csrMath.h

   1 // Util
   2 // ==================================================================================================================
   3
   4 #define CSR_PIf 3.14159265358979323846264338327950288f
   5
   6 float csr_minf( float a, float b )
   7 {
   8         if( a < b )
   9                 return a;
  10         return b;
  11 }
  12
  13 float csr_maxf( float a, float b )
  14 {
  15         if( a > b )
  16                 return a;
  17         return b;
  18 }
  19
  20 int csr_min( int a, int b )
  21 {
  22         if( a < b )
  23                 return a;
  24         return b;
  25 }
  26
  27 int csr_max( int a, int b )
  28 {
  29         if( a > b )
  30                 return a;
  31         return b;
  32 }
  33
  34 void v3d_v3f( double a[3], float b[3] )
  35 {
  36         b[0] = a[0];
  37         b[1] = a[1];
  38         b[2] = a[2];
  39 }
  40
  41 float csr_rad( float deg )
  42 {
  43         return deg * CSR_PIf / 180.0f;
  44 }
  45
  46 // Vector 2
  47 // ==================================================================================================================
  48
  49 void v2_copy( v2f a, v2f b )
  50 {
  51         b[0] = a[0]; b[1] = a[1];
  52 }
  53
  54 void v2_minv( v2f a, v2f b, v2f dest )
  55 {
  56         dest[0] = csr_minf(a[0], b[0]);
  57         dest[1] = csr_minf(a[1], b[1]);
  58 }
  59
  60 void v2_maxv( v2f a, v2f b, v2f dest )
  61 {
  62         dest[0] = csr_maxf(a[0], b[0]);
  63         dest[1] = csr_maxf(a[1], b[1]);
  64 }
  65
  66 void v2_sub( v2f a, v2f b, v2f d )
  67 {
  68         d[0] = a[0]-b[0]; d[1] = a[1]-b[1];
  69 }
  70
  71 float v2_cross( v2f a, v2f b )
  72 {
  73         return a[0] * b[1] - a[1] * b[0];
  74 }
  75
  76 void v2_add( v2f a, v2f b, v2f d )
  77 {
  78         d[0] = a[0]+b[0]; d[1] = a[1]+b[1];
  79 }
  80
  81 // Vector 3
  82 // ==================================================================================================================
  83
  84 void v3_zero( v3f a )
  85 {
  86         a[0] = 0.f; a[1] = 0.f; a[2] = 0.f;
  87 }
  88
  89 void v3_copy( v3f a, v3f b )
  90 {
  91         b[0] = a[0]; b[1] = a[1]; b[2] = a[2];
  92 }
  93
  94 void v3_add( v3f a, v3f b, v3f d )
  95 {
  96         d[0] = a[0]+b[0]; d[1] = a[1]+b[1]; d[2] = a[2]+b[2];
  97 }
  98
  99 void v3_sub( v3f a, v3f b, v3f d )
 100 {
 101         d[0] = a[0]-b[0]; d[1] = a[1]-b[1]; d[2] = a[2]-b[2];
 102 }
 103
 104 void v3_mul( v3f a, v3f b, v3f d )
 105 {
 106         d[0] = a[0]*b[0]; d[1] = a[1]*b[1]; d[2] = a[2]*b[2];
 107 }
 108
 109 void v3_div( v3f a, v3f b, v3f d )
 110 {
 111         d[0] = a[0]/b[0]; d[1] = a[1]/b[1];     d[2] = a[2]/b[2];
 112 }
 113
 114 void v3_muls( v3f a, float s, v3f d )
 115 {
 116         d[0] = a[0]*s; d[1] = a[1]*s; d[2] = a[2]*s;
 117 }
 118
 119 void v3_divs( v3f a, float s, v3f d )
 120 {
 121         d[0] = a[0]/s; d[1] = a[1]/s; d[2] = a[2]/s;
 122 }
 123
 124 void v3_muladds( v3f a, v3f b, float s, v3f d )
 125 {
 126         d[0] = a[0]+b[0]*s; d[1] = a[1]+b[1]*s; d[2] = a[2]+b[2]*s;
 127 }
 128
 129 float v3_dot( v3f a, v3f b )
