mathlib.c

   1 /*
   2 Copyright (C) 1996-1997 Id Software, Inc.
   3
   4 This program is free software; you can redistribute it and/or
   5 modify it under the terms of the GNU General Public License
   6 as published by the Free Software Foundation; either version 2
   7 of the License, or (at your option) any later version.
   8
   9 This program is distributed in the hope that it will be useful,
  10 but WITHOUT ANY WARRANTY; without even the implied warranty of
  11 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
  12
  13 See the GNU General Public License for more details.
  14
  15 You should have received a copy of the GNU General Public License
  16 along with this program; if not, write to the Free Software
  17 Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.
  18
  19 */
  20 // mathlib.c -- math primitives
  21
  22 #include "quakedef.h"
  23
  24 #include <math.h>
  25
  26 vec3_t vec3_origin = {0,0,0};
  27 float ixtable[4096];
  28
  29 /*-----------------------------------------------------------------*/
  30
  31 float m_bytenormals[NUMVERTEXNORMALS][3] =
  32 {
  33 {-0.525731, 0.000000, 0.850651}, {-0.442863, 0.238856, 0.864188},
  34 {-0.295242, 0.000000, 0.955423}, {-0.309017, 0.500000, 0.809017},
  35 {-0.162460, 0.262866, 0.951056}, {0.000000, 0.000000, 1.000000},
  36 {0.000000, 0.850651, 0.525731}, {-0.147621, 0.716567, 0.681718},
  37 {0.147621, 0.716567, 0.681718}, {0.000000, 0.525731, 0.850651},
  38 {0.309017, 0.500000, 0.809017}, {0.525731, 0.000000, 0.850651},
  39 {0.295242, 0.000000, 0.955423}, {0.442863, 0.238856, 0.864188},
  40 {0.162460, 0.262866, 0.951056}, {-0.681718, 0.147621, 0.716567},
  41 {-0.809017, 0.309017, 0.500000}, {-0.587785, 0.425325, 0.688191},
  42 {-0.850651, 0.525731, 0.000000}, {-0.864188, 0.442863, 0.238856},
  43 {-0.716567, 0.681718, 0.147621}, {-0.688191, 0.587785, 0.425325},
  44 {-0.500000, 0.809017, 0.309017}, {-0.238856, 0.864188, 0.442863},
  45 {-0.425325, 0.688191, 0.587785}, {-0.716567, 0.681718, -0.147621},
  46 {-0.500000, 0.809017, -0.309017}, {-0.525731, 0.850651, 0.000000},
  47 {0.000000, 0.850651, -0.525731}, {-0.238856, 0.864188, -0.442863},
  48 {0.000000, 0.955423, -0.295242}, {-0.262866, 0.951056, -0.162460},
  49 {0.000000, 1.000000, 0.000000}, {0.000000, 0.955423, 0.295242},
  50 {-0.262866, 0.951056, 0.162460}, {0.238856, 0.864188, 0.442863},
  51 {0.262866, 0.951056, 0.162460}, {0.500000, 0.809017, 0.309017},
  52 {0.238856, 0.864188, -0.442863}, {0.262866, 0.951056, -0.162460},
  53 {0.500000, 0.809017, -0.309017}, {0.850651, 0.525731, 0.000000},
  54 {0.716567, 0.681718, 0.147621}, {0.716567, 0.681718, -0.147621},
  55 {0.525731, 0.850651, 0.000000}, {0.425325, 0.688191, 0.587785},
  56 {0.864188, 0.442863, 0.238856}, {0.688191, 0.587785, 0.425325},
  57 {0.809017, 0.309017, 0.500000}, {0.681718, 0.147621, 0.716567},
  58 {0.587785, 0.425325, 0.688191}, {0.955423, 0.295242, 0.000000},
  59 {1.000000, 0.000000, 0.000000}, {0.951056, 0.162460, 0.262866},
  60 {0.850651, -0.525731, 0.000000}, {0.955423, -0.295242, 0.000000},
  61 {0.864188, -0.442863, 0.238856}, {0.951056, -0.162460, 0.262866},
  62 {0.809017, -0.309017, 0.500000}, {0.681718, -0.147621, 0.716567},
  63 {0.850651, 0.000000, 0.525731}, {0.864188, 0.442863, -0.238856},
  64 {0.809017, 0.309017, -0.500000}, {0.951056, 0.162460, -0.262866},
  65 {0.525731, 0.000000, -0.850651}, {0.681718, 0.147621, -0.716567},
  66 {0.681718, -0.147621, -0.716567}, {0.850651, 0.000000, -0.525731},
  67 {0.809017, -0.309017, -0.500000}, {0.864188, -0.442863, -0.238856},
  68 {0.951056, -0.162460, -0.262866}, {0.147621, 0.716567, -0.681718},
  69 {0.309017, 0.500000, -0.809017}, {0.425325, 0.688191, -0.587785},
  70 {0.442863, 0.238856, -0.864188}, {0.587785, 0.425325, -0.688191},
  71 {0.688191, 0.587785, -0.425325}, {-0.147621, 0.716567, -0.681718},
  72 {-0.309017, 0.500000, -0.809017}, {0.000000, 0.525731, -0.850651},
  73 {-0.525731, 0.000000, -0.850651}, {-0.442863, 0.238856, -0.864188},
  74 {-0.295242, 0.000000, -0.955423}, {-0.162460, 0.262866, -0.951056},
  75 {0.000000, 0.000000, -1.000000}, {0.295242, 0.000000, -0.955423},
  76 {0.162460, 0.262866, -0.951056}, {-0.442863, -0.238856, -0.864188},
  77 {-0.309017, -0.500000, -0.809017}, {-0.162460, -0.262866, -0.951056},
  78 {0.000000, -0.850651, -0.525731}, {-0.147621, -0.716567, -0.681718},
  79 {0.147621, -0.716567, -0.681718}, {0.000000, -0.525731, -0.850651},
  80 {0.309017, -0.500000, -0.809017}, {0.442863, -0.238856, -0.864188},
  81 {0.162460, -0.262866, -0.951056}, {0.238856, -0.864188, -0.442863},
  82 {0.500000, -0.809017, -0.309017}, {0.425325, -0.688191, -0.587785},
  83 {0.716567, -0.681718, -0.147621}, {0.688191, -0.587785, -0.425325},
  84 {0.587785, -0.425325, -0.688191}, {0.000000, -0.955423, -0.295242},
  85 {0.000000, -1.000000, 0.000000}, {0.262866, -0.951056, -0.162460},
