csrMath.h

   1 // Util
   2 // ==================================================================================================================
   3
   4 #define CSR_PIf 3.14159265358979323846264338327950288f
   5
   6 // Simple min/max replacements
   7 float csr_minf( float a, float b )
   8 {
   9         return a < b? a: b;
  10 }
  11
  12 float csr_maxf( float a, float b )
  13 {
  14         return a > b? a: b;
  15 }
  16
  17 int csr_min( int a, int b )
  18 {
  19         return a < b? a: b;
  20 }
  21
  22 int csr_max( int a, int b )
  23 {
  24         return a > b? a: b;
  25 }
  26
  27 // Convert double precision vec3 into single
  28 void v3d_v3f( double a[3], float b[3] )
  29 {
  30         b[0] = a[0];
  31         b[1] = a[1];
  32         b[2] = a[2];
  33 }
  34
  35 // Convert degrees to radians
  36 float csr_rad( float deg )
  37 {
  38         return deg * CSR_PIf / 180.0f;
  39 }
  40
  41 // Vector 2
  42 // ==================================================================================================================
  43
  44 void v2_copy( v2f a, v2f b )
  45 {
  46         b[0] = a[0]; b[1] = a[1];
  47 }
  48
  49 void v2_minv( v2f a, v2f b, v2f dest )
  50 {
  51         dest[0] = csr_minf(a[0], b[0]);
  52         dest[1] = csr_minf(a[1], b[1]);
  53 }
  54
  55 void v2_maxv( v2f a, v2f b, v2f dest )
  56 {
  57         dest[0] = csr_maxf(a[0], b[0]);
  58         dest[1] = csr_maxf(a[1], b[1]);
  59 }
  60
  61 void v2_sub( v2f a, v2f b, v2f d )
  62 {
  63         d[0] = a[0]-b[0]; d[1] = a[1]-b[1];
  64 }
  65
  66 float v2_cross( v2f a, v2f b )
  67 {
  68         return a[0] * b[1] - a[1] * b[0];
  69 }
  70
  71 void v2_add( v2f a, v2f b, v2f d )
  72 {
  73         d[0] = a[0]+b[0]; d[1] = a[1]+b[1];
  74 }
  75
  76 void v2_muls( v2f a, float s, v2f d )
  77 {
  78         d[0] = a[0]*s; d[1] = a[1]*s;
  79 }
  80
  81 void v2_mul( v2f a, v2f b, v2f d )
  82 {
  83         d[0] = a[0]*b[0]; d[1] = a[1]*b[1];
  84 }
  85
  86 // Vector 3
  87 // ==================================================================================================================
  88
  89 void v3_zero( v3f a )
  90 {
  91         a[0] = 0.f; a[1] = 0.f; a[2] = 0.f;
  92 }
  93
  94 void v3_copy( v3f a, v3f b )
  95 {
  96         b[0] = a[0]; b[1] = a[1]; b[2] = a[2];
  97 }
  98
  99 void v3_add( 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_sub( 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_mul( 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_div( v3f a, v3f b, v3f d )
 115 {
 116         d[0] = a[0]/b[0]; d[1] = a[1]/b[1];     d[2] = a[2]/b[2];
 117 }
 118
 119 void v3_muls( 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_divs( v3f a, float s, v3f d )
 125 {
 126         d[0] = a[0]/s; d[1] = a[1]/s; d[2] = a[2]/s;
 127 }
 128
 129 void v3_muladds( v3f a, v3f b, float s, v3f d )
 130 {
 131         d[0] = a[0]+b[0]*s; d[1] = a[1]+b[1]*s; d[2] = a[2]+b[2]*s;
 132 }
 133
 134 float v3_dot( v3f a, v3f b )
 135 {
 136         return a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
 137 }
 138
 139 void v3_cross( v3f a, v3f b, v3f d )
 140 {
 141   d[0] = a[1] * b[2] - a[2] * b[1];
 142   d[1] = a[2] * b[0] - a[0] * b[2];
 143   d[2] = a[0] * b[1] - a[1] * b[0];
 144 }
 145
 146 float v3_length2( v3f a )
 147 {
 148         return v3_dot( a, a );
 149 }
 150
 151 float v3_length( v3f a )
 152 {
 153         return sqrtf( v3_length2( a ) );
 154 }
 155
 156 float v3_dist2( v3f a, v3f b )
 157 {
 158         v3f delta;
