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         float d;
 202
 203         right[0] = forward[2];
 204         right[1] = -forward[0];
 205         right[2] = forward[1];
 206         // BUG!
 207         //   assume forward = {sqrt(1/3), sqrt(1/3), -sqrt(1/3)}
 208         //   then right will be {-sqrt(1/3), -sqrt(1/3), sqrt(1/3)}
 209         //   PROBLEM?
 210
 211         d = DotProduct(forward, right);
 212         VectorMA(right, -d, forward, right);
 213         VectorNormalize(right);
 214         CrossProduct(right, forward, up);
 215         VectorNormalize(up); // CrossProduct in this case returns 'up thats length is not 1
 216 }
 217
 218 void VectorVectorsDouble(const double *forward, double *right, double *up)
 219 {
 220         double d;
 221
 222         right[0] = forward[2];
 223         right[1] = -forward[0];
 224         right[2] = forward[1];
 225
 226         d = DotProduct(forward, right);
 227         VectorMA(right, -d, forward, right);
 228         VectorNormalize(right);
 229         CrossProduct(right, forward, up);
 230 }
 231
 232 void RotatePointAroundVector( vec3_t dst, const vec3_t dir, const vec3_t point, float degrees )
 233 {
 234         float t0, t1;
 235         float angle, c, s;
 236         vec3_t vr, vu, vf;
 237
 238         angle = DEG2RAD(degrees);
 239         c = cos(angle);
 240         s = sin(angle);
 241         VectorCopy(dir, vf);
 242         VectorVectors(vf, vr, vu);
 243
 244         t0 = vr[0] *  c + vu[0] * -s;
 245         t1 = vr[0] *  s + vu[0] *  c;
 246         dst[0] = (t0 * vr[0] + t1 * vu[0] + vf[0] * vf[0]) * point[0]
 247                + (t0 * vr[1] + t1 * vu[1] + vf[0] * vf[1]) * point[1]
 248                + (t0 * vr[2] + t1 * vu[2] + vf[0] * vf[2]) * point[2];
 249
 250         t0 = vr[1] *  c + vu[1] * -s;
 251         t1 = vr[1] *  s + vu[1] *  c;
 252         dst[1] = (t0 * vr[0] + t1 * vu[0] + vf[1] * vf[0]) * point[0]
 253                + (t0 * vr[1] + t1 * vu[1] + vf[1] * vf[1]) * point[1]
 254                + (t0 * vr[2] + t1 * vu[2] + vf[1] * vf[2]) * point[2];
 255
 256         t0 = vr[2] *  c + vu[2] * -s;
 257         t1 = vr[2] *  s + vu[2] *  c;
 258         dst[2] = (t0 * vr[0] + t1 * vu[0] + vf[2] * vf[0]) * point[0]
 259                + (t0 * vr[1] + t1 * vu[1] + vf[2] * vf[1]) * point[1]
 260                + (t0 * vr[2] + t1 * vu[2] + vf[2] * vf[2]) * point[2];
 261 }
 262
 263 /*-----------------------------------------------------------------*/
 264
 265 // returns the smallest integer greater than or equal to "value", or 0 if "value" is too big
 266 unsigned int CeilPowerOf2(unsigned int value)
 267 {
 268         unsigned int ceilvalue;
 269
 270         if (value > (1U << (sizeof(int) * 8 - 1)))
 271                 return 0;
 272
 273         ceilvalue = 1;
 274         while (ceilvalue < value)
 275                 ceilvalue <<= 1;
 276
 277         return ceilvalue;
 278 }
 279
 280
 281 /*-----------------------------------------------------------------*/
 282
 283
 284 void PlaneClassify(mplane_t *p)
 285 {
 286         // for optimized plane comparisons
 287         if (p->normal[0] == 1)
 288                 p->type = 0;
 289         else if (p->normal[1] == 1)
 290                 p->type = 1;
 291         else if (p->normal[2] == 1)
 292                 p->type = 2;
 293         else
 294                 p->type = 3;
 295         // for BoxOnPlaneSide
 296         p->signbits = 0;
 297         if (p->normal[0] < 0) // 1
 298                 p->signbits |= 1;
 299         if (p->normal[1] < 0) // 2
 300                 p->signbits |= 2;
 301         if (p->normal[2] < 0) // 4
 302                 p->signbits |= 4;
 303 }
 304
 305 int BoxOnPlaneSide(const vec3_t emins, const vec3_t emaxs, const mplane_t *p)
 306 {
 307         if (p->type < 3)
 308                 return ((emaxs[p->type] >= p->dist) | ((emins[p->type] < p->dist) << 1));
 309         switch(p->signbits)
 310         {
 311         default:
 312         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));
 313         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));
 314         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));
 315         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));
 316         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));
 317         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));
 318         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));
 319         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));
 320         }
 321 }
 322
 323 #if 0
 324 int BoxOnPlaneSide_Separate(const vec3_t emins, const vec3_t emaxs, const vec3_t normal, const vec_t dist)
 325 {
 326         switch((normal[0] < 0) | ((normal[1] < 0) << 1) | ((normal[2] < 0) << 2))
 327         {
 328         default:
 329         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));
 330         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));
 331         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));
 332         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));
 333         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));
 334         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));
 335         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));
 336         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));
 337         }
 338 }
 339 #endif
 340
 341 void BoxPlaneCorners(const vec3_t emins, const vec3_t emaxs, const mplane_t *p, vec3_t outnear, vec3_t outfar)
 342 {
 343         if (p->type < 3)
 344         {
 345                 outnear[0] = outnear[1] = outnear[2] = outfar[0] = outfar[1] = outfar[2] = 0;
