rigidbody.h

   1 /*
   2  * Resources: Box2D - Erin Catto
   3  *            qu3e  - Randy Gaul
   4  */
   5
   6 #include "common.h"
   7 static void rb_tangent_basis( v3f n, v3f tx, v3f ty );
   8
   9 #ifndef RIGIDBODY_H
  10 #define RIGIDBODY_H
  11
  12 #include "bvh.h"
  13
  14 #define RB_DEPR
  15
  16 #define k_rb_delta (1.0f/60.0f)
  17
  18 typedef struct rigidbody rigidbody;
  19 struct rigidbody
  20 {
  21    v3f co, v, I;
  22    v4f q;
  23    boxf bbx, bbx_world;
  24    float inv_mass;
  25
  26    struct contact
  27    {
  28       v3f co, n, delta;
  29       v3f t[2];
  30       float bias, norm_impulse, tangent_impulse[2];
  31    }
  32    manifold[12];
  33    int manifold_count;
  34
  35    v3f delta;  /* where is the origin of this in relation to a parent body */
  36    m4x3f to_world, to_local;
  37 };
  38
  39 static void rb_update_transform( rigidbody *rb )
  40 {
  41    q_normalize( rb->q );
  42    q_m3x3( rb->q, rb->to_world );
  43    v3_copy( rb->co, rb->to_world[3] );
  44
  45    m4x3_invert_affine( rb->to_world, rb->to_local );
  46
  47    box_copy( rb->bbx, rb->bbx_world );
  48    m4x3_transform_aabb( rb->to_world, rb->bbx_world );
  49 }
  50
  51 static void rb_init( rigidbody *rb )
  52 {
  53    q_identity( rb->q );
  54    v3_zero( rb->v );
  55    v3_zero( rb->I );
  56
  57    v3f dims;
  58    v3_sub( rb->bbx[1], rb->bbx[0], dims );
  59
  60    rb->inv_mass = 1.0f/(8.0f*dims[0]*dims[1]*dims[2]);
  61
  62    rb_update_transform( rb );
  63 }
  64
  65 static void rb_iter( rigidbody *rb )
  66 {
  67    v3f gravity = { 0.0f, -9.6f, 0.0f };
  68    v3_muladds( rb->v, gravity, k_rb_delta, rb->v );
  69
  70    /* intergrate velocity */
  71    v3_muladds( rb->co, rb->v, k_rb_delta, rb->co );
  72
  73    v3_lerp( rb->I, (v3f){0.0f,0.0f,0.0f}, 0.0025f, rb->I );
  74
  75    /* inegrate inertia */
  76    if( v3_length2( rb->I ) > 0.0f )
  77    {
  78       v4f rotation;
  79       v3f axis;
  80       v3_copy( rb->I, axis );
  81
  82       float mag = v3_length( axis );
  83       v3_divs( axis, mag, axis );
  84       q_axis_angle( rotation, axis, mag*k_rb_delta );
  85       q_mul( rotation, rb->q, rb->q );
  86    }
  87 }
  88
  89 static void rb_torque( rigidbody *rb, v3f axis, float mag )
  90 {
  91    v3_muladds( rb->I, axis, mag*k_rb_delta, rb->I );
  92 }
  93
  94 static void rb_tangent_basis( v3f n, v3f tx, v3f ty )
  95 {
  96    /* Compute tangent basis (box2d) */
  97    if( fabsf( n[0] ) >= 0.57735027f )
  98    {
  99       tx[0] =  n[1];
 100       tx[1] = -n[0];
 101       tx[2] =  0.0f;
 102    }
 103    else
 104    {
 105       tx[0] =  0.0f;
 106       tx[1] =  n[2];
 107       tx[2] = -n[1];
 108    }
 109
 110    v3_normalize( tx );
 111    v3_cross( n, tx, ty );
 112 }
 113
 114 #include "world.h"
 115
 116 static void rb_manifold_reset( rigidbody *rb )
 117 {
 118    rb->manifold_count = 0;
 119 }
 120
 121 static void rb_build_manifold_terrain( rigidbody *rb )