 159         v3_sub( a, b, delta );
 160         return v3_length2( delta );
 161 }
 162
 163 float v3_dist( v3f a, v3f b )
 164 {
 165         return sqrtf( v3_dist2( a, b ) );
 166 }
 167
 168 void v3_normalize( v3f a )
 169 {
 170         v3_muls( a, 1.f / v3_length( a ), a );
 171 }
 172
 173 float csr_lerpf( float a, float b, float t )
 174 {
 175         return a + t*(b-a);
 176 }
 177
 178 void v3_lerp( v3f a, v3f b, float t, v3f d )
 179 {
 180         d[0] = a[0] + t*(b[0]-a[0]);
 181         d[1] = a[1] + t*(b[1]-a[1]);
 182         d[2] = a[2] + t*(b[2]-a[2]);
 183 }
 184
 185 void v3_minv( v3f a, v3f b, v3f dest )
 186 {
 187         dest[0] = csr_minf(a[0], b[0]);
 188         dest[1] = csr_minf(a[1], b[1]);
 189         dest[2] = csr_minf(a[2], b[2]);
 190 }
 191
 192 void v3_maxv( v3f a, v3f b, v3f dest )
 193 {
 194         dest[0] = csr_maxf(a[0], b[0]);
 195         dest[1] = csr_maxf(a[1], b[1]);
 196         dest[2] = csr_maxf(a[2], b[2]);
 197 }
 198
 199 float v3_minf( v3f a )
 200 {
 201         return csr_minf( csr_minf( a[0], a[1] ), a[2] );
 202 }
 203
 204 float v3_maxf( v3f a )
 205 {
 206         return csr_maxf( csr_maxf( a[0], a[1] ), a[2] );
 207 }
 208
 209 void v3_fill( v3f a, float v )
 210 {
 211         a[0] = v;
 212         a[1] = v;
 213         a[2] = v;
 214 }
 215
 216 // Vector 4
 217 // ==================================================================================================================
 218
 219 void v4_copy( v4f a, v4f b )
 220 {
 221         b[0] = a[0]; b[1] = a[1]; b[2] = a[2]; b[3] = a[3];
 222 }
 223
 224 void v4_zero( v4f a )
 225 {
 226         a[0] = 0.f; a[1] = 0.f; a[2] = 0.f; a[3] = 0.f;
 227 }
 228
 229 // Matrix 3x3
 230 //======================================================================================================
 231
 232 void m3x3_inv_transpose( m3x3f src, m3x3f dest )
 233 {
 234         float a = src[0][0], b = src[0][1], c = src[0][2],
 235                         d = src[1][0], e = src[1][1], f = src[1][2],
 236                         g = src[2][0], h = src[2][1], i = src[2][2];
 237
 238         float det =    1.f /
 239                                         (+a*(e*i-h*f)
 240                 -b*(d*i-f*g)
 241                 +c*(d*h-e*g));
 242
 243         dest[0][0] =  (e*i-h*f)*det;
 244         dest[1][0] = -(b*i-c*h)*det;
 245         dest[2][0] =  (b*f-c*e)*det;
 246         dest[0][1] = -(d*i-f*g)*det;
 247         dest[1][1] =  (a*i-c*g)*det;
 248         dest[2][1] = -(a*f-d*c)*det;
 249         dest[0][2] =  (d*h-g*e)*det;
 250         dest[1][2] = -(a*h-g*b)*det;
 251         dest[2][2] =  (a*e-d*b)*det;
 252 }
 253
 254 void m3x3_mulv( m3x3f m, v3f v, v3f d )
 255 {
 256         v3f res;
 257
 258         res[0] = m[0][0]*v[0] + m[1][0]*v[1] + m[2][0]*v[2];
 259         res[1] = m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2];
 260         res[2] = m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2];
 261
 262         v3_copy( res, d );
 263 }
 264
 265 // Matrix 4x3
 266 // ==================================================================================================================
 267
 268 #define M4X3_IDENTITY   {{1.0f, 0.0f, 0.0f, },\
 269                                                                 { 0.0f, 1.0f, 0.0f, },\
 270                                                                 { 0.0f, 0.0f, 1.0f, },\
 271                                                                 { 0.0f, 0.0f, 0.0f }}
 272
 273 void m4x3_to_3x3( m4x3f a, m3x3f b )
 274 {
