src/cxr_math.h

   1 // Copyright (C) 2021 Harry Godden (hgn)
   2
   3 #define CXR_INLINE static inline
   4 #define CXR_PIf 3.14159265358979323846264338327950288f
   5
   6 // Simple min/max replacements
   7 CXR_INLINE double cxr_minf( double a, double b )
   8 {
   9         return a < b? a: b;
  10 }
  11
  12 CXR_INLINE double cxr_maxf( double a, double b )
  13 {
  14         return a > b? a: b;
  15 }
  16
  17 CXR_INLINE int cxr_min( int a, int b )
  18 {
  19         return a < b? a: b;
  20 }
  21
  22 CXR_INLINE int cxr_max( int a, int b )
  23 {
  24         return a > b? a: b;
  25 }
  26
  27 // Convert degrees to radians
  28 CXR_INLINE double cxr_rad( double deg )
  29 {
  30         return deg * CXR_PIf / 180.0f;
  31 }
  32
  33 // Vector 2
  34 // ==================================================================================================================
  35
  36 CXR_INLINE void v2_zero( v2f a )
  37 {
  38    a[0] = 0.0; a[1] = 0.0;
  39 }
  40
  41 CXR_INLINE void v2_copy( v2f a, v2f b )
  42 {
  43         b[0] = a[0]; b[1] = a[1];
  44 }
  45
  46 CXR_INLINE void v2_minv( v2f a, v2f b, v2f dest )
  47 {
  48         dest[0] = cxr_minf(a[0], b[0]);
  49         dest[1] = cxr_minf(a[1], b[1]);
  50 }
  51
  52 CXR_INLINE void v2_maxv( v2f a, v2f b, v2f dest )
  53 {
  54         dest[0] = cxr_maxf(a[0], b[0]);
  55         dest[1] = cxr_maxf(a[1], b[1]);
  56 }
  57
  58 CXR_INLINE void v2_sub( v2f a, v2f b, v2f d )
  59 {
  60         d[0] = a[0]-b[0]; d[1] = a[1]-b[1];
  61 }
  62
  63 CXR_INLINE double v2_cross( v2f a, v2f b )
  64 {
  65         return a[0] * b[1] - a[1] * b[0];
  66 }
  67
  68 CXR_INLINE void v2_add( v2f a, v2f b, v2f d )
  69 {
  70         d[0] = a[0]+b[0]; d[1] = a[1]+b[1];
  71 }
  72
  73 CXR_INLINE void v2_muls( v2f a, double s, v2f d )
  74 {
  75         d[0] = a[0]*s; d[1] = a[1]*s;
  76 }
  77
  78 CXR_INLINE void v2_mul( v2f a, v2f b, v2f d )
  79 {
  80         d[0] = a[0]*b[0]; d[1] = a[1]*b[1];
  81 }
  82
  83 CXR_INLINE void v2_muladds( v2f a, v2f b, double s, v2f d )
  84 {
  85         d[0] = a[0]+b[0]*s; d[1] = a[1]+b[1]*s;
  86 }
  87
  88 CXR_INLINE double v2_dot( v2f a, v2f b )
  89 {
  90         return a[0] * b[0] + a[1] * b[1];
  91 }
  92
  93 CXR_INLINE void v2_div( v2f a, v2f b, v2f d )
  94 {
  95         d[0] = a[0]/b[0]; d[1] = a[1]/b[1];
  96 }
  97
  98 CXR_INLINE double v2_length2( v2f a )
  99 {
 100         return v2_dot( a, a );
 101 }
 102
 103 CXR_INLINE double v2_length( v2f a )
 104 {
 105         return sqrt( v2_length2( a ) );
 106 }
 107
 108 CXR_INLINE double v2_dist2( v2f a, v2f b )
 109 {
 110         v2f delta;
 111         v2_sub( a, b, delta );
 112         return v2_length2( delta );
 113 }
 114
 115 CXR_INLINE double v2_dist( v2f a, v2f b )
 116 {
 117         return sqrt( v2_dist2( a, b ) );
 118 }
 119
 120 CXR_INLINE void v2_normalize( v2f a )
 121 {
 122         v2_muls( a, 1.0 / v2_length( a ), a );
 123 }
 124
 125 // Vector 3
 126 // ==================================================================================================================
 127
 128 CXR_INLINE void v3_zero( v3f a )