 122 {
 123    v3f *box = rb->bbx;
 124    v3f pts[8];
 125    float *p000 = pts[0], *p001 = pts[1], *p010 = pts[2], *p011 = pts[3],
 126          *p100 = pts[4], *p101 = pts[5], *p110 = pts[6], *p111 = pts[7];
 127
 128    p000[0]=box[0][0];p000[1]=box[0][1];p000[2]=box[0][2];
 129    p001[0]=box[0][0];p001[1]=box[0][1];p001[2]=box[1][2];
 130    p010[0]=box[0][0];p010[1]=box[1][1];p010[2]=box[0][2];
 131    p011[0]=box[0][0];p011[1]=box[1][1];p011[2]=box[1][2];
 132
 133    p100[0]=box[1][0];p100[1]=box[0][1];p100[2]=box[0][2];
 134    p101[0]=box[1][0];p101[1]=box[0][1];p101[2]=box[1][2];
 135    p110[0]=box[1][0];p110[1]=box[1][1];p110[2]=box[0][2];
 136    p111[0]=box[1][0];p111[1]=box[1][1];p111[2]=box[1][2];
 137
 138    m4x3_mulv( rb->to_world, p000, p000 );
 139    m4x3_mulv( rb->to_world, p001, p001 );
 140    m4x3_mulv( rb->to_world, p010, p010 );
 141    m4x3_mulv( rb->to_world, p011, p011 );
 142    m4x3_mulv( rb->to_world, p100, p100 );
 143    m4x3_mulv( rb->to_world, p101, p101 );
 144    m4x3_mulv( rb->to_world, p110, p110 );
 145    m4x3_mulv( rb->to_world, p111, p111 );
 146
 147    int count = 0;
 148
 149    for( int i=0; i<8; i++ )
 150    {
 151       float *point = pts[i];
 152       struct contact *ct = &rb->manifold[rb->manifold_count];
 153
 154       v3f surface;
 155       v3_copy( point, surface );
 156       surface[1] += 4.0f;
 157
 158       ray_hit hit;
 159       hit.dist = INFINITY;
 160       if( !ray_world( surface, (v3f){0.0f,-1.0f,0.0f}, &hit ))
 161          continue;
 162
 163       v3_copy( hit.normal, ct->n );
 164       v3_copy( hit.pos, surface );
 165
 166       float p = vg_minf( surface[1] - point[1], 1.0f );
 167
 168       if( p > 0.0f )
 169       {
 170          v3_add( point, surface, ct->co );
 171          v3_muls( ct->co, 0.5f, ct->co );
 172
 173          //vg_line_pt3( ct->co, 0.0125f, 0xff0000ff );
 174
 175          v3_sub( ct->co, rb->co, ct->delta );
 176          ct->bias = -0.2f * (1.0f/k_rb_delta) * vg_minf( 0.0f, -p+0.04f );
 177          rb_tangent_basis( ct->n, ct->t[0], ct->t[1] );
 178
 179          ct->norm_impulse = 0.0f;
 180          ct->tangent_impulse[0] = 0.0f;
 181          ct->tangent_impulse[1] = 0.0f;
 182
 183          rb->manifold_count ++;
 184          count ++;
 185          if( count == 4 )
 186             break;
 187       }
 188    }
 189 }
 190
 191 static void rb_constraint_manifold( rigidbody *rb )
 192 {
 193    float k_friction = 0.1f;
 194
 195    /* Friction Impulse */
 196    for( int i=0; i<rb->manifold_count; i++ )
 197    {
 198       struct contact *ct = &rb->manifold[i];
 199
 200       v3f dv;
 201       v3_cross( rb->I, ct->delta, dv );
 202       v3_add( rb->v, dv, dv );
 203
 204       for( int j=0; j<2; j++ )
 205       {
 206          float vt = vg_clampf( -v3_dot( dv, ct->t[j] ),
 207                -k_friction, k_friction );
 208
 209          vt = -v3_dot( dv, ct->t[j] );
 210