  86 {0.000000, -0.850651, 0.525731}, {0.000000, -0.955423, 0.295242},
  87 {0.238856, -0.864188, 0.442863}, {0.262866, -0.951056, 0.162460},
  88 {0.500000, -0.809017, 0.309017}, {0.716567, -0.681718, 0.147621},
  89 {0.525731, -0.850651, 0.000000}, {-0.238856, -0.864188, -0.442863},
  90 {-0.500000, -0.809017, -0.309017}, {-0.262866, -0.951056, -0.162460},
  91 {-0.850651, -0.525731, 0.000000}, {-0.716567, -0.681718, -0.147621},
  92 {-0.716567, -0.681718, 0.147621}, {-0.525731, -0.850651, 0.000000},
  93 {-0.500000, -0.809017, 0.309017}, {-0.238856, -0.864188, 0.442863},
  94 {-0.262866, -0.951056, 0.162460}, {-0.864188, -0.442863, 0.238856},
  95 {-0.809017, -0.309017, 0.500000}, {-0.688191, -0.587785, 0.425325},
  96 {-0.681718, -0.147621, 0.716567}, {-0.442863, -0.238856, 0.864188},
  97 {-0.587785, -0.425325, 0.688191}, {-0.309017, -0.500000, 0.809017},
  98 {-0.147621, -0.716567, 0.681718}, {-0.425325, -0.688191, 0.587785},
  99 {-0.162460, -0.262866, 0.951056}, {0.442863, -0.238856, 0.864188},
 100 {0.162460, -0.262866, 0.951056}, {0.309017, -0.500000, 0.809017},
 101 {0.147621, -0.716567, 0.681718}, {0.000000, -0.525731, 0.850651},
 102 {0.425325, -0.688191, 0.587785}, {0.587785, -0.425325, 0.688191},
 103 {0.688191, -0.587785, 0.425325}, {-0.955423, 0.295242, 0.000000},
 104 {-0.951056, 0.162460, 0.262866}, {-1.000000, 0.000000, 0.000000},
 105 {-0.850651, 0.000000, 0.525731}, {-0.955423, -0.295242, 0.000000},
 106 {-0.951056, -0.162460, 0.262866}, {-0.864188, 0.442863, -0.238856},
 107 {-0.951056, 0.162460, -0.262866}, {-0.809017, 0.309017, -0.500000},
 108 {-0.864188, -0.442863, -0.238856}, {-0.951056, -0.162460, -0.262866},
 109 {-0.809017, -0.309017, -0.500000}, {-0.681718, 0.147621, -0.716567},
 110 {-0.681718, -0.147621, -0.716567}, {-0.850651, 0.000000, -0.525731},
 111 {-0.688191, 0.587785, -0.425325}, {-0.587785, 0.425325, -0.688191},
 112 {-0.425325, 0.688191, -0.587785}, {-0.425325, -0.688191, -0.587785},
 113 {-0.587785, -0.425325, -0.688191}, {-0.688191, -0.587785, -0.425325},
 114 };
 115
 116 #if 0
 117 unsigned char NormalToByte(const vec3_t n)
 118 {
 119         int i, best;
 120         float bestdistance, distance;
 121
 122         best = 0;
 123         bestdistance = DotProduct (n, m_bytenormals[0]);
 124         for (i = 1;i < NUMVERTEXNORMALS;i++)
 125         {
 126                 distance = DotProduct (n, m_bytenormals[i]);
 127                 if (distance > bestdistance)
 128                 {
 129                         bestdistance = distance;
 130                         best = i;
 131                 }
 132         }
 133         return best;
 134 }
 135
 136 // note: uses byte partly to force unsigned for the validity check
 137 void ByteToNormal(unsigned char num, vec3_t n)
 138 {
 139         if (num < NUMVERTEXNORMALS)
 140                 VectorCopy(m_bytenormals[num], n);
 141         else
 142                 VectorClear(n); // FIXME: complain?
 143 }
 144
 145 // assumes "src" is normalized
 146 void PerpendicularVector( vec3_t dst, const vec3_t src )
 147 {
 148         // LordHavoc: optimized to death and beyond
 149         int pos;
 150         float minelem;
 151
 152         if (src[0])
 153         {
 154                 dst[0] = 0;
 155                 if (src[1])
 156                 {
 157                         dst[1] = 0;
 158                         if (src[2])
 159                         {
 160                                 dst[2] = 0;
 161                                 pos = 0;
 162                                 minelem = fabs(src[0]);
 163                                 if (fabs(src[1]) < minelem)
 164                                 {
 165                                         pos = 1;
 166                                         minelem = fabs(src[1]);
 167                                 }
 168                                 if (fabs(src[2]) < minelem)
 169                                         pos = 2;
 170
 171                                 dst[pos] = 1;
 172                                 dst[0] -= src[pos] * src[0];
 173                                 dst[1] -= src[pos] * src[1];
 174                                 dst[2] -= src[pos] * src[2];
 175
 176                                 // normalize the result
 177                                 VectorNormalize(dst);
 178                         }
 179                         else
 180                                 dst[2] = 1;
 181                 }
 182                 else
 183                 {
 184                         dst[1] = 1;
 185                         dst[2] = 0;
 186                 }
 187         }
 188         else
 189         {
 190                 dst[0] = 1;
 191                 dst[1] = 0;
 192                 dst[2] = 0;
 193         }
 194 }
 195 #endif
 196
 197
 198 // LordHavoc: like AngleVectors, but taking a forward vector instead of angles, useful!