 129 {
 130         a[0] = 0.f; a[1] = 0.f; a[2] = 0.f;
 131 }
 132
 133 CXR_INLINE void v3_copy( v3f a, v3f b )
 134 {
 135         b[0] = a[0]; b[1] = a[1]; b[2] = a[2];
 136 }
 137
 138 CXR_INLINE void v3_add( v3f a, v3f b, v3f d )
 139 {
 140         d[0] = a[0]+b[0]; d[1] = a[1]+b[1]; d[2] = a[2]+b[2];
 141 }
 142
 143 CXR_INLINE void v3_sub( v3f a, v3f b, v3f d )
 144 {
 145         d[0] = a[0]-b[0]; d[1] = a[1]-b[1]; d[2] = a[2]-b[2];
 146 }
 147
 148 CXR_INLINE void v3_mul( v3f a, v3f b, v3f d )
 149 {
 150         d[0] = a[0]*b[0]; d[1] = a[1]*b[1]; d[2] = a[2]*b[2];
 151 }
 152
 153 CXR_INLINE void v3_div( v3f a, v3f b, v3f d )
 154 {
 155         d[0] = a[0]/b[0]; d[1] = a[1]/b[1];     d[2] = a[2]/b[2];
 156 }
 157
 158 CXR_INLINE void v3_muls( v3f a, double s, v3f d )
 159 {
 160         d[0] = a[0]*s; d[1] = a[1]*s; d[2] = a[2]*s;
 161 }
 162
 163 CXR_INLINE void v3_divs( v3f a, double s, v3f d )
 164 {
 165         d[0] = a[0]/s; d[1] = a[1]/s; d[2] = a[2]/s;
 166 }
 167
 168 CXR_INLINE void v3_muladds( v3f a, v3f b, double s, v3f d )
 169 {
 170         d[0] = a[0]+b[0]*s; d[1] = a[1]+b[1]*s; d[2] = a[2]+b[2]*s;
 171 }
 172
 173 CXR_INLINE double v3_dot( v3f a, v3f b )
 174 {
 175         return a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
 176 }
 177
 178 CXR_INLINE void v3_cross( v3f a, v3f b, v3f d )
 179 {
 180   d[0] = a[1] * b[2] - a[2] * b[1];
 181   d[1] = a[2] * b[0] - a[0] * b[2];
 182   d[2] = a[0] * b[1] - a[1] * b[0];
 183 }
 184
 185 CXR_INLINE double v3_length2( v3f a )
 186 {
 187         return v3_dot( a, a );
 188 }
 189
 190 CXR_INLINE double v3_length( v3f a )
 191 {
 192         return sqrt( v3_length2( a ) );
 193 }
 194
 195 CXR_INLINE double v3_dist2( v3f a, v3f b )
 196 {
 197         v3f delta;
 198         v3_sub( a, b, delta );
 199         return v3_length2( delta );
 200 }
 201
 202 CXR_INLINE double v3_dist( v3f a, v3f b )
 203 {
 204         return sqrt( v3_dist2( a, b ) );
 205 }
 206
 207 CXR_INLINE void v3_normalize( v3f a )
 208 {
 209         v3_muls( a, 1.0 / v3_length( a ), a );
 210 }
 211
 212 CXR_INLINE void v3_negate( v3f a, v3f dest )
 213 {
 214    v3_muls( a, -1.0, dest );
 215 }
 216
 217 CXR_INLINE double cxr_lerpf( double a, double b, double t )
 218 {
 219         return a + t*(b-a);
 220 }
 221
 222 CXR_INLINE void v3_lerp( v3f a, v3f b, double t, v3f d )
 223 {
 224         d[0] = a[0] + t*(b[0]-a[0]);
 225         d[1] = a[1] + t*(b[1]-a[1]);
 226         d[2] = a[2] + t*(b[2]-a[2]);
 227 }
 228
 229 CXR_INLINE void v3_minv( v3f a, v3f b, v3f dest )
 230 {
 231         dest[0] = cxr_minf(a[0], b[0]);
 232         dest[1] = cxr_minf(a[1], b[1]);
 233         dest[2] = cxr_minf(a[2], b[2]);
 234 }
 235
 236 CXR_INLINE void v3_maxv( v3f a, v3f b, v3f dest )
 237 {
 238         dest[0] = cxr_maxf(a[0], b[0]);
 239         dest[1] = cxr_maxf(a[1], b[1]);
 240         dest[2] = cxr_maxf(a[2], b[2]);
 241 }
 242
 243 CXR_INLINE double v3_minf( v3f a )
 244 {
 245         return cxr_minf( cxr_minf( a[0], a[1] ), a[2] );
 246 }
 247
 248 CXR_INLINE double v3_maxf( v3f a )
 249 {