 211          float temp = ct->tangent_impulse[j];
 212          ct->tangent_impulse[j] = vg_clampf( temp+vt, -k_friction, k_friction );
 213          vt = ct->tangent_impulse[j] - temp;
 214
 215          v3f impulse;
 216
 217          v3_muls( ct->t[j], vt, impulse );
 218          v3_add( impulse, rb->v, rb->v );
 219          v3_cross( ct->delta, impulse, impulse );
 220          v3_add( impulse, rb->I, rb->I );
 221       }
 222    }
 223
 224    /* Normal Impulse */
 225    for( int i=0; i<rb->manifold_count; i++ )
 226    {
 227       struct contact *ct = &rb->manifold[i];
 228
 229       v3f dv;
 230       v3_cross( rb->I, ct->delta, dv );
 231       v3_add( rb->v, dv, dv );
 232
 233       float vn = -v3_dot( dv, ct->n );
 234       vn += ct->bias;
 235
 236       float temp = ct->norm_impulse;
 237       ct->norm_impulse = vg_maxf( temp + vn, 0.0f );
 238       vn = ct->norm_impulse - temp;
 239
 240       v3f impulse;
 241
 242       v3_muls( ct->n, vn, impulse );
 243       v3_add( impulse, rb->v, rb->v );
 244       v3_cross( ct->delta, impulse, impulse );
 245       v3_add( impulse, rb->I, rb->I );
 246    }
 247 }
 248
 249 struct rb_angle_limit
 250 {
 251    rigidbody *rba, *rbb;
 252    v3f axis;
 253    float impulse, bias;
 254 };
 255
 256 static int rb_angle_limit_force(  rigidbody *rba, v3f va,
 257                                   rigidbody *rbb, v3f vb,
 258                                   float max )
 259 {
 260    v3f wva, wvb;
 261    m3x3_mulv( rba->to_world, va, wva );
 262    m3x3_mulv( rbb->to_world, vb, wvb );
 263
 264    float dt = v3_dot(wva,wvb)*0.999f,
 265         ang = fabsf(dt);
 266    ang = acosf( dt );
 267    if( ang > max )
 268    {
 269       float correction = max-ang;
 270
 271       v3f axis;
 272       v3_cross( wva, wvb, axis );
 273
 274       v4f rotation;
 275       q_axis_angle( rotation, axis, -correction*0.25f );
 276       q_mul( rotation, rba->q, rba->q );
 277
 278       q_axis_angle( rotation, axis,  correction*0.25f );
 279       q_mul( rotation, rbb->q, rbb->q );
 280
 281       return 1;
 282    }
 283
 284    return 0;
 285 }
 286
 287 static void rb_constraint_angle_limit( struct rb_angle_limit *limit )
 288 {
 289
 290 }
 291
 292
 293 RB_DEPR
 294 static void rb_constraint_angle( rigidbody *rba, v3f va,
 295                                  rigidbody *rbb, v3f vb,
 296                                  float max, float spring )
 297 {
 298    v3f wva, wvb;
 299    m3x3_mulv( rba->to_world, va, wva );
 300    m3x3_mulv( rbb->to_world, vb, wvb );
 301
 302    float dt = v3_dot(wva,wvb)*0.999f,
 303         ang = fabsf(dt);
 304
 305    v3f axis;
 306    v3_cross( wva, wvb, axis );
 307    v3_muladds( rba->I, axis,  ang*spring*0.5f, rba->I );
 308    v3_muladds( rbb->I, axis, -ang*spring*0.5f, rbb->I );
 309
 310    return;
 311
 312    /* TODO: convert max into the dot product value so we dont have to always
 313     *       evaluate acosf, only if its greater than the angle specified */