 346                 outnear[p->type] = emins[p->type];
 347                 outfar[p->type] = emaxs[p->type];
 348                 return;
 349         }
 350         switch(p->signbits)
 351         {
 352         default:
 353         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;
 354         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;
 355         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;
 356         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;
 357         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;
 358         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;
 359         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;
 360         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;
 361         }
 362 }
 363
 364 void BoxPlaneCorners_Separate(const vec3_t emins, const vec3_t emaxs, const vec3_t normal, vec3_t outnear, vec3_t outfar)
 365 {
 366         switch((normal[0] < 0) | ((normal[1] < 0) << 1) | ((normal[2] < 0) << 2))
 367         {
 368         default:
 369         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;
 370         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;
 371         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;
 372         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;
 373         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;
 374         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;
 375         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;
 376         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;
 377         }
 378 }
 379
 380 void BoxPlaneCornerDistances(const vec3_t emins, const vec3_t emaxs, const mplane_t *p, vec_t *outneardist, vec_t *outfardist)
 381 {
 382         if (p->type < 3)
 383         {
 384                 *outneardist = emins[p->type] - p->dist;
 385                 *outfardist = emaxs[p->type] - p->dist;
 386                 return;
 387         }
 388         switch(p->signbits)
 389         {
 390         default:
 391         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;
 392         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;
 393         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;
 394         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;
 395         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;
 396         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;
 397         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;
 398         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;
 399         }
 400 }
 401
 402 void BoxPlaneCornerDistances_Separate(const vec3_t emins, const vec3_t emaxs, const vec3_t normal, vec_t *outneardist, vec_t *outfardist)
 403 {
 404         switch((normal[0] < 0) | ((normal[1] < 0) << 1) | ((normal[2] < 0) << 2))
 405         {
 406         default:
 407         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;
 408         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;
 409         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;
 410         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;
 411         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;
 412         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;
 413         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;
 414         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;
 415         }
 416 }
 417
 418 void AngleVectors (const vec3_t angles, vec3_t forward, vec3_t right, vec3_t up)
 419 {
 420         double angle, sr, sp, sy, cr, cp, cy;
 421
 422         angle = angles[YAW] * (M_PI*2 / 360);
 423         sy = sin(angle);
 424         cy = cos(angle);
 425         angle = angles[PITCH] * (M_PI*2 / 360);
 426         sp = sin(angle);
 427         cp = cos(angle);
 428         if (forward)
 429         {
 430                 forward[0] = cp*cy;
 431                 forward[1] = cp*sy;
 432                 forward[2] = -sp;
 433         }
 434         if (right || up)
 435         {
 436                 if (angles[ROLL])
 437                 {
 438                         angle = angles[ROLL] * (M_PI*2 / 360);
 439                         sr = sin(angle);
 440                         cr = cos(angle);
 441                         if (right)
 442                         {
 443                                 right[0] = -1*(sr*sp*cy+cr*-sy);
 444                                 right[1] = -1*(sr*sp*sy+cr*cy);
 445                                 right[2] = -1*(sr*cp);
 446                         }
 447                         if (up)
 448                         {
 449                                 up[0] = (cr*sp*cy+-sr*-sy);
 450                                 up[1] = (cr*sp*sy+-sr*cy);
 451                                 up[2] = cr*cp;
 452                         }
 453                 }
 454                 else
 455                 {
 456                         if (right)
 457                         {
 458                                 right[0] = sy;
 459                                 right[1] = -cy;
 460                                 right[2] = 0;
 461                         }
 462                         if (up)
 463                         {
 464                                 up[0] = (sp*cy);
 465                                 up[1] = (sp*sy);
 466                                 up[2] = cp;
 467                         }
 468                 }
 469         }
 470 }
 471
 472 void AngleVectorsFLU (const vec3_t angles, vec3_t forward, vec3_t left, vec3_t up)
 473 {
 474         double angle, sr, sp, sy, cr, cp, cy;
 475
 476         angle = angles[YAW] * (M_PI*2 / 360);
 477         