 199 void VectorVectors(const vec3_t forward, vec3_t right, vec3_t up)
 200 {
 201         // NOTE: this is consistent to AngleVectors applied to AnglesFromVectors
 202         if (forward[0] == 0 && forward[1] == 0)
 203         {
 204                 if(forward[2] > 0)
 205                 {
 206                         VectorSet(right, 0, -1, 0);
 207                         VectorSet(up, -1, 0, 0);
 208                 }
 209                 else
 210                 {
 211                         VectorSet(right, 0, -1, 0);
 212                         VectorSet(up, 1, 0, 0);
 213                 }
 214         }
 215         else
 216         {
 217                 right[0] = forward[1];
 218                 right[1] = -forward[0];
 219                 right[2] = 0;
 220                 VectorNormalize(right);
 221
 222                 up[0] = (-forward[2]*forward[0]);
 223                 up[1] = (-forward[2]*forward[1]);
 224                 up[2] = (forward[0]*forward[0] + forward[1]*forward[1]);
 225                 VectorNormalize(up);
 226         }
 227 }
 228
 229 void VectorVectorsDouble(const double *forward, double *right, double *up)
 230 {
 231         if (forward[0] == 0 && forward[1] == 0)
 232         {
 233                 if(forward[2] > 0)
 234                 {
 235                         VectorSet(right, 0, -1, 0);
 236                         VectorSet(up, -1, 0, 0);
 237                 }
 238                 else
 239                 {
 240                         VectorSet(right, 0, -1, 0);
 241                         VectorSet(up, 1, 0, 0);
 242                 }
 243         }
 244         else
 245         {
 246                 right[0] = forward[1];
 247                 right[1] = -forward[0];
 248                 right[2] = 0;
 249                 VectorNormalize(right);
 250
 251                 up[0] = (-forward[2]*forward[0]);
 252                 up[1] = (-forward[2]*forward[1]);
 253                 up[2] = (forward[0]*forward[0] + forward[1]*forward[1]);
 254                 VectorNormalize(up);
 255         }
 256 }
 257
 258 void RotatePointAroundVector( vec3_t dst, const vec3_t dir, const vec3_t point, float degrees )
 259 {
 260         float t0, t1;
 261         float angle, c, s;
 262         vec3_t vr, vu, vf;
 263
 264         angle = DEG2RAD(degrees);
 265         c = cos(angle);
 266         s = sin(angle);
 267         VectorCopy(dir, vf);
 268         VectorVectors(vf, vr, vu);
 269
 270         t0 = vr[0] *  c + vu[0] * -s;
 271         t1 = vr[0] *  s + vu[0] *  c;
 272         dst[0] = (t0 * vr[0] + t1 * vu[0] + vf[0] * vf[0]) * point[0]
 273                + (t0 * vr[1] + t1 * vu[1] + vf[0] * vf[1]) * point[1]
 274                + (t0 * vr[2] + t1 * vu[2] + vf[0] * vf[2]) * point[2];
 275
 276         t0 = vr[1] *  c + vu[1] * -s;
 277         t1 = vr[1] *  s + vu[1] *  c;
 278         dst[1] = (t0 * vr[0] + t1 * vu[0] + vf[1] * vf[0]) * point[0]
 279                + (t0 * vr[1] + t1 * vu[1] + vf[1] * vf[1]) * point[1]
 280                + (t0 * vr[2] + t1 * vu[2] + vf[1] * vf[2]) * point[2];
 281
 282         t0 = vr[2] *  c + vu[2] * -s;
 283         t1 = vr[2] *  s + vu[2] *  c;
 284         dst[2] = (t0 * vr[0] + t1 * vu[0] + vf[2] * vf[0]) * point[0]
 285                + (t0 * vr[1] + t1 * vu[1] + vf[2] * vf[1]) * point[1]
 286                + (t0 * vr[2] + t1 * vu[2] + vf[2] * vf[2]) * point[2];
 287 }
 288
 289 /*-----------------------------------------------------------------*/
 290
 291 // returns the smallest integer greater than or equal to "value", or 0 if "value" is too big
 292 unsigned int CeilPowerOf2(unsigned int value)
 293 {
 294         unsigned int ceilvalue;
 295
 296         if (value > (1U << (sizeof(int) * 8 - 1)))
 297                 return 0;
 298
 299         ceilvalue = 1;
 300         while (ceilvalue < value)
 301                 ceilvalue <<= 1;
 302
 303         return ceilvalue;
 304 }
 305
 306
 307 /*-----------------------------------------------------------------*/
 308
 309
 310 void PlaneClassify(mplane_t *p)
 311 {
 312         // for optimized plane comparisons
 313         if (p->normal[0] == 1)
 314                 p->type = 0;
 315         else if (p->normal[1] == 1)
 316                 p->type = 1;
 317         else if (p->normal[2] == 1)
 318                 p->type = 2;
 319         else
 320                 p->type = 3;
 321         // for BoxOnPlaneSide
 322         p->signbits = 0;
 323         if (p->normal[0] < 0) // 1
 324                 p->signbits |= 1;
 325         if (p->normal[1] < 0) // 2
 326                 p->signbits |= 2;
 327         if (p->normal[2] < 0) // 4
 328                 p->signbits |= 4;
 329 }
 330
 331 int BoxOnPlaneSide(const vec3_t emins, const vec3_t emaxs, const mplane_t *p)
 332 {
 333         if (p->type < 3)
 334                 return ((emaxs[p->type] >= p->dist) | ((emins[p->type] < p->dist) << 1));
 335         switch(p->signbits)
 336         {
 337         default:
 338         case 0: return (((p->normal[0] * emaxs[0] + p->normal[1] * emaxs[1] + p->normal[2] * emaxs[2]) >= p->dist) | (((p->normal[0] * emins[0] + p->normal[1] * emins[1] + p->normal[2] * emins[2]) < p->dist) << 1));
 339         case 1: return (((p->normal[0] * emins[0] + p->normal[1] * emaxs[1] + p->normal[2] * emaxs[2]) >= p->dist) | (((p->normal[0] * emaxs[0] + p->normal[1] * emins[1] + p->normal[2] * emins[2]) < p->dist) << 1));