 250         return cxr_maxf( cxr_maxf( a[0], a[1] ), a[2] );
 251 }
 252
 253 CXR_INLINE void v3_fill( v3f a, double v )
 254 {
 255         a[0] = v;
 256         a[1] = v;
 257         a[2] = v;
 258 }
 259
 260 // Vector 4
 261 // ==================================================================================================================
 262
 263 CXR_INLINE void v4_copy( v4f a, v4f b )
 264 {
 265         b[0] = a[0]; b[1] = a[1]; b[2] = a[2]; b[3] = a[3];
 266 }
 267
 268 CXR_INLINE void v4_zero( v4f a )
 269 {
 270         a[0] = 0.f; a[1] = 0.f; a[2] = 0.f; a[3] = 0.f;
 271 }
 272
 273 CXR_INLINE void v4_muls( v4f a, double s, v4f d )
 274 {
 275         d[0] = a[0]*s; d[1] = a[1]*s; d[2] = a[2]*s; d[3] = a[3]*s;
 276 }
 277
 278 // Matrix 3x3
 279 //======================================================================================================
 280
 281 CXR_INLINE void m3x3_inv_transpose( m3x3f src, m3x3f dest )
 282 {
 283         double a = src[0][0], b = src[0][1], c = src[0][2],
 284                         d = src[1][0], e = src[1][1], f = src[1][2],
 285                         g = src[2][0], h = src[2][1], i = src[2][2];
 286
 287         double det =    1.f /
 288                                         (+a*(e*i-h*f)
 289                 -b*(d*i-f*g)
 290                 +c*(d*h-e*g));
 291
 292         dest[0][0] =  (e*i-h*f)*det;
 293         dest[1][0] = -(b*i-c*h)*det;
 294         dest[2][0] =  (b*f-c*e)*det;
 295         dest[0][1] = -(d*i-f*g)*det;
 296         dest[1][1] =  (a*i-c*g)*det;
 297         dest[2][1] = -(a*f-d*c)*det;
 298         dest[0][2] =  (d*h-g*e)*det;
 299         dest[1][2] = -(a*h-g*b)*det;
 300         dest[2][2] =  (a*e-d*b)*det;
 301 }
 302
 303 CXR_INLINE void m3x3_mulv( m3x3f m, v3f v, v3f d )
 304 {
 305         v3f res;
 306
 307         res[0] = m[0][0]*v[0] + m[1][0]*v[1] + m[2][0]*v[2];
 308         res[1] = m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2];
 309         res[2] = m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2];
 310
 311         v3_copy( res, d );
 312 }
 313
 314 // Matrix 4x3
 315 // ==================================================================================================================
 316
 317 #define M4X3_IDENTITY   {{1.0f, 0.0f, 0.0f, },\
 318                                                                 { 0.0f, 1.0f, 0.0f, },\
 319                                                                 { 0.0f, 0.0f, 1.0f, },\
 320                                                                 { 0.0f, 0.0f, 0.0f }}
 321
 322 CXR_INLINE void m4x3_to_3x3( m4x3f a, m3x3f b )
 323 {
 324         v3_copy( a[0], b[0] );
 325         v3_copy( a[1], b[1] );
 326         v3_copy( a[2], b[2] );
 327 }
 328
 329 CXR_INLINE void m4x3_copy( m4x3f a, m4x3f b )
 330 {
 331         v3_copy( a[0], b[0] );
 332         v3_copy( a[1], b[1] );
 333         v3_copy( a[2], b[2] );
 334         v3_copy( a[3], b[3] );
 335 }
 336
 337 CXR_INLINE void m4x3_identity( m4x3f a )
 338 {
 339         m4x3f id = M4X3_IDENTITY;
 340         m4x3_copy( id, a );
 341 }
 342
 343 CXR_INLINE void m4x3_mul( m4x3f a, m4x3f b, m4x3f d )
