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 // Vector 3
  77 // ==================================================================================================================
  78
  79 void v3_zero( v3f a )
  80 {
  81         a[0] = 0.f; a[1] = 0.f; a[2] = 0.f;
  82 }
  83
  84 void v3_copy( v3f a, v3f b )
  85 {
  86         b[0] = a[0]; b[1] = a[1]; b[2] = a[2];
  87 }
  88
  89 void v3_add( v3f a, v3f b, v3f d )
  90 {
  91         d[0] = a[0]+b[0]; d[1] = a[1]+b[1]; d[2] = a[2]+b[2];
  92 }
  93
  94 void v3_sub( 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_mul( 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_div( 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_muls( v3f a, float s, v3f d )
 110 {
 111         d[0] = a[0]*s; d[1] = a[1]*s; d[2] = a[2]*s;
 112 }
 113
 114 void v3_divs( 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_muladds( v3f a, v3f b, float s, v3f d )
 120 {
 121         d[0] = a[0]+b[0]*s; d[1] = a[1]+b[1]*s; d[2] = a[2]+b[2]*s;
 122 }
 123
 124 float v3_dot( v3f a, v3f b )
 125 {
 126         return a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
 127 }
 128
 129 void v3_cross( v3f a, v3f b, v3f d )
 130 {
 131   d[0] = a[1] * b[2] - a[2] * b[1];
 132   d[1] = a[2] * b[0] - a[0] * b[2];
 133   d[2] = a[0] * b[1] - a[1] * b[0];
 134 }
 135
 136 float v3_length2( v3f a )
 137 {
 138         return v3_dot( a, a );
 139 }
 140
 141 float v3_length( v3f a )
 142 {
 143         return sqrtf( v3_length2( a ) );
 144 }
 145
 146 float v3_dist2( v3f a, v3f b )
 147 {
 148         v3f delta;
 149         v3_sub( a, b, delta );
 150         return v3_length2( delta );
 151 }
 152
 153 float v3_dist( v3f a, v3f b )
 154 {
 155         return sqrtf( v3_dist2( a, b ) );
 156 }
 157
 158 void v3_normalize( v3f a )
 159 {
 160         v3_muls( a, 1.f / v3_length( a ), a );
 161 }
 162
 163 float csr_lerpf( float a, float b, float t )
 164 {
 165         return a + t*(b-a);
 166 }
 167
 168 void v3_lerp( v3f a, v3f b, float t, v3f d )
 169 {
 170         d[0] = a[0] + t*(b[0]-a[0]);
 171         d[1] = a[1] + t*(b[1]-a[1]);
 172         d[2] = a[2] + t*(b[2]-a[2]);
 173 }
 174
 175 void v3_minv( v3f a, v3f b, v3f dest )
 176 {
 177         dest[0] = csr_minf(a[0], b[0]);
 178         dest[1] = csr_minf(a[1], b[1]);
 179         dest[2] = csr_minf(a[2], b[2]);
 180 }
 181
 182 void v3_maxv( v3f a, v3f b, v3f dest )
 183 {
 184         dest[0] = csr_maxf(a[0], b[0]);
 185         dest[1] = csr_maxf(a[1], b[1]);
 186         dest[2] = csr_maxf(a[2], b[2]);
 187 }
 188
 189 float v3_minf( v3f a )
 190 {
 191         return csr_minf( csr_minf( a[0], a[1] ), a[2] );
 192 }
 193
 194 float v3_maxf( v3f a )
 195 {
 196         return csr_maxf( csr_maxf( a[0], a[1] ), a[2] );
 197 }
 198