 340         case 2: return (((p->normal[0] * emaxs[0] + p->normal[1] * emins[1] + p->normal[2] * emaxs[2]) >= p->dist) | (((p->normal[0] * emins[0] + p->normal[1] * emaxs[1] + p->normal[2] * emins[2]) < p->dist) << 1));
 341         case 3: return (((p->normal[0] * emins[0] + p->normal[1] * emins[1] + p->normal[2] * emaxs[2]) >= p->dist) | (((p->normal[0] * emaxs[0] + p->normal[1] * emaxs[1] + p->normal[2] * emins[2]) < p->dist) << 1));
 342         case 4: return (((p->normal[0] * emaxs[0] + p->normal[1] * emaxs[1] + p->normal[2] * emins[2]) >= p->dist) | (((p->normal[0] * emins[0] + p->normal[1] * emins[1] + p->normal[2] * emaxs[2]) < p->dist) << 1));
 343         case 5: return (((p->normal[0] * emins[0] + p->normal[1] * emaxs[1] + p->normal[2] * emins[2]) >= p->dist) | (((p->normal[0] * emaxs[0] + p->normal[1] * emins[1] + p->normal[2] * emaxs[2]) < p->dist) << 1));
 344         case 6: return (((p->normal[0] * emaxs[0] + p->normal[1] * emins[1] + p->normal[2] * emins[2]) >= p->dist) | (((p->normal[0] * emins[0] + p->normal[1] * emaxs[1] + p->normal[2] * emaxs[2]) < p->dist) << 1));
 345         case 7: return (((p->normal[0] * emins[0] + p->normal[1] * emins[1] + p->normal[2] * emins[2]) >= p->dist) | (((p->normal[0] * emaxs[0] + p->normal[1] * emaxs[1] + p->normal[2] * emaxs[2]) < p->dist) << 1));
 346         }
 347 }
 348
 349 #if 0
 350 int BoxOnPlaneSide_Separate(const vec3_t emins, const vec3_t emaxs, const vec3_t normal, const vec_t dist)
 351 {
 352         switch((normal[0] < 0) | ((normal[1] < 0) << 1) | ((normal[2] < 0) << 2))
 353         {
 354         default:
 355         case 0: return (((normal[0] * emaxs[0] + normal[1] * emaxs[1] + normal[2] * emaxs[2]) >= dist) | (((normal[0] * emins[0] + normal[1] * emins[1] + normal[2] * emins[2]) < dist) << 1));
 356         case 1: return (((normal[0] * emins[0] + normal[1] * emaxs[1] + normal[2] * emaxs[2]) >= dist) | (((normal[0] * emaxs[0] + normal[1] * emins[1] + normal[2] * emins[2]) < dist) << 1));
 357         case 2: return (((normal[0] * emaxs[0] + normal[1] * emins[1] + normal[2] * emaxs[2]) >= dist) | (((normal[0] * emins[0] + normal[1] * emaxs[1] + normal[2] * emins[2]) < dist) << 1));
 358         case 3: return (((normal[0] * emins[0] + normal[1] * emins[1] + normal[2] * emaxs[2]) >= dist) | (((normal[0] * emaxs[0] + normal[1] * emaxs[1] + normal[2] * emins[2]) < dist) << 1));
 359         case 4: return (((normal[0] * emaxs[0] + normal[1] * emaxs[1] + normal[2] * emins[2]) >= dist) | (((normal[0] * emins[0] + normal[1] * emins[1] + normal[2] * emaxs[2]) < dist) << 1));
 360         case 5: return (((normal[0] * emins[0] + normal[1] * emaxs[1] + normal[2] * emins[2]) >= dist) | (((normal[0] * emaxs[0] + normal[1] * emins[1] + normal[2] * emaxs[2]) < dist) << 1));
 361         case 6: return (((normal[0] * emaxs[0] + normal[1] * emins[1] + normal[2] * emins[2]) >= dist) | (((normal[0] * emins[0] + normal[1] * emaxs[1] + normal[2] * emaxs[2]) < dist) << 1));
 362         case 7: return (((normal[0] * emins[0] + normal[1] * emins[1] + normal[2] * emins[2]) >= dist) | (((normal[0] * emaxs[0] + normal[1] * emaxs[1] + normal[2] * emaxs[2]) < dist) << 1));
 363         }
 364 }
 365 #endif
 366
 367 void BoxPlaneCorners(const vec3_t emins, const vec3_t emaxs, const mplane_t *p, vec3_t outnear, vec3_t outfar)
 368 {
 369         if (p->type < 3)
 370         {
 371                 outnear[0] = outnear[1] = outnear[2] = outfar[0] = outfar[1] = outfar[2] = 0;
 372                 outnear[p->type] = emins[p->type];
 373                 outfar[p->type] = emaxs[p->type];
 374                 return;
 375         }
 376         switch(p->signbits)
 377         {
 378         default:
 379         case 0: outnear[0] = emaxs[0];outnear[1] = emaxs[1];outnear[2] = emaxs[2];outfar[0] = emins[0];outfar[1] = emins[1];outfar[2] = emins[2];break;
 380         case 1: outnear[0] = emins[0];outnear[1] = emaxs[1];outnear[2] = emaxs[2];outfar[0] = emaxs[0];outfar[1] = emins[1];outfar[2] = emins[2];break;
 381         case 2: outnear[0] = emaxs[0];outnear[1] = emins[1];outnear[2] = emaxs[2];outfar[0] = emins[0];outfar[1] = emaxs[1];outfar[2] = emins[2];break;
 382         case 3: outnear[0] = emins[0];outnear[1] = emins[1];outnear[2] = emaxs[2];outfar[0] = emaxs[0];outfar[1] = emaxs[1];outfar[2] = emins[2];break;
 383         case 4: outnear[0] = emaxs[0];outnear[1] = emaxs[1];outnear[2] = emins[2];outfar[0] = emins[0];outfar[1] = emins[1];outfar[2] = emaxs[2];break;
 384         case 5: outnear[0] = emins[0];outnear[1] = emaxs[1];outnear[2] = emins[2];outfar[0] = emaxs[0];outfar[1] = emins[1];outfar[2] = emaxs[2];break;
 385         case 6: outnear[0] = emaxs[0];outnear[1] = emins[1];outnear[2] = emins[2];outfar[0] = emins[0];outfar[1] = emaxs[1];outfar[2] = emaxs[2];break;
 386         case 7: outnear[0] = emins[0];outnear[1] = emins[1];outnear[2] = emins[2];outfar[0] = emaxs[0];outfar[1] = emaxs[1];outfar[2] = emaxs[2];break;
 387         }
 388 }
 389
 390 void BoxPlaneCorners_Separate(const vec3_t emins, const vec3_t emaxs, const vec3_t normal, vec3_t outnear, vec3_t outfar)
 391 {
 392         switch((normal[0] < 0) | ((normal[1] < 0) << 1) | ((normal[2] < 0) << 2))
 393         {
 394         default:
 395         case 0: outnear[0] = emaxs[0];outnear[1] = emaxs[1];outnear[2] = emaxs[2];outfar[0] = emins[0];outfar[1] = emins[1];outfar[2] = emins[2];break;
 396         case 1: outnear[0] = emins[0];outnear[1] = emaxs[1];outnear[2] = emaxs[2];outfar[0] = emaxs[0];outfar[1] = emins[1];outfar[2] = emins[2];break;
 397         case 2: outnear[0] = emaxs[0];outnear[1] = emins[1];outnear[2] = emaxs[2];outfar[0] = emins[0];outfar[1] = emaxs[1];outfar[2] = emins[2];break;