 344 {
 345         double
 346         a00 = a[0][0], a01 = a[0][1], a02 = a[0][2],
 347         a10 = a[1][0], a11 = a[1][1], a12 = a[1][2],
 348         a20 = a[2][0], a21 = a[2][1], a22 = a[2][2],
 349         a30 = a[3][0], a31 = a[3][1], a32 = a[3][2],
 350         b00 = b[0][0], b01 = b[0][1], b02 = b[0][2],
 351         b10 = b[1][0], b11 = b[1][1], b12 = b[1][2],
 352         b20 = b[2][0], b21 = b[2][1], b22 = b[2][2],
 353         b30 = b[3][0], b31 = b[3][1], b32 = b[3][2];
 354
 355         d[0][0] = a00*b00 + a10*b01 + a20*b02;
 356         d[0][1] = a01*b00 + a11*b01 + a21*b02;
 357         d[0][2] = a02*b00 + a12*b01 + a22*b02;
 358         d[1][0] = a00*b10 + a10*b11 + a20*b12;
 359         d[1][1] = a01*b10 + a11*b11 + a21*b12;
 360         d[1][2] = a02*b10 + a12*b11 + a22*b12;
 361         d[2][0] = a00*b20 + a10*b21 + a20*b22;
 362         d[2][1] = a01*b20 + a11*b21 + a21*b22;
 363         d[2][2] = a02*b20 + a12*b21 + a22*b22;
 364         d[3][0] = a00*b30 + a10*b31 + a20*b32 + a30;
 365         d[3][1] = a01*b30 + a11*b31 + a21*b32 + a31;
 366         d[3][2] = a02*b30 + a12*b31 + a22*b32 + a32;
 367 }
 368
 369 CXR_INLINE void m4x3_mulv( m4x3f m, v3f v, v3f d )
 370 {
 371         v3f res;
 372
 373         res[0] = m[0][0]*v[0] + m[1][0]*v[1] + m[2][0]*v[2] + m[3][0];
 374         res[1] = m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2] + m[3][1];
 375         res[2] = m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2] + m[3][2];
 376
 377         v3_copy( res, d );
 378 }
 379
 380 // Affine transforms
 381
 382 CXR_INLINE void m4x3_translate( m4x3f m, v3f v )
 383 {
 384         v3_muladds( m[3], m[0], v[0], m[3] );
 385         v3_muladds( m[3], m[1], v[1], m[3] );
 386         v3_muladds( m[3], m[2], v[2], m[3] );
 387 }
 388
 389 CXR_INLINE void m4x3_scale( m4x3f m, double s )
 390 {
 391         v3_muls( m[0], s, m[0] );
 392         v3_muls( m[1], s, m[1] );
 393         v3_muls( m[2], s, m[2] );
 394 }
 395
 396 CXR_INLINE void m4x3_rotate_x( m4x3f m, double angle )
 397 {
 398         m4x3f t = M4X3_IDENTITY;
 399         double c, s;
 400
 401         c = cosf( angle );
 402         s = sinf( angle );
 403
 404         t[1][1] =  c;
 405         t[1][2] =  s;
 406         t[2][1] = -s;
 407         t[2][2] =  c;
 408
 409         m4x3_mul( m, t, m );
 410 }
 411
 412 CXR_INLINE void m4x3_rotate_y( m4x3f m, double angle )
 413 {
 414         m4x3f t = M4X3_IDENTITY;
 415         double c, s;
 416
 417         c = cosf( angle );
 418         s = sinf( angle );
 419
 420         t[0][0] =  c;
 421         t[0][2] = -s;
 422         t[2][0] =  s;
 423         t[2][2] =  c;
 424
 425         m4x3_mul( m, t, m );
 426 }
 427
 428 CXR_INLINE void m4x3_rotate_z( m4x3f m, double angle )
 429 {
 430         m4x3f t = M4X3_IDENTITY;
 431         double c, s;
 432
 433         c = cosf( angle );
 434         s = sinf( angle );
 435
 436         t[0][0] =  c;
 437         t[0][1] =  s;
 438         t[1][0] = -s;
 439         t[1][1] =  c;
 440
 441         m4x3_mul( m, t, m );
 442 }
 443
 444 // Warning: These functions are unoptimized..