 275         v3_copy( a[0], b[0] );
 276         v3_copy( a[1], b[1] );
 277         v3_copy( a[2], b[2] );
 278 }
 279
 280 void m4x3_copy( m4x3f a, m4x3f b )
 281 {
 282         v3_copy( a[0], b[0] );
 283         v3_copy( a[1], b[1] );
 284         v3_copy( a[2], b[2] );
 285         v3_copy( a[3], b[3] );
 286 }
 287
 288 void m4x3_identity( m4x3f a )
 289 {
 290         m4x3f id = M4X3_IDENTITY;
 291         m4x3_copy( id, a );
 292 }
 293
 294 void m4x3_mul( m4x3f a, m4x3f b, m4x3f d )
 295 {
 296         float
 297         a00 = a[0][0], a01 = a[0][1], a02 = a[0][2],
 298         a10 = a[1][0], a11 = a[1][1], a12 = a[1][2],
 299         a20 = a[2][0], a21 = a[2][1], a22 = a[2][2],
 300         a30 = a[3][0], a31 = a[3][1], a32 = a[3][2],
 301         b00 = b[0][0], b01 = b[0][1], b02 = b[0][2],
 302         b10 = b[1][0], b11 = b[1][1], b12 = b[1][2],
 303         b20 = b[2][0], b21 = b[2][1], b22 = b[2][2],
 304         b30 = b[3][0], b31 = b[3][1], b32 = b[3][2];
 305
 306         d[0][0] = a00*b00 + a10*b01 + a20*b02;
 307         d[0][1] = a01*b00 + a11*b01 + a21*b02;
 308         d[0][2] = a02*b00 + a12*b01 + a22*b02;
 309         d[1][0] = a00*b10 + a10*b11 + a20*b12;
 310         d[1][1] = a01*b10 + a11*b11 + a21*b12;
 311         d[1][2] = a02*b10 + a12*b11 + a22*b12;
 312         d[2][0] = a00*b20 + a10*b21 + a20*b22;
 313         d[2][1] = a01*b20 + a11*b21 + a21*b22;
 314         d[2][2] = a02*b20 + a12*b21 + a22*b22;
 315         d[3][0] = a00*b30 + a10*b31 + a20*b32 + a30;
 316         d[3][1] = a01*b30 + a11*b31 + a21*b32 + a31;
 317         d[3][2] = a02*b30 + a12*b31 + a22*b32 + a32;
 318 }
 319
 320 void m4x3_mulv( m4x3f m, v3f v, v3f d )
 321 {
 322         v3f res;
 323
 324         res[0] = m[0][0]*v[0] + m[1][0]*v[1] + m[2][0]*v[2] + m[3][0];
 325         res[1] = m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2] + m[3][1];
 326         res[2] = m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2] + m[3][2];
 327
 328         v3_copy( res, d );
 329 }
 330
 331 // Affine transforms
 332
 333 void m4x3_translate( m4x3f m, v3f v )
 334 {
 335         v3_muladds( m[3], m[0], v[0], m[3] );
 336         v3_muladds( m[3], m[1], v[1], m[3] );
 337         v3_muladds( m[3], m[2], v[2], m[3] );
 338 }
 339
 340 void m4x3_scale( m4x3f m, float s )
 341 {
 342         v3_muls( m[0], s, m[0] );
 343         v3_muls( m[1], s, m[1] );
 344         v3_muls( m[2], s, m[2] );
 345 }
 346
 347 void m4x3_rotate_x( m4x3f m, float angle )
 348 {
 349         m4x3f t = M4X3_IDENTITY;
 350         float c, s;
 351
 352         c = cosf( angle );
 353         s = sinf( angle );
 354
 355         t[1][1] =  c;
 356         t[1][2] =  s;
 357         t[2][1] = -s;
 358         t[2][2] =  c;
 359
 360         m4x3_mul( m, t, m );
 361 }
 362
 363 void m4x3_rotate_y( m4x3f m, float angle )
 364 {
 365         m4x3f t = M4X3_IDENTITY;
 366         float c, s;
 367
 368         c = cosf( angle );
 369         s = sinf( angle );
 370
 371         t[0][0] =  c;
 372         t[0][2] = -s;
 373         t[2][0] =  s;
 374         t[2][2] =  c;
 375
 376         m4x3_mul( m, t, m );
 377 }
 378
 379 void m4x3_rotate_z( m4x3f m, float angle )
 380 {
 381         m4x3f t = M4X3_IDENTITY;
 382         float c, s;
 383
 384         c = cosf( angle );
 385         s = sinf( angle );
 386
 387         t[0][0] =  c;
 388         t[0][1] =  s;
 389         t[1][0] = -s;
 390         t[1][1] =  c;
 391
 392         m4x3_mul( m, t, m );
 393 }
 394
 395 // Warning: These functions are unoptimized..