 398         case 3: outnear[0] = emins[0];outnear[1] = emins[1];outnear[2] = emaxs[2];outfar[0] = emaxs[0];outfar[1] = emaxs[1];outfar[2] = emins[2];break;
 399         case 4: outnear[0] = emaxs[0];outnear[1] = emaxs[1];outnear[2] = emins[2];outfar[0] = emins[0];outfar[1] = emins[1];outfar[2] = emaxs[2];break;
 400         case 5: outnear[0] = emins[0];outnear[1] = emaxs[1];outnear[2] = emins[2];outfar[0] = emaxs[0];outfar[1] = emins[1];outfar[2] = emaxs[2];break;
 401         case 6: outnear[0] = emaxs[0];outnear[1] = emins[1];outnear[2] = emins[2];outfar[0] = emins[0];outfar[1] = emaxs[1];outfar[2] = emaxs[2];break;
 402         case 7: outnear[0] = emins[0];outnear[1] = emins[1];outnear[2] = emins[2];outfar[0] = emaxs[0];outfar[1] = emaxs[1];outfar[2] = emaxs[2];break;
 403         }
 404 }
 405
 406 void BoxPlaneCornerDistances(const vec3_t emins, const vec3_t emaxs, const mplane_t *p, vec_t *outneardist, vec_t *outfardist)
 407 {
 408         if (p->type < 3)
 409         {
 410                 *outneardist = emins[p->type] - p->dist;
 411                 *outfardist = emaxs[p->type] - p->dist;
 412                 return;
 413         }
 414         switch(p->signbits)
 415         {
 416         default:
 417         case 0: *outneardist = p->normal[0] * emaxs[0] + p->normal[1] * emaxs[1] + p->normal[2] * emaxs[2] - p->dist;*outfardist = p->normal[0] * emins[0] + p->normal[1] * emins[1] + p->normal[2] * emins[2] - p->dist;break;
 418         case 1: *outneardist = p->normal[0] * emins[0] + p->normal[1] * emaxs[1] + p->normal[2] * emaxs[2] - p->dist;*outfardist = p->normal[0] * emaxs[0] + p->normal[1] * emins[1] + p->normal[2] * emins[2] - p->dist;break;
 419         case 2: *outneardist = p->normal[0] * emaxs[0] + p->normal[1] * emins[1] + p->normal[2] * emaxs[2] - p->dist;*outfardist = p->normal[0] * emins[0] + p->normal[1] * emaxs[1] + p->normal[2] * emins[2] - p->dist;break;
 420         case 3: *outneardist = p->normal[0] * emins[0] + p->normal[1] * emins[1] + p->normal[2] * emaxs[2] - p->dist;*outfardist = p->normal[0] * emaxs[0] + p->normal[1] * emaxs[1] + p->normal[2] * emins[2] - p->dist;break;
 421         case 4: *outneardist = p->normal[0] * emaxs[0] + p->normal[1] * emaxs[1] + p->normal[2] * emins[2] - p->dist;*outfardist = p->normal[0] * emins[0] + p->normal[1] * emins[1] + p->normal[2] * emaxs[2] - p->dist;break;
 422         case 5: *outneardist = p->normal[0] * emins[0] + p->normal[1] * emaxs[1] + p->normal[2] * emins[2] - p->dist;*outfardist = p->normal[0] * emaxs[0] + p->normal[1] * emins[1] + p->normal[2] * emaxs[2] - p->dist;break;
 423         case 6: *outneardist = p->normal[0] * emaxs[0] + p->normal[1] * emins[1] + p->normal[2] * emins[2] - p->dist;*outfardist = p->normal[0] * emins[0] + p->normal[1] * emaxs[1] + p->normal[2] * emaxs[2] - p->dist;break;
 424         case 7: *outneardist = p->normal[0] * emins[0] + p->normal[1] * emins[1] + p->normal[2] * emins[2] - p->dist;*outfardist = p->normal[0] * emaxs[0] + p->normal[1] * emaxs[1] + p->normal[2] * emaxs[2] - p->dist;break;
 425         }
 426 }
 427
 428 void BoxPlaneCornerDistances_Separate(const vec3_t emins, const vec3_t emaxs, const vec3_t normal, vec_t *outneardist, vec_t *outfardist)
 429 {
 430         switch((normal[0] < 0) | ((normal[1] < 0) << 1) | ((normal[2] < 0) << 2))
 431         {
 432         default:
 433         case 0: *outneardist = normal[0] * emaxs[0] + normal[1] * emaxs[1] + normal[2] * emaxs[2];*outfardist = normal[0] * emins[0] + normal[1] * emins[1] + normal[2] * emins[2];break;
 434         case 1: *outneardist = normal[0] * emins[0] + normal[1] * emaxs[1] + normal[2] * emaxs[2];*outfardist = normal[0] * emaxs[0] + normal[1] * emins[1] + normal[2] * emins[2];break;
 435         case 2: *outneardist = normal[0] * emaxs[0] + normal[1] * emins[1] + normal[2] * emaxs[2];*outfardist = normal[0] * emins[0] + normal[1] * emaxs[1] + normal[2] * emins[2];break;
 436         case 3: *outneardist = normal[0] * emins[0] + normal[1] * emins[1] + normal[2] * emaxs[2];*outfardist = normal[0] * emaxs[0] + normal[1] * emaxs[1] + normal[2] * emins[2];break;
 437         case 4: *outneardist = normal[0] * emaxs[0] + normal[1] * emaxs[1] + normal[2] * emins[2];*outfardist = normal[0] * emins[0] + normal[1] * emins[1] + normal[2] * emaxs[2];break;
 438         case 5: *outneardist = normal[0] * emins[0] + normal[1] * emaxs[1] + normal[2] * emins[2];*outfardist = normal[0] * emaxs[0] + normal[1] * emins[1] + normal[2] * emaxs[2];break;
 439         case 6: *outneardist = normal[0] * emaxs[0] + normal[1] * emins[1] + normal[2] * emins[2];*outfardist = normal[0] * emins[0] + normal[1] * emaxs[1] + normal[2] * emaxs[2];break;
 440         case 7: *outneardist = normal[0] * emins[0] + normal[1] * emins[1] + normal[2] * emins[2];*outfardist = normal[0] * emaxs[0] + normal[1] * emaxs[1] + normal[2] * emaxs[2];break;
 441         }
 442 }
 443
 444 void AngleVectors (const vec3_t angles, vec3_t forward, vec3_t right, vec3_t up)
 445 {
 446         double angle, sr, sp, sy, cr, cp, cy;
 447
 448         angle = angles[YAW] * (M_PI*2 / 360);
 449         sy = sin(angle);
 450         cy = cos(angle);
 451         angle = angles[PITCH] * (M_PI*2 / 360);
 452         sp = sin(angle);
 453         cp = cos(angle);
 454         if (forward)
 455         {
 456                 forward[0] = cp*cy;
 457                 forward[1] = cp*sy;
 458                 forward[2] = -sp;
 459         }
 460         if (right || up)