 199 void v3_fill( v3f a, float v )
 200 {
 201         a[0] = v;
 202         a[1] = v;
 203         a[2] = v;
 204 }
 205
 206 // Vector 4
 207 void v4_copy( v4f a, v4f b )
 208 {
 209         b[0] = a[0]; b[1] = a[1]; b[2] = a[2]; b[3] = a[3];
 210 }
 211
 212 // Matrix 3x3
 213 //======================================================================================================
 214
 215 void m3x3_inv_transpose( m3x3f src, m3x3f dest )
 216 {
 217         float a = src[0][0], b = src[0][1], c = src[0][2],
 218                         d = src[1][0], e = src[1][1], f = src[1][2],
 219                         g = src[2][0], h = src[2][1], i = src[2][2];
 220
 221         float det =    1.f /
 222                                         (+a*(e*i-h*f)
 223                 -b*(d*i-f*g)
 224                 +c*(d*h-e*g));
 225
 226         dest[0][0] =  (e*i-h*f)*det;
 227         dest[1][0] = -(b*i-c*h)*det;
 228         dest[2][0] =  (b*f-c*e)*det;
 229         dest[0][1] = -(d*i-f*g)*det;
 230         dest[1][1] =  (a*i-c*g)*det;
 231         dest[2][1] = -(a*f-d*c)*det;
 232         dest[0][2] =  (d*h-g*e)*det;
 233         dest[1][2] = -(a*h-g*b)*det;
 234         dest[2][2] =  (a*e-d*b)*det;
 235 }
 236
 237 void m3x3_mulv( m3x3f m, v3f v, v3f d )
 238 {
 239         v3f res;
 240
 241         res[0] = m[0][0]*v[0] + m[1][0]*v[1] + m[2][0]*v[2];
 242         res[1] = m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2];
 243         res[2] = m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2];
 244
 245         v3_copy( res, d );
 246 }
 247
 248 // Matrix 4x3
 249 // ==================================================================================================================
 250
 251 #define M4X3_IDENTITY   {{1.0f, 0.0f, 0.0f, },\
 252                                                                 { 0.0f, 1.0f, 0.0f, },\
 253                                                                 { 0.0f, 0.0f, 1.0f, },\
 254                                                                 { 0.0f, 0.0f, 0.0f }}
 255
 256 void m4x3_to_3x3( m4x3f a, m3x3f b )
 257 {
 258         v3_copy( a[0], b[0] );
 259         v3_copy( a[1], b[1] );
 260         v3_copy( a[2], b[2] );
 261 }
 262
 263 void m4x3_copy( m4x3f a, m4x3f b )
 264 {
 265         v3_copy( a[0], b[0] );
 266         v3_copy( a[1], b[1] );
 267         v3_copy( a[2], b[2] );
 268         v3_copy( a[3], b[3] );
 269 }
 270
 271 void m4x3_identity( m4x3f a )
 272 {
 273         m4x3f id = M4X3_IDENTITY;
 274         m4x3_copy( id, a );
 275 }
 276
 277 void m4x3_mul( m4x3f a, m4x3f b, m4x3f d )
 278 {
 279         float
 280         a00 = a[0][0], a01 = a[0][1], a02 = a[0][2],
 281         a10 = a[1][0], a11 = a[1][1], a12 = a[1][2],
 282         a20 = a[2][0], a21 = a[2][1], a22 = a[2][2],