 130 {
 131         return a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
 132 }
 133
 134 void v3_cross( v3f a, v3f b, v3f d )
 135 {
 136   d[0] = a[1] * b[2] - a[2] * b[1];
 137   d[1] = a[2] * b[0] - a[0] * b[2];
 138   d[2] = a[0] * b[1] - a[1] * b[0];
 139 }
 140
 141 float v3_length2( v3f a )
 142 {
 143         return v3_dot( a, a );
 144 }
 145
 146 float v3_length( v3f a )
 147 {
 148         return sqrtf( v3_length2( a ) );
 149 }
 150
 151 float v3_dist2( v3f a, v3f b )
 152 {
 153         v3f delta;
 154         v3_sub( a, b, delta );
 155         return v3_length2( delta );
 156 }
 157
 158 float v3_dist( v3f a, v3f b )
 159 {
 160         return sqrtf( v3_dist2( a, b ) );
 161 }
 162
 163 void v3_normalize( v3f a )
 164 {
 165         v3_muls( a, 1.f / v3_length( a ), a );
 166 }
 167
 168 float csr_lerpf( float a, float b, float t )
 169 {
 170         return a + t*(b-a);
 171 }
 172
 173 void v3_lerp( v3f a, v3f b, float t, v3f d )
 174 {
 175         d[0] = a[0] + t*(b[0]-a[0]);
 176         d[1] = a[1] + t*(b[1]-a[1]);
 177         d[2] = a[2] + t*(b[2]-a[2]);
 178 }
 179
 180 void v3_minv( v3f a, v3f b, v3f dest )
 181 {
 182         dest[0] = csr_minf(a[0], b[0]);
 183         dest[1] = csr_minf(a[1], b[1]);
 184         dest[2] = csr_minf(a[2], b[2]);
 185 }
 186
 187 void v3_maxv( v3f a, v3f b, v3f dest )
 188 {
 189         dest[0] = csr_maxf(a[0], b[0]);
 190         dest[1] = csr_maxf(a[1], b[1]);
 191         dest[2] = csr_maxf(a[2], b[2]);
 192 }
 193
 194 float v3_minf( v3f a )
 195 {
 196         return csr_minf( csr_minf( a[0], a[1] ), a[2] );
 197 }
 198
 199 float v3_maxf( v3f a )
 200 {
 201         return csr_maxf( csr_maxf( a[0], a[1] ), a[2] );
 202 }
 203
 204 void v3_fill( v3f a, float v )
 205 {
 206         a[0] = v;
 207         a[1] = v;
 208         a[2] = v;
 209 }
 210
 211 // Vector 4
 212 void v4_copy( v4f a, v4f b )
 213 {
 214         b[0] = a[0]; b[1] = a[1]; b[2] = a[2]; b[3] = a[3];
 215 }
 216
 217 // Matrix 3x3
 218 //======================================================================================================
 219
 220 void m3x3_inv_transpose( m3x3f src, m3x3f dest )
 221 {
 222         float a = src[0][0], b = src[0][1], c = src[0][2],
 223                         d = src[1][0], e = src[1][1], f = src[1][2],
 224                         g = src[2][0], h = src[2][1], i = src[2][2];
 225
 226         float det =    1.f /
 227                                         (+a*(e*i-h*f)
 228                 -b*(d*i-f*g)
 229                 +c*(d*h-e*g));
 230
 231         dest[0][0] =  (e*i-h*f)*det;
 232         dest[1][0] = -(b*i-c*h)*det;
 233         dest[2][0] =  (b*f-c*e)*det;
 234         dest[0][1] = -(d*i-f*g)*det;
 235         dest[1][1] =  (a*i-c*g)*det;
 236         dest[2][1] = -(a*f-d*c)*det;
 237         dest[0][2] =  (d*h-g*e)*det;
 238         dest[1][2] = -(a*h-g*b)*det;
 239         dest[2][2] =  (a*e-d*b)*det;
 240 }
 241
 242 void m3x3_mulv( m3x3f m, v3f v, v3f d )
 243 {
 244         v3f res;
 245
 246         res[0] = m[0][0]*v[0] + m[1][0]*v[1] + m[2][0]*v[2];