 445 CXR_INLINE void m4x3_expand_aabb_point( m4x3f m, boxf box, v3f point )
 446 {
 447         v3f v;
 448         m4x3_mulv( m, point, v );
 449
 450         v3_minv( box[0], v, box[0] );
 451         v3_maxv( box[1], v, box[1] );
 452 }
 453
 454 CXR_INLINE void box_concat( boxf a, boxf b )
 455 {
 456         v3_minv( a[0], b[0], a[0] );
 457         v3_maxv( a[1], b[1], a[1] );
 458 }
 459
 460 CXR_INLINE void box_copy( boxf a, boxf b )
 461 {
 462         v3_copy( a[0], b[0] );
 463         v3_copy( a[1], b[1] );
 464 }
 465
 466 CXR_INLINE void m4x3_transform_aabb( m4x3f m, boxf box )
 467 {
 468         v3f a; v3f b;
 469
 470         v3_copy( box[0], a );
 471         v3_copy( box[1], b );
 472         v3_fill( box[0],  INFINITY );
 473         v3_fill( box[1], -INFINITY );
 474
 475         m4x3_expand_aabb_point( m, box, a );
 476         m4x3_expand_aabb_point( m, box, (v3f){ a[0], b[1], a[2] } );
 477         m4x3_expand_aabb_point( m, box, (v3f){ b[0], a[1], a[2] } );
 478         m4x3_expand_aabb_point( m, box, (v3f){ b[0], b[1], a[2] } );
 479         m4x3_expand_aabb_point( m, box, b );
 480         m4x3_expand_aabb_point( m, box, (v3f){ a[0], b[1], b[2] } );
 481         m4x3_expand_aabb_point( m, box, (v3f){ b[0], a[1], b[2] } );
 482         m4x3_expand_aabb_point( m, box, (v3f){ b[0], b[1], b[2] } );
 483 }
 484
 485 CXR_INLINE void tri_normal( v3f p0, v3f p1, v3f p2, v3f normal )
 486 {
 487    v3f v0, v1;
 488    v3_sub( p1, p0, v0 );
 489    v3_sub( p2, p0, v1 );
 490    v3_cross( v0, v1, normal );
 491    v3_normalize( normal );
 492 }
 493
 494 CXR_INLINE void tri_to_plane( v3f a, v3f b, v3f c, v4f plane )
 495 {
 496    tri_normal( a,b,c, plane );
 497    plane[3] = v3_dot( plane, a );
 498 }
 499
 500 // TODO update this code to use normal v3_x functions
 501 CXR_INLINE void tri_to_plane1( double a[3], double b[3], double c[3], double p[4] )
 502 {
 503         double edge0[3];
 504         double edge1[3];
 505         double l;
 506
 507         edge0[0] = b[0] - a[0];
 508         edge0[1] = b[1] - a[1];
 509         edge0[2] = b[2] - a[2];
 510
 511         edge1[0] = c[0] - a[0];
 512         edge1[1] = c[1] - a[1];
 513         edge1[2] = c[2] - a[2];
 514
 515         p[0] = edge0[1] * edge1[2] - edge0[2] * edge1[1];
 516         p[1] = edge0[2] * edge1[0] - edge0[0] * edge1[2];
 517         p[2] = edge0[0] * edge1[1] - edge0[1] * edge1[0];
 518
 519         l = sqrt(p[0] * p[0] + p[1] * p[1] + p[2] * p[2]);
 520         p[3] = (p[0] * a[0] + p[1] * a[1] + p[2] * a[2]) / l;
 521
 522         p[0] = p[0] / l;
 523         p[1] = p[1] / l;
 524         p[2] = p[2] / l;
 525 }
 526
 527 CXR_INLINE int plane_intersect( double a[4], double b[4], double c[4], double p[3] )
 528 {
 529         double const epsilon = 0.001;
 530
 531         double x[3];
 532         double d;
 533
 534         x[0] = a[1] * b[2] - a[2] * b[1];
 535         x[1] = a[2] * b[0] - a[0] * b[2];
 536         x[2] = a[0] * b[1] - a[1] * b[0];
 537
 538         d = x[0] * c[0] + x[1] * c[1] + x[2] * c[2];
 539
 540         if( d < epsilon && d > -epsilon ) return 0;
 541
 542         p[0] = (b[1] * c[2] - b[2] * c[1]) * -a[3];
 543         p[1] = (b[2] * c[0] - b[0] * c[2]) * -a[3];
 544         p[2] = (b[0] * c[1] - b[1] * c[0]) * -a[3];
 545
 546         p[0] += (c[1] * a[2] - c[2] * a[1]) * -b[3];
 547         p[1] += (c[2] * a[0] - c[0] * a[2]) * -b[3];
 548         p[2] += (c[0] * a[1] - c[1] * a[0]) * -b[3];
 549
 550         p[0] += (a[1] * b[2] - a[2] * b[1]) * -c[3];
 551         p[1] += (a[2] * b[0] - a[0] * b[2]) * -c[3];
 552         p[2] += (a[0] * b[1] - a[1] * b[0]) * -c[3];
 553
 554         p[0] = -p[0] / d;
 555         p[1] = -p[1] / d;
 556         p[2] = -p[2] / d;
 557
 558         return 1;
 559 }
 560
 561 CXR_INLINE void normal_to_plane( v3f normal, v3f p, v4f plane )
 562 {
 563    v3_copy( normal, plane );
 564    plane[3] = v3_dot( normal, p );
 565 }
 566
 567 CXR_INLINE double plane_polarity( double p[4], double a[3] )
 568 {
 569         return
 570         (a[0] * p[0] + a[1] * p[1] + a[2] * p[2])
 571         -(p[0]*p[3] * p[0] + p[1]*p[3] * p[1] + p[2]*p[3] * p[2])
 572         ;
 573 }