 314    ang = acosf( dt );
 315    if( ang > max )
 316    {
 317       float correction = max-ang;
 318
 319       v4f rotation;
 320       q_axis_angle( rotation, axis, -correction*0.125f );
 321       q_mul( rotation, rba->q, rba->q );
 322
 323       q_axis_angle( rotation, axis,  correction*0.125f );
 324       q_mul( rotation, rbb->q, rbb->q );
 325    }
 326 }
 327
 328 static void rb_relative_velocity( rigidbody *ra, v3f lca,
 329                                   rigidbody *rb, v3f lcb, v3f rcv )
 330 {
 331    v3f wca, wcb;
 332    m3x3_mulv( ra->to_world, lca, wca );
 333    m3x3_mulv( rb->to_world, lcb, wcb );
 334
 335    v3_sub( ra->v, rb->v, rcv );
 336
 337    v3f rcv_Ra, rcv_Rb;
 338    v3_cross( ra->I, wca, rcv_Ra );
 339    v3_cross( rb->I, wcb, rcv_Rb );
 340    v3_add( rcv_Ra, rcv, rcv );
 341    v3_sub( rcv, rcv_Rb, rcv );
 342 }
 343
 344 static void rb_constraint_position( rigidbody *ra, v3f lca,
 345                                     rigidbody *rb, v3f lcb )
 346 {
 347    /* C = (COa + Ra*LCa) - (COb + Rb*LCb) = 0 */
 348    v3f wca, wcb;
 349    m3x3_mulv( ra->to_world, lca, wca );
 350    m3x3_mulv( rb->to_world, lcb, wcb );
 351
 352    v3f delta;
 353    v3_add( wcb, rb->co, delta );
 354    v3_sub( delta, wca, delta );
 355    v3_sub( delta, ra->co, delta );
 356
 357    v3_muladds( ra->co, delta,  0.5f, ra->co );
 358    v3_muladds( rb->co, delta, -0.5f, rb->co );
 359
 360    v3f rcv;
 361    v3_sub( ra->v, rb->v, rcv );
 362
 363    v3f rcv_Ra, rcv_Rb;
 364    v3_cross( ra->I, wca, rcv_Ra );
 365    v3_cross( rb->I, wcb, rcv_Rb );
 366    v3_add( rcv_Ra, rcv, rcv );
 367    v3_sub( rcv, rcv_Rb, rcv );
 368
 369    float nm = 0.5f/(rb->inv_mass + ra->inv_mass);
 370
 371    float mass_a = 1.0f/ra->inv_mass,
 372          mass_b = 1.0f/rb->inv_mass,
 373          total_mass = mass_a+mass_b;
 374
 375    v3f impulse;
 376    v3_muls( rcv, 1.0f, impulse );
 377    v3_muladds( rb->v, impulse, mass_b/total_mass, rb->v );
 378    v3_cross( wcb, impulse, impulse );
 379    v3_add( impulse, rb->I, rb->I );
 380
 381    v3_muls( rcv, -1.0f, impulse );
 382    v3_muladds( ra->v, impulse, mass_a/total_mass, ra->v );
 383    v3_cross( wca, impulse, impulse );
 384    v3_add( impulse, ra->I, ra->I );
 385
 386 #if 0
 387    v3f impulse;
 388    v3_muls( delta, 0.5f*spring, impulse );
 389
 390    v3_add( impulse, ra->v, ra->v );
 391    v3_cross( wca, impulse, impulse );
 392    v3_add( impulse, ra->I, ra->I );
 393
 394    v3_muls( delta, -0.5f*spring, impulse );
 395
 396    v3_add( impulse, rb->v, rb->v );
 397    v3_cross( wcb, impulse, impulse );
 398    v3_add( impulse, rb->I, rb->I );
 399 #endif
 400 }
 401
 402 static void rb_debug( rigidbody *rb, u32 colour )
 403 {
 404    v3f *box = rb->bbx;
 405    v3f p000, p001, p010, p011, p100, p101, p110, p111;
 406
 407    p000[0]=box[0][0];p000[1]=box[0][1];p000[2]=box[0][2];
 408    p001[0]=box[0][0];p001[1]=box[0][1];p001[2]=box[1][2];