 247         res[1] = m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2];
 248         res[2] = m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2];
 249
 250         v3_copy( res, d );
 251 }
 252
 253 // Matrix 4x3
 254 // ==================================================================================================================
 255
 256 #define M4X3_IDENTITY   {{1.0f, 0.0f, 0.0f, },\
 257                                                                 { 0.0f, 1.0f, 0.0f, },\
 258                                                                 { 0.0f, 0.0f, 1.0f, },\
 259                                                                 { 0.0f, 0.0f, 0.0f }}
 260
 261 void m4x3_to_3x3( m4x3f a, m3x3f b )
 262 {
 263         v3_copy( a[0], b[0] );
 264         v3_copy( a[1], b[1] );
 265         v3_copy( a[2], b[2] );
 266 }
 267
 268 void m4x3_copy( m4x3f a, m4x3f b )
 269 {
 270         v3_copy( a[0], b[0] );
 271         v3_copy( a[1], b[1] );
 272         v3_copy( a[2], b[2] );
 273         v3_copy( a[3], b[3] );
 274 }
 275
 276 void m4x3_identity( m4x3f a )
 277 {
 278         m4x3f id = M4X3_IDENTITY;
 279         m4x3_copy( id, a );
 280 }
 281
 282 void m4x3_mul( m4x3f a, m4x3f b, m4x3f d )
 283 {
 284         float
 285         a00 = a[0][0], a01 = a[0][1], a02 = a[0][2],
 286         a10 = a[1][0], a11 = a[1][1], a12 = a[1][2],
 287         a20 = a[2][0], a21 = a[2][1], a22 = a[2][2],
 288         a30 = a[3][0], a31 = a[3][1], a32 = a[3][2],
 289         b00 = b[0][0], b01 = b[0][1], b02 = b[0][2],
 290         b10 = b[1][0], b11 = b[1][1], b12 = b[1][2],
 291         b20 = b[2][0], b21 = b[2][1], b22 = b[2][2],
 292         b30 = b[3][0], b31 = b[3][1], b32 = b[3][2];
 293
 294         d[0][0] = a00*b00 + a10*b01 + a20*b02;
 295         d[0][1] = a01*b00 + a11*b01 + a21*b02;
 296         d[0][2] = a02*b00 + a12*b01 + a22*b02;
 297         d[1][0] = a00*b10 + a10*b11 + a20*b12;
 298         d[1][1] = a01*b10 + a11*b11 + a21*b12;
 299         d[1][2] = a02*b10 + a12*b11 + a22*b12;
 300         d[2][0] = a00*b20 + a10*b21 + a20*b22;
 301         d[2][1] = a01*b20 + a11*b21 + a21*b22;
 302         d[2][2] = a02*b20 + a12*b21 + a22*b22;
 303         d[3][0] = a00*b30 + a10*b31 + a20*b32 + a30;
 304         d[3][1] = a01*b30 + a11*b31 + a21*b32 + a31;
 305         d[3][2] = a02*b30 + a12*b31 + a22*b32 + a32;
 306 }
 307
 308 void m4x3_mulv( m4x3f m, v3f v, v3f d )
 309 {
 310         v3f res;
 311
 312         res[0] = m[0][0]*v[0] + m[1][0]*v[1] + m[2][0]*v[2] + m[3][0];
 313         res[1] = m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2] + m[3][1];
 314         res[2] = m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2] + m[3][2];
 315
 316         v3_copy( res, d );
 317 }
 318
 319 // Affine transforms
 320
 321 void m4x3_translate( m4x3f m, v3f v )
 322 {
 323         v3_muladds( m[3], m[0], v[0], m[3] );
 324         v3_muladds( m[3], m[1], v[1], m[3] );
 325         v3_muladds( m[3], m[2], v[2], m[3] );
 326 }
 327
 328 void m4x3_scale( m4x3f m, float s )
 329 {
 330         v3_muls( m[0], s, m[0] );
