3_muladds( rbb->co, d, -1.0f * amt, rbb->co );
2134 rb_update_transform( rbb );
2135 }
2136 }
2137
2138 VG_STATIC void rb_correct_swingtwist_constraints( rb_constr_swingtwist *buf,
2139 int len, float amt )
2140 {
2141 for( int i=0; i<len; i++ ){
2142 rb_constr_swingtwist *st = &buf[i];
2143
2144 if( !st->tangent_violation )
2145 continue;
2146
2147 v3f va;
2148 m3x3_mulv( st->rbb->to_world, st->coneva, va );
2149
2150 float angle = v3_dot( va, st->tangent_target );
2151
2152 if( fabsf(angle) < 0.9999f ){
2153 v3f axis;
2154 v3_cross( va, st->tangent_target, axis );
2155
2156 v4f correction;
2157 q_axis_angle( correction, axis, acosf(angle) * amt );
2158 q_mul( correction, st->rbb->q, st->rbb->q );
2159 rb_update_transform( st->rbb );
2160 }
2161 }
2162
2163 for( int i=0; i<len; i++ ){
2164 rb_constr_swingtwist *st = &buf[i];
2165
2166 if( !st->axis_violation )
2167 continue;
2168
2169 v3f vxb;
2170 m3x3_mulv( st->rbb->to_world, st->conevxb, vxb );
2171
2172 float angle = v3_dot( vxb, st->axis_target );
2173
2174 if( fabsf(angle) < 0.9999f ){
2175 v3f axis;
2176 v3_cross( vxb, st->axis_target, axis );
2177
2178 v4f correction;
2179 q_axis_angle( correction, axis, acosf(angle) * amt );
2180 q_mul( correction, st->rbb->q, st->rbb->q );
2181 rb_update_transform( st->rbb );
2182 }
2183 }
2184 }
2185
2186 VG_STATIC void rb_correct_contact_constraints( rb_ct *buf, int len, float amt )
2187 {
2188 for( int i=0; i<len; i++ ){
2189 rb_ct *ct = &buf[i];
2190 rigidbody *rba = ct->rba,
2191 *rbb = ct->rbb;
2192
2193 float mass_total = 1.0f / (rba->inv_mass + rbb->inv_mass);
2194
2195 v3_muladds( rba->co, ct->n, -mass_total * rba->inv_mass, rba->co );
2196 v3_muladds( rbb->co, ct->n, mass_total * rbb->inv_mass, rbb->co );
2197 }
2198 }
2199
2200
2201 /*
2202 * Effectors
2203 */
2204
2205 VG_STATIC void rb_effect_simple_bouyency( rigidbody *ra, v4f plane,
2206 float amt, float drag )
2207 {
2208 /* float */
2209 float depth = v3_dot( plane, ra->co ) - plane[3],
2210 lambda = vg_clampf( -depth, 0.0f, 1.0f ) * amt;
2211
2212 v3_muladds( ra->v, plane, lambda * k_rb_delta, ra->v );
2213
2214 if( depth < 0.0f )
2215 v3_muls( ra->v, 1.0f-(drag*k_rb_delta), ra->v );
2216 }
2217
2218 /* apply a spring&dampener force to match ra(worldspace) on rigidbody, to
2219 * rt(worldspace)
2220 */
2221 VG_STATIC void rb_effect_spring_target_vector( rigidbody *rba, v3f ra, v3f rt,
2222 float spring, float dampening,
2223 float timestep )
2224 {
2225 float d = v3_dot( rt, ra );
2226 float a = vg_signf( d ) * acosf( vg_clampf( d, -1.0f, 1.0f ) );
2227
2228 v3f axis;
2229 v3_cross( rt, ra, axis );
2230
2231 float Fs = -a * spring,
2232 Fd = -v3_dot( rba->w, axis ) * dampening;
2233
2234 v3_muladds( rba->w, axis, (Fs+Fd) * timestep, rba->w );
2235 }
2236
2237 #endif /* RIGIDBODY_H */
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