 396 void m4x3_expand_aabb_point( m4x3f m, boxf box, v3f point )
 397 {
 398         v3f v;
 399         m4x3_mulv( m, point, v );
 400
 401         v3_minv( box[0], v, box[0] );
 402         v3_maxv( box[1], v, box[1] );
 403 }
 404
 405 void box_concat( boxf a, boxf b )
 406 {
 407         v3_minv( a[0], b[0], a[0] );
 408         v3_maxv( a[1], b[1], a[1] );
 409 }
 410
 411 void box_copy( boxf a, boxf b )
 412 {
 413         v3_copy( a[0], b[0] );
 414         v3_copy( a[1], b[1] );
 415 }
 416
 417 void m4x3_transform_aabb( m4x3f m, boxf box )
 418 {
 419         v3f a; v3f b;
 420
 421         v3_copy( box[0], a );
 422         v3_copy( box[1], b );
 423         v3_fill( box[0],  INFINITY );
 424         v3_fill( box[1], -INFINITY );
 425
 426         m4x3_expand_aabb_point( m, box, a );
 427         m4x3_expand_aabb_point( m, box, (v3f){ a[0], b[1], a[2] } );
 428         m4x3_expand_aabb_point( m, box, (v3f){ b[0], a[1], a[2] } );
 429         m4x3_expand_aabb_point( m, box, (v3f){ b[0], b[1], a[2] } );
 430         m4x3_expand_aabb_point( m, box, b );
 431         m4x3_expand_aabb_point( m, box, (v3f){ a[0], b[1], b[2] } );
 432         m4x3_expand_aabb_point( m, box, (v3f){ b[0], a[1], b[2] } );
 433         m4x3_expand_aabb_point( m, box, (v3f){ b[0], b[1], b[2] } );
 434 }
 435
 436 // Planes (double precision)
 437 // ==================================================================================================================
 438
 439 void tri_to_plane( double a[3], double b[3], double c[3], double p[4] )
 440 {
 441         double edge0[3];
 442         double edge1[3];
 443         double l;
 444
 445         edge0[0] = b[0] - a[0];
 446         edge0[1] = b[1] - a[1];
 447         edge0[2] = b[2] - a[2];
 448
 449         edge1[0] = c[0] - a[0];
 450         edge1[1] = c[1] - a[1];
 451         edge1[2] = c[2] - a[2];
 452
 453         p[0] = edge0[1] * edge1[2] - edge0[2] * edge1[1];
 454         p[1] = edge0[2] * edge1[0] - edge0[0] * edge1[2];
 455         p[2] = edge0[0] * edge1[1] - edge0[1] * edge1[0];
 456
 457         l = sqrt(p[0] * p[0] + p[1] * p[1] + p[2] * p[2]);
 458         p[3] = (p[0] * a[0] + p[1] * a[1] + p[2] * a[2]) / l;
 459
 460         p[0] = p[0] / l;
 461         p[1] = p[1] / l;
 462         p[2] = p[2] / l;
 463 }
 464
 465 int plane_intersect( double a[4], double b[4], double c[4], double p[4] )
 466 {
 467         double const epsilon = 1e-8f;
 468
 469         double x[3];
 470         double d;
 471
 472         x[0] = a[1] * b[2] - a[2] * b[1];
 473         x[1] = a[2] * b[0] - a[0] * b[2];
 474         x[2] = a[0] * b[1] - a[1] * b[0];
 475
 476         d = x[0] * c[0] + x[1] * c[1] + x[2] * c[2];
 477
 478         if( d < epsilon && d > -epsilon ) return 0;
 479
 480         p[0] = (b[1] * c[2] - b[2] * c[1]) * -a[3];
 481         p[1] = (b[2] * c[0] - b[0] * c[2]) * -a[3];
 482         p[2] = (b[0] * c[1] - b[1] * c[0]) * -a[3];
 483
 484         p[0] += (c[1] * a[2] - c[2] * a[1]) * -b[3];
 485         p[1] += (c[2] * a[0] - c[0] * a[2]) * -b[3];
 486         p[2] += (c[0] * a[1] - c[1] * a[0]) * -b[3];
 487
 488         p[0] += (a[1] * b[2] - a[2] * b[1]) * -c[3];
 489         p[1] += (a[2] * b[0] - a[0] * b[2]) * -c[3];
 490         p[2] += (a[0] * b[1] - a[1] * b[0]) * -c[3];
 491
 492         p[0] = -p[0] / d;
 493         p[1] = -p[1] / d;
 494         p[2] = -p[2] / d;
 495
 496         return 1;
 497 }
 498
 499 double plane_polarity( double p[4], double a[3] )
 500 {
 501         return
 502         (a[0] * p[0] + a[1] * p[1] + a[2] * p[2])
 503         -(p[0]*p[3] * p[0] + p[1]*p[3] * p[1] + p[2]*p[3] * p[2])
 504         ;
 505 }