 409    p010[0]=box[0][0];p010[1]=box[1][1];p010[2]=box[0][2];
 410    p011[0]=box[0][0];p011[1]=box[1][1];p011[2]=box[1][2];
 411
 412    p100[0]=box[1][0];p100[1]=box[0][1];p100[2]=box[0][2];
 413    p101[0]=box[1][0];p101[1]=box[0][1];p101[2]=box[1][2];
 414    p110[0]=box[1][0];p110[1]=box[1][1];p110[2]=box[0][2];
 415    p111[0]=box[1][0];p111[1]=box[1][1];p111[2]=box[1][2];
 416
 417    m4x3_mulv( rb->to_world, p000, p000 );
 418    m4x3_mulv( rb->to_world, p001, p001 );
 419    m4x3_mulv( rb->to_world, p010, p010 );
 420    m4x3_mulv( rb->to_world, p011, p011 );
 421    m4x3_mulv( rb->to_world, p100, p100 );
 422    m4x3_mulv( rb->to_world, p101, p101 );
 423    m4x3_mulv( rb->to_world, p110, p110 );
 424    m4x3_mulv( rb->to_world, p111, p111 );
 425
 426    vg_line( p000, p001, colour );
 427    vg_line( p001, p011, colour );
 428    vg_line( p011, p010, colour );
 429    vg_line( p010, p000, colour );
 430
 431    vg_line( p100, p101, colour );
 432    vg_line( p101, p111, colour );
 433    vg_line( p111, p110, colour );
 434    vg_line( p110, p100, colour );
 435
 436    vg_line( p100, p000, colour );
 437    vg_line( p101, p001, colour );
 438    vg_line( p110, p010, colour );
 439    vg_line( p111, p011, colour );
 440
 441    vg_line( p000, p110, colour );
 442    vg_line( p100, p010, colour );
 443 }
 444
 445 /*
 446  * out penetration distance, normal
 447  */
 448 static int rb_point_in_body( rigidbody *rb, v3f pos, float *pen, v3f normal )
 449 {
 450    v3f local;
 451    m4x3_mulv( rb->to_local, pos, local );
 452
 453    if( local[0] > rb->bbx[0][0] && local[0] < rb->bbx[1][0] &&
 454        local[1] > rb->bbx[0][1] && local[1] < rb->bbx[1][1] &&
 455        local[2] > rb->bbx[0][2] && local[2] < rb->bbx[1][2] )
 456    {
 457       v3f area, com, comrel;
 458       v3_add( rb->bbx[0], rb->bbx[1], com );
 459       v3_muls( com, 0.5f, com );
 460
 461       v3_sub( rb->bbx[1], rb->bbx[0], area );
 462       v3_sub( local, com, comrel );
 463       v3_div( comrel, area, comrel );
 464
 465       int axis = 0;
 466       float max_mag = fabsf(comrel[0]);
 467
 468       if( fabsf(comrel[1]) > max_mag )
 469       {
 470          axis = 1;
 471          max_mag = fabsf(comrel[1]);
 472       }
 473       if( fabsf(comrel[2]) > max_mag )
 474       {
 475          axis = 2;
 476          max_mag = fabsf(comrel[2]);
 477       }
 478
 479       v3_zero( normal );
 480       normal[axis] = vg_signf(comrel[axis]);
 481
 482       if( normal[axis] < 0.0f )
 483          *pen = local[axis] - rb->bbx[0][axis];
 484       else
 485          *pen = rb->bbx[1][axis] - local[axis];
 486
 487       m3x3_mulv( rb->to_world, normal, normal );
 488       return 1;
 489    }
 490
 491    return 0;
 492 }
 493
 494 static void rb_build_manifold_rb_static( rigidbody *ra, rigidbody *rb_static )
 495 {
 496    v3f verts[8];
 497
 498    v3f a, b;
 499    v3_copy( ra->bbx[0], a );