 461         {
 462                 if (angles[ROLL])
 463                 {
 464                         angle = angles[ROLL] * (M_PI*2 / 360);
 465                         sr = sin(angle);
 466                         cr = cos(angle);
 467                         if (right)
 468                         {
 469                                 right[0] = -1*(sr*sp*cy+cr*-sy);
 470                                 right[1] = -1*(sr*sp*sy+cr*cy);
 471                                 right[2] = -1*(sr*cp);
 472                         }
 473                         if (up)
 474                         {
 475                                 up[0] = (cr*sp*cy+-sr*-sy);
 476                                 up[1] = (cr*sp*sy+-sr*cy);
 477                                 up[2] = cr*cp;
 478                         }
 479                 }
 480                 else
 481                 {
 482                         if (right)
 483                         {
 484                                 right[0] = sy;
 485                                 right[1] = -cy;
 486                                 right[2] = 0;
 487                         }
 488                         if (up)
 489                         {
 490                                 up[0] = (sp*cy);
 491                                 up[1] = (sp*sy);
 492                                 up[2] = cp;
 493                         }
 494                 }
 495         }
 496 }
 497
 498 void AngleVectorsFLU (const vec3_t angles, vec3_t forward, vec3_t left, vec3_t up)
 499 {
 500         double angle, sr, sp, sy, cr, cp, cy;
 501
 502         angle = angles[YAW] * (M_PI*2 / 360);
 503         sy = sin(angle);
 504         cy = cos(angle);
 505         angle = angles[PITCH] * (M_PI*2 / 360);
 506         sp = sin(angle);
 507         cp = cos(angle);
 508         if (forward)
 509         {
 510                 forward[0] = cp*cy;
 511                 forward[1] = cp*sy;
 512                 forward[2] = -sp;
 513         }
 514         if (left || up)
 515         {
 516                 if (angles[ROLL])
 517                 {
 518                         angle = angles[ROLL] * (M_PI*2 / 360);
 519                         sr = sin(angle);
 520                         cr = cos(angle);
 521                         if (left)
 522                         {
 523                                 left[0] = sr*sp*cy+cr*-sy;
 524                                 left[1] = sr*sp*sy+cr*cy;
 525                                 left[2] = sr*cp;
 526                         }
 527                         if (up)
 528                         {
 529                                 up[0] = cr*sp*cy+-sr*-sy;
 530                                 up[1] = cr*sp*sy+-sr*cy;
 531                                 up[2] = cr*cp;
 532                         }
 533                 }
 534                 else
 535                 {
 536                         if (left)
 537                         {
 538                                 left[0] = -sy;
 539                                 left[1] = cy;
 540                                 left[2] = 0;
 541                         }
 542                         if (up)
 543                         {
 544                                 up[0] = sp*cy;
 545                                 up[1] = sp*sy;
 546                                 up[2] = cp;
 547                         }
 548                 }
 549         }
 550 }
 551
 552 // LordHavoc: calculates pitch/yaw/roll angles from forward and up vectors
 553 void AnglesFromVectors (vec3_t angles, const vec3_t forward, const vec3_t up, qboolean flippitch)
 554 {
 555         if (forward[0] == 0 && forward[1] == 0)
 556         {
 557                 if(forward[2] > 0)
 558                 {
 559                         angles[PITCH] = -M_PI * 0.5;
 560                         angles[YAW] = up ? atan2(-up[1], -up[0]) : 0;
 561                 }
 562                 else
 563                 {
 564                         angles[PITCH] = M_PI * 0.5;
 565                         angles[YAW] = up ? atan2(up[1], up[0]) : 0;
 566                 }
 567                 angles[ROLL] = 0;
 568         }
 569         else
 570         {
 571                 angles[YAW] = atan2(forward[1], forward[0]);
 572                 angles[PITCH] = -atan2(forward[2], sqrt(forward[0]*forward[0] + forward[1]*forward[1]));
 573                 // note: we know that angles[PITCH] is in ]-pi/2..pi/2[ due to atan2(anything, positive)
 574                 if (up)
 575                 {
 576                         vec_t cp = cos(angles[PITCH]), sp = sin(angles[PITCH]);
 577                         // note: we know cp > 0, due to the range angles[pitch] is in
 578                         vec_t cy = cos(angles[YAW]), sy = sin(angles[YAW]);
 579                         vec3_t tleft, tup;
 580                         tleft[0] = -sy;
 581                         tleft[1] = cy;
 582                         tleft[2] = 0;
 583                         tup[0] = sp*cy;
 584                         tup[1] = sp*sy;
 585                         tup[2] = cp;
 586                         angles[ROLL] = -atan2(DotProduct(up, tleft), DotProduct(up, tup));
 587                         // for up == '0 0 1', this is
 588                         // angles[ROLL] = -atan2(0, cp);
 589                         // which is 0
 590                 }
 591                 else
 592                         angles[ROLL] = 0;
 593
 594                 // so no up vector is equivalent to '1 0 0'!