 283         a30 = a[3][0], a31 = a[3][1], a32 = a[3][2],
 284         b00 = b[0][0], b01 = b[0][1], b02 = b[0][2],
 285         b10 = b[1][0], b11 = b[1][1], b12 = b[1][2],
 286         b20 = b[2][0], b21 = b[2][1], b22 = b[2][2],
 287         b30 = b[3][0], b31 = b[3][1], b32 = b[3][2];
 288
 289         d[0][0] = a00*b00 + a10*b01 + a20*b02;
 290         d[0][1] = a01*b00 + a11*b01 + a21*b02;
 291         d[0][2] = a02*b00 + a12*b01 + a22*b02;
 292         d[1][0] = a00*b10 + a10*b11 + a20*b12;
 293         d[1][1] = a01*b10 + a11*b11 + a21*b12;
 294         d[1][2] = a02*b10 + a12*b11 + a22*b12;
 295         d[2][0] = a00*b20 + a10*b21 + a20*b22;
 296         d[2][1] = a01*b20 + a11*b21 + a21*b22;
 297         d[2][2] = a02*b20 + a12*b21 + a22*b22;
 298         d[3][0] = a00*b30 + a10*b31 + a20*b32 + a30;
 299         d[3][1] = a01*b30 + a11*b31 + a21*b32 + a31;
 300         d[3][2] = a02*b30 + a12*b31 + a22*b32 + a32;
 301 }
 302
 303 void m4x3_mulv( m4x3f 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] + m[3][0];
 308         res[1] = m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2] + m[3][1];
 309         res[2] = m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2] + m[3][2];
 310
 311         v3_copy( res, d );
 312 }
 313
 314 // Affine transforms
 315
 316 void m4x3_translate( m4x3f m, v3f v )
 317 {
 318         v3_muladds( m[3], m[0], v[0], m[3] );
 319         v3_muladds( m[3], m[1], v[1], m[3] );
 320         v3_muladds( m[3], m[2], v[2], m[3] );
 321 }
 322
 323 void m4x3_scale( m4x3f m, float s )
 324 {
 325         v3_muls( m[0], s, m[0] );
 326         v3_muls( m[1], s, m[1] );
 327         v3_muls( m[2], s, m[2] );
 328 }
 329
 330 void m4x3_rotate_x( m4x3f m, float angle )
 331 {
 332         m4x3f t = M4X3_IDENTITY;
 333         float c, s;
 334
 335         c = cosf( angle );
 336         s = sinf( angle );
 337
 338         t[1][1] =  c;
 339         t[1][2] =  s;
 340         t[2][1] = -s;
 341         t[2][2] =  c;
 342
 343         m4x3_mul( m, t, m );
 344 }
 345
 346 void m4x3_rotate_y( m4x3f m, float angle )
 347 {
 348         m4x3f t = M4X3_IDENTITY;
 349         float c, s;
 350
 351         c = cosf( angle );
 352         s = sinf( angle );
 353
 354         t[0][0] =  c;
 355         t[0][2] = -s;
 356         t[2][0] =  s;
 357         t[2][2] =  c;
 358
 359         m4x3_mul( m, t, m );
 360 }
 361
 362 void m4x3_rotate_z( m4x3f m, float angle )
 363 {
 364         m4x3f t = M4X3_IDENTITY;
 365         float c, s;
 366
 367         c = cosf( angle );
 368         s = sinf( angle );
 369
 370         t[0][0] =  c;
 371         t[0][1] =  s;
 372         t[1][0] = -s;
 373         t[1][1] =  c;
 374
 375         m4x3_mul( m, t, m );
 376 }
 377
 378 // Warning: These functions are unoptimized..