 500    v3_copy( ra->bbx[1], b );
 501
 502         m4x3_mulv( ra->to_world, (v3f){ a[0], a[1], a[2] }, verts[0] );
 503         m4x3_mulv( ra->to_world, (v3f){ a[0], b[1], a[2] }, verts[1] );
 504         m4x3_mulv( ra->to_world, (v3f){ b[0], b[1], a[2] }, verts[2] );
 505         m4x3_mulv( ra->to_world, (v3f){ b[0], a[1], a[2] }, verts[3] );
 506         m4x3_mulv( ra->to_world, (v3f){ a[0], a[1], b[2] }, verts[4] );
 507         m4x3_mulv( ra->to_world, (v3f){ a[0], b[1], b[2] }, verts[5] );
 508         m4x3_mulv( ra->to_world, (v3f){ b[0], b[1], b[2] }, verts[6] );
 509         m4x3_mulv( ra->to_world, (v3f){ b[0], a[1], b[2] }, verts[7] );
 510
 511    int count = 0;
 512
 513    for( int i=0; i<8; i++ )
 514    {
 515       if( ra->manifold_count == vg_list_size(ra->manifold) )
 516          return;
 517
 518       struct contact *ct = &ra->manifold[ ra->manifold_count ];
 519
 520       float p;
 521       v3f normal;
 522
 523       if( rb_point_in_body( rb_static, verts[i], &p, normal ))
 524       {
 525          v3_copy( normal, ct->n );
 526          v3_muladds( verts[i], ct->n, p*0.5f, ct->co );
 527          v3_sub( ct->co, ra->co, ct->delta );
 528
 529          vg_line_pt3( ct->co, 0.0125f, 0xffff00ff );
 530
 531          ct->bias = -0.2f * (1.0f/k_rb_delta) * vg_minf( 0.0f, -p+0.04f );
 532          rb_tangent_basis( ct->n, ct->t[0], ct->t[1] );
 533
 534          ct->norm_impulse = 0.0f;
 535          ct->tangent_impulse[0] = 0.0f;
 536          ct->tangent_impulse[1] = 0.0f;
 537
 538          ra->manifold_count ++;
 539          count ++;
 540          if( count == 4 )
 541             return;
 542       }
 543    }
 544 }
 545
 546 /*
 547  * BVH implementation, this is ONLY for static rigidbodies, its to slow for
 548  * realtime use.
 549  */
 550
 551 static void rb_bh_expand_bound( void *user, boxf bound, u32 item_index )
 552 {
 553    rigidbody *rb = &((rigidbody *)user)[ item_index ];
 554    box_concat( bound, rb->bbx_world );
 555 }
 556
 557 static float rb_bh_centroid( void *user, u32 item_index, int axis )
 558 {
 559    rigidbody *rb = &((rigidbody *)user)[ item_index ];
 560    return (rb->bbx_world[axis][0] + rb->bbx_world[1][axis]) * 0.5f;
 561 }
 562
 563 static void rb_bh_swap( void *user, u32 ia, u32 ib )
 564 {
 565    rigidbody temp, *rba, *rbb;
 566    rba = &((rigidbody *)user)[ ia ];
 567    rbb = &((rigidbody *)user)[ ib ];
 568
 569    temp = *rba;
 570    *rba = *rbb;
 571    *rbb = temp;
 572 }
 573
 574 static void rb_bh_debug( void *user, u32 item_index )
 575 {
 576    rigidbody *rb = &((rigidbody *)user)[ item_index ];
 577    rb_debug( rb, 0xff00ffff );
 578 }
 579
 580 static bh_system bh_system_rigidbodies =
 581 {
 582    .expand_bound = rb_bh_expand_bound,
 583    .item_centroid = rb_bh_centroid,
 584    .item_swap = rb_bh_swap,
 585    .item_debug = rb_bh_debug,
 586    .cast_ray = NULL,
 587
 588    .item_size = sizeof(rigidbody)
 589 };
 590
 591 #endif /* RIGIDBODY_H */