 331         v3_muls( m[1], s, m[1] );
 332         v3_muls( m[2], s, m[2] );
 333 }
 334
 335 void m4x3_rotate_x( m4x3f m, float angle )
 336 {
 337         m4x3f t = M4X3_IDENTITY;
 338         float c, s;
 339
 340         c = cosf( angle );
 341         s = sinf( angle );
 342
 343         t[1][1] =  c;
 344         t[1][2] =  s;
 345         t[2][1] = -s;
 346         t[2][2] =  c;
 347
 348         m4x3_mul( m, t, m );
 349 }
 350
 351 void m4x3_rotate_y( m4x3f m, float angle )
 352 {
 353         m4x3f t = M4X3_IDENTITY;
 354         float c, s;
 355
 356         c = cosf( angle );
 357         s = sinf( angle );
 358
 359         t[0][0] =  c;
 360         t[0][2] = -s;
 361         t[2][0] =  s;
 362         t[2][2] =  c;
 363
 364         m4x3_mul( m, t, m );
 365 }
 366
 367 void m4x3_rotate_z( m4x3f m, float angle )
 368 {
 369         m4x3f t = M4X3_IDENTITY;
 370         float c, s;
 371
 372         c = cosf( angle );
 373         s = sinf( angle );
 374
 375         t[0][0] =  c;
 376         t[0][1] =  s;
 377         t[1][0] = -s;
 378         t[1][1] =  c;
 379
 380         m4x3_mul( m, t, m );
 381 }
 382
 383 // Warning: These functions are unoptimized..
 384 void m4x3_expand_aabb_point( m4x3f m, boxf box, v3f point )
 385 {
 386         v3f v;
 387         m4x3_mulv( m, point, v );
 388
 389         v3_minv( box[0], v, box[0] );
 390         v3_maxv( box[1], v, box[1] );
 391 }
 392
 393 void box_concat( boxf a, boxf b )
 394 {
 395         v3_minv( a[0], b[0], a[0] );
 396         v3_maxv( a[1], b[1], a[1] );
 397 }
 398
 399 void box_copy( boxf a, boxf b )
 400 {
 401         v3_copy( a[0], b[0] );
 402         v3_copy( a[1], b[1] );
 403 }
 404
 405 void m4x3_transform_aabb( m4x3f m, boxf box )
 406 {
 407         v3f a; v3f b;
 408
 409         v3_copy( box[0], a );
 410         v3_copy( box[1], b );
 411
 412         m4x3_expand_aabb_point( m, box, a );
 413         m4x3_expand_aabb_point( m, box, (v3f){ a[0], b[1], a[2] } );
 414         m4x3_expand_aabb_point( m, box, (v3f){ b[0], a[1], a[2] } );
 415         m4x3_expand_aabb_point( m, box, (v3f){ b[0], b[1], a[2] } );
 416         m4x3_expand_aabb_point( m, box, b );
 417         m4x3_expand_aabb_point( m, box, (v3f){ a[0], b[1], b[2] } );
 418         m4x3_expand_aabb_point( m, box, (v3f){ b[0], a[1], b[2] } );
 419         m4x3_expand_aabb_point( m, box, (v3f){ b[0], b[1], b[2] } );
 420 }
 421
 422 // Planes (double precision)
 423 // ==================================================================================================================
 424
 425 void tri_to_plane( double a[3], double b[3], double c[3], double p[4] )
 426 {
 427         double edge0[3];
 428         double edge1[3];
 429         double l;
 430
 431         edge0[0] = b[0] - a[0];
 432         edge0[1] = b[1] - a[1];
 433         edge0[2] = b[2] - a[2];
 434
 435         edge1[0] = c[0] - a[0];
 436         edge1[1] = c[1] - a[1];
 437         edge1[2] = c[2] - a[2];
 438
 439         p[0] = edge0[1] * edge1[2] - edge0[2] * edge1[1];
 440         p[1] = edge0[2] * edge1[0] - edge0[0] * edge1[2];