 379 void m4x3_expand_aabb_point( m4x3f m, boxf box, v3f point )
 380 {
 381         v3f v;
 382         m4x3_mulv( m, point, v );
 383
 384         v3_minv( box[0], v, box[0] );
 385         v3_maxv( box[1], v, box[1] );
 386 }
 387
 388 void box_concat( boxf a, boxf b )
 389 {
 390         v3_minv( a[0], b[0], a[0] );
 391         v3_maxv( a[1], b[1], a[1] );
 392 }
 393
 394 void box_copy( boxf a, boxf b )
 395 {
 396         v3_copy( a[0], b[0] );
 397         v3_copy( a[1], b[1] );
 398 }
 399
 400 void m4x3_transform_aabb( m4x3f m, boxf box )
 401 {
 402         v3f a; v3f b;
 403
 404         v3_copy( box[0], a );
 405         v3_copy( box[1], b );
 406         v3_fill( box[0],  INFINITY );
 407         v3_fill( box[1], -INFINITY );
 408
 409         m4x3_expand_aabb_point( m, box, a );
 410         m4x3_expand_aabb_point( m, box, (v3f){ a[0], b[1], a[2] } );
 411         m4x3_expand_aabb_point( m, box, (v3f){ b[0], a[1], a[2] } );
 412         m4x3_expand_aabb_point( m, box, (v3f){ b[0], b[1], a[2] } );
 413         m4x3_expand_aabb_point( m, box, b );
 414         m4x3_expand_aabb_point( m, box, (v3f){ a[0], b[1], b[2] } );
 415         m4x3_expand_aabb_point( m, box, (v3f){ b[0], a[1], b[2] } );
 416         m4x3_expand_aabb_point( m, box, (v3f){ b[0], b[1], b[2] } );
 417 }
 418
 419 // Planes (double precision)
 420 // ==================================================================================================================
 421
 422 void tri_to_plane( double a[3], double b[3], double c[3], double p[4] )
 423 {
 424         double edge0[3];
 425         double edge1[3];
 426         double l;
 427
 428         edge0[0] = b[0] - a[0];
 429         edge0[1] = b[1] - a[1];
 430         edge0[2] = b[2] - a[2];
 431
 432         edge1[0] = c[0] - a[0];
 433         edge1[1] = c[1] - a[1];
 434         edge1[2] = c[2] - a[2];
 435
 436         p[0] = edge0[1] * edge1[2] - edge0[2] * edge1[1];
 437         p[1] = edge0[2] * edge1[0] - edge0[0] * edge1[2];
 438         p[2] = edge0[0] * edge1[1] - edge0[1] * edge1[0];
 439
 440         l = sqrt(p[0] * p[0] + p[1] * p[1] + p[2] * p[2]);
 441         p[3] = (p[0] * a[0] + p[1] * a[1] + p[2] * a[2]) / l;
 442
 443         p[0] = p[0] / l;
 444         p[1] = p[1] / l;
 445         p[2] = p[2] / l;
 446 }
 447
 448 int plane_intersect( double a[4], double b[4], double c[4], double p[4] )
 449 {
 450         double const epsilon = 1e-8f;
 451
 452         double x[3];
 453         double d;
 454
 455         x[0] = a[1] * b[2] - a[2] * b[1];
 456         x[1] = a[2] * b[0] - a[0] * b[2];
 457         x[2] = a[0] * b[1] - a[1] * b[0];
 458
 459         d = x[0] * c[0] + x[1] * c[1] + x[2] * c[2];
 460
 461         if( d < epsilon && d > -epsilon ) return 0;
 462
 463         p[0] = (b[1] * c[2] - b[2] * c[1]) * -a[3];
 464         p[1] = (b[2] * c[0] - b[0] * c[2]) * -a[3];
 465         p[2] = (b[0] * c[1] - b[1] * c[0]) * -a[3];
 466
 467         p[0] += (c[1] * a[2] - c[2] * a[1]) * -b[3];
 468         p[1] += (c[2] * a[0] - c[0] * a[2]) * -b[3];
 469         p[2] += (c[0] * a[1] - c[1] * a[0]) * -b[3];
 470
 471         p[0] += (a[1] * b[2] - a[2] * b[1]) * -c[3];
 472         p[1] += (a[2] * b[0] - a[0] * b[2]) * -c[3];
 473         p[2] += (a[0] * b[1] - a[1] * b[0]) * -c[3];
 474
 475         p[0] = -p[0] / d;
 476         p[1] = -p[1] / d;
 477         p[2] = -p[2] / d;
 478
 479         return 1;
 480 }
 481
 482 double plane_polarity( double p[4], double a[3] )
 483 {
 484         return
 485         (a[0] * p[0] + a[1] * p[1] + a[2] * p[2])
 486         -(p[0]*p[3] * p[0] + p[1]*p[3] * p[1] + p[2]*p[3] * p[2])
 487         ;
 488 }