 595         }
 596
 597         // now convert radians to degrees, and make all values positive
 598         VectorScale(angles, 180.0 / M_PI, angles);
 599         if (flippitch)
 600                 angles[PITCH] *= -1;
 601         if (angles[PITCH] < 0) angles[PITCH] += 360;
 602         if (angles[YAW] < 0) angles[YAW] += 360;
 603         if (angles[ROLL] < 0) angles[ROLL] += 360;
 604
 605 #if 0
 606 {
 607         // debugging code
 608         vec3_t tforward, tleft, tup, nforward, nup;
 609         VectorCopy(forward, nforward);
 610         VectorNormalize(nforward);
 611         if (up)
 612         {
 613                 VectorCopy(up, nup);
 614                 VectorNormalize(nup);
 615                 AngleVectors(angles, tforward, tleft, tup);
 616                 if (VectorDistance(tforward, nforward) > 0.01 || VectorDistance(tup, nup) > 0.01)
 617                 {
 618                         Con_Printf("vectoangles('%f %f %f', '%f %f %f') = %f %f %f\n", nforward[0], nforward[1], nforward[2], nup[0], nup[1], nup[2], angles[0], angles[1], angles[2]);
 619                         Con_Printf("^3But that is '%f %f %f', '%f %f %f'\n", tforward[0], tforward[1], tforward[2], tup[0], tup[1], tup[2]);
 620                 }
 621         }
 622         else
 623         {
 624                 AngleVectors(angles, tforward, tleft, tup);
 625                 if (VectorDistance(tforward, nforward) > 0.01)
 626                 {
 627                         Con_Printf("vectoangles('%f %f %f') = %f %f %f\n", nforward[0], nforward[1], nforward[2], angles[0], angles[1], angles[2]);
 628                         Con_Printf("^3But that is '%f %f %f'\n", tforward[0], tforward[1], tforward[2]);
 629                 }
 630         }
 631 }
 632 #endif
 633 }
 634
 635 #if 0
 636 void AngleMatrix (const vec3_t angles, const vec3_t translate, vec_t matrix[][4])
 637 {
 638         double angle, sr, sp, sy, cr, cp, cy;
 639
 640         angle = angles[YAW] * (M_PI*2 / 360);
 641         sy = sin(angle);
 642         cy = cos(angle);
 643         angle = angles[PITCH] * (M_PI*2 / 360);
 644         sp = sin(angle);
 645         cp = cos(angle);
 646         angle = angles[ROLL] * (M_PI*2 / 360);
 647         sr = sin(angle);
 648         cr = cos(angle);
 649         matrix[0][0] = cp*cy;
 650         matrix[0][1] = sr*sp*cy+cr*-sy;
 651         matrix[0][2] = cr*sp*cy+-sr*-sy;
 652         matrix[0][3] = translate[0];
 653         matrix[1][0] = cp*sy;
 654         matrix[1][1] = sr*sp*sy+cr*cy;
 655         matrix[1][2] = cr*sp*sy+-sr*cy;
 656         matrix[1][3] = translate[1];
 657         matrix[2][0] = -sp;
 658         matrix[2][1] = sr*cp;
 659         matrix[2][2] = cr*cp;
 660         matrix[2][3] = translate[2];
 661 }
 662 #endif
 663
 664
 665 // LordHavoc: renamed this to Length, and made the normal one a #define
 666 float VectorNormalizeLength (vec3_t v)
 667 {
 668         float length, ilength;
 669
 670         length = v[0]*v[0] + v[1]*v[1] + v[2]*v[2];
 671         length = sqrt (length);
 672
 673         if (length)
 674         {
 675                 ilength = 1/length;
 676                 v[0] *= ilength;
 677                 v[1] *= ilength;
 678                 v[2] *= ilength;
 679         }
 680
 681         return length;
 682
 683 }
 684
 685
 686 /*
 687 ================
 688 R_ConcatRotations
 689 ================
 690 */
 691 void R_ConcatRotations (const float in1[3*3], const float in2[3*3], float out[3*3])
 692 {
 693         out[0*3+0] = in1[0*3+0] * in2[0*3+0] + in1[0*3+1] * in2[1*3+0] + in1[0*3+2] * in2[2*3+0];
 694         out[0*3+1] = in1[0*3+0] * in2[0*3+1] + in1[0*3+1] * in2[1*3+1] + in1[0*3+2] * in2[2*3+1];
 695         out[0*3+2] = in1[0*3+0] * in2[0*3+2] + in1[0*3+1] * in2[1*3+2] + in1[0*3+2] * in2[2*3+2];
 696         out[1*3+0] = in1[1*3+0] * in2[0*3+0] + in1[1*3+1] * in2[1*3+0] + in1[1*3+2] * in2[2*3+0];
 697         out[1*3+1] = in1[1*3+0] * in2[0*3+1] + in1[1*3+1] * in2[1*3+1] + in1[1*3+2] * in2[2*3+1];
 698         out[1*3+2] = in1[1*3+0] * in2[0*3+2] + in1[1*3+1] * in2[1*3+2] + in1[1*3+2] * in2[2*3+2];
 699         out[2*3+0] = in1[2*3+0] * in2[0*3+0] + in1[2*3+1] * in2[1*3+0] + in1[2*3+2] * in2[2*3+0];
 700         out[2*3+1] = in1[2*3+0] * in2[0*3+1] + in1[2*3+1] * in2[1*3+1] + in1[2*3+2] * in2[2*3+1];
 701         out[2*3+2] = in1[2*3+0] * in2[0*3+2] + in1[2*3+1] * in2[1*3+2] + in1[2*3+2] * in2[2*3+2];
 702 }
 703
 704