 441         p[2] = edge0[0] * edge1[1] - edge0[1] * edge1[0];
 442
 443         l = sqrt(p[0] * p[0] + p[1] * p[1] + p[2] * p[2]);
 444         p[3] = (p[0] * a[0] + p[1] * a[1] + p[2] * a[2]) / l;
 445
 446         p[0] = p[0] / l;
 447         p[1] = p[1] / l;
 448         p[2] = p[2] / l;
 449 }
 450
 451 int plane_intersect( double a[4], double b[4], double c[4], double p[4] )
 452 {
 453         double const epsilon = 1e-8f;
 454
 455         double x[3];
 456         double d;
 457
 458         x[0] = a[1] * b[2] - a[2] * b[1];
 459         x[1] = a[2] * b[0] - a[0] * b[2];
 460         x[2] = a[0] * b[1] - a[1] * b[0];
 461
 462         d = x[0] * c[0] + x[1] * c[1] + x[2] * c[2];
 463
 464         if( d < epsilon && d > -epsilon ) return 0;
 465
 466         p[0] = (b[1] * c[2] - b[2] * c[1]) * -a[3];
 467         p[1] = (b[2] * c[0] - b[0] * c[2]) * -a[3];
 468         p[2] = (b[0] * c[1] - b[1] * c[0]) * -a[3];
 469
 470         p[0] += (c[1] * a[2] - c[2] * a[1]) * -b[3];
 471         p[1] += (c[2] * a[0] - c[0] * a[2]) * -b[3];
 472         p[2] += (c[0] * a[1] - c[1] * a[0]) * -b[3];
 473
 474         p[0] += (a[1] * b[2] - a[2] * b[1]) * -c[3];
 475         p[1] += (a[2] * b[0] - a[0] * b[2]) * -c[3];
 476         p[2] += (a[0] * b[1] - a[1] * b[0]) * -c[3];
 477
 478         p[0] = -p[0] / d;
 479         p[1] = -p[1] / d;
 480         p[2] = -p[2] / d;
 481
 482         return 1;
 483 }
 484
 485 double plane_polarity( double p[4], double a[3] )
 486 {
 487         return
 488         (a[0] * p[0] + a[1] * p[1] + a[2] * p[2])
 489         -(p[0]*p[3] * p[0] + p[1]*p[3] * p[1] + p[2]*p[3] * p[2])
 490         ;
 491 }
 492
 493 // Raycasting
 494 // ==================================================================================================================
 495
 496 int csr_slabs( v3f box[2], v3f o, v3f id )
 497 {
 498         v3f t0; v3f t1;
 499         v3f tmin; v3f tmax;
 500
 501         v3_sub( box[0], o, t0 );
 502         v3_sub( box[1], o, t1 );
 503         v3_mul( t0, id, t0 );
 504         v3_mul( t1, id, t1 );
 505
 506         v3_minv( t0, t1, tmin );
 507         v3_maxv( t0, t1, tmax );
 508
 509         return v3_maxf( tmin ) <= v3_minf( tmax );
 510 }
 511
 512 float csr_ray_tri( v3f o, v3f d, v3f v0, v3f v1, v3f v2, float *u, float *v )
 513 {
 514         float const k_cullEpsilon = 0.000001f;
 515
 516         v3f v0v1;
 517         v3f v0v2;
 518         v3f p;
 519         float det, inv;
 520
 521         v3f tv;
 522         v3f qv;
 523
 524         v3_sub( v1, v0, v0v1 );
 525         v3_sub( v2, v0, v0v2 );
 526         v3_cross( d, v0v2, p );
 527
 528         det = v3_dot( v0v1, p );
 529
 530         if( det < k_cullEpsilon ) return -INFINITY;
 531
 532         inv = 1.f / det;
 533
 534         v3_sub( o, v0, tv );
 535         *u = v3_dot( tv, p ) * inv;
 536
 537         if( *u < 0.f || *u > 1.f ) return -INFINITY;
 538
 539         v3_cross( tv, v0v1, qv );
 540         *v = v3_dot( d, qv ) * inv;
 541
 542         if( *v < 0.f || *u + *v > 1.f ) return -INFINITY;
 543
 544         return v3_dot( v0v2, qv ) * inv;
 545 }