 705 /*
 706 ================
 707 R_ConcatTransforms
 708 ================
 709 */
 710 void R_ConcatTransforms (const float in1[3*4], const float in2[3*4], float out[3*4])
 711 {
 712         out[0*4+0] = in1[0*4+0] * in2[0*4+0] + in1[0*4+1] * in2[1*4+0] + in1[0*4+2] * in2[2*4+0];
 713         out[0*4+1] = in1[0*4+0] * in2[0*4+1] + in1[0*4+1] * in2[1*4+1] + in1[0*4+2] * in2[2*4+1];
 714         out[0*4+2] = in1[0*4+0] * in2[0*4+2] + in1[0*4+1] * in2[1*4+2] + in1[0*4+2] * in2[2*4+2];
 715         out[0*4+3] = in1[0*4+0] * in2[0*4+3] + in1[0*4+1] * in2[1*4+3] + in1[0*4+2] * in2[2*4+3] + in1[0*4+3];
 716         out[1*4+0] = in1[1*4+0] * in2[0*4+0] + in1[1*4+1] * in2[1*4+0] + in1[1*4+2] * in2[2*4+0];
 717         out[1*4+1] = in1[1*4+0] * in2[0*4+1] + in1[1*4+1] * in2[1*4+1] + in1[1*4+2] * in2[2*4+1];
 718         out[1*4+2] = in1[1*4+0] * in2[0*4+2] + in1[1*4+1] * in2[1*4+2] + in1[1*4+2] * in2[2*4+2];
 719         out[1*4+3] = in1[1*4+0] * in2[0*4+3] + in1[1*4+1] * in2[1*4+3] + in1[1*4+2] * in2[2*4+3] + in1[1*4+3];
 720         out[2*4+0] = in1[2*4+0] * in2[0*4+0] + in1[2*4+1] * in2[1*4+0] + in1[2*4+2] * in2[2*4+0];
 721         out[2*4+1] = in1[2*4+0] * in2[0*4+1] + in1[2*4+1] * in2[1*4+1] + in1[2*4+2] * in2[2*4+1];
 722         out[2*4+2] = in1[2*4+0] * in2[0*4+2] + in1[2*4+1] * in2[1*4+2] + in1[2*4+2] * in2[2*4+2];
 723         out[2*4+3] = in1[2*4+0] * in2[0*4+3] + in1[2*4+1] * in2[1*4+3] + in1[2*4+2] * in2[2*4+3] + in1[2*4+3];
 724 }
 725
 726 float RadiusFromBounds (const vec3_t mins, const vec3_t maxs)
 727 {
 728         vec3_t m1, m2;
 729         VectorMultiply(mins, mins, m1);
 730         VectorMultiply(maxs, maxs, m2);
 731         return sqrt(max(m1[0], m2[0]) + max(m1[1], m2[1]) + max(m1[2], m2[2]));
 732 }
 733
 734 float RadiusFromBoundsAndOrigin (const vec3_t mins, const vec3_t maxs, const vec3_t origin)
 735 {
 736         vec3_t m1, m2;
 737         VectorSubtract(mins, origin, m1);VectorMultiply(m1, m1, m1);
 738         VectorSubtract(maxs, origin, m2);VectorMultiply(m2, m2, m2);
 739         return sqrt(max(m1[0], m2[0]) + max(m1[1], m2[1]) + max(m1[2], m2[2]));
 740 }
 741
 742 void Mathlib_Init(void)
 743 {
 744         int a;
 745
 746         // LordHavoc: setup 1.0f / N table for quick recipricols of integers
 747         ixtable[0] = 0;
 748         for (a = 1;a < 4096;a++)
 749                 ixtable[a] = 1.0f / a;
 750 }
 751
 752 #include "matrixlib.h"
 753
 754 void Matrix4x4_Print(const matrix4x4_t *in)
 755 {
 756         Con_Printf("%f %f %f %f\n%f %f %f %f\n%f %f %f %f\n%f %f %f %f\n"
 757         , in->m[0][0], in->m[0][1], in->m[0][2], in->m[0][3]
 758         , in->m[1][0], in->m[1][1], in->m[1][2], in->m[1][3]
 759         , in->m[2][0], in->m[2][1], in->m[2][2], in->m[2][3]
 760         , in->m[3][0], in->m[3][1], in->m[3][2], in->m[3][3]);
 761 }
 762
 763 int Math_atov(const char *s, prvm_vec3_t out)
 764 {
 765         int i;
 766         VectorClear(out);
 767         if (*s == '\'')
 768                 s++;
 769         for (i = 0;i < 3;i++)
 770         {
 771                 while (*s == ' ' || *s == '\t')
 772                         s++;
 773                 out[i] = atof (s);
 774                 if (out[i] == 0 && *s != '-' && *s != '+' && (*s < '0' || *s > '9'))
 775                         break; // not a number
 776                 while (*s && *s != ' ' && *s !='\t' && *s != '\'')
 777                         s++;
 778                 if (*s == '\'')
 779                         break;
 780         }
 781         return i;
 782 }
 783
 784 void BoxFromPoints(vec3_t mins, vec3_t maxs, int numpoints, vec_t *point3f)
 785 {
 786         int i;
 787         VectorCopy(point3f, mins);
 788         VectorCopy(point3f, maxs);
 789         for (i = 1, point3f += 3;i < numpoints;i++, point3f += 3)
 790         {
 791                 mins[0] = min(mins[0], point3f[0]);maxs[0] = max(maxs[0], point3f[0]);
 792                 mins[1] = min(mins[1], point3f[1]);maxs[1] = max(maxs[1], point3f[1]);
 793                 mins[2] = min(mins[2], point3f[2]);maxs[2] = max(maxs[2], point3f[2]);
 794         }
 795 }
 796
 797 // LordHavoc: this has to be done right or you get severe precision breakdown
 798 int LoopingFrameNumberFromDouble(double t, int loopframes)
 799 {
 800         if (loopframes)
 801                 return (int)(t - floor(t/loopframes)*loopframes);
 802         else
 803                 return (int)t;
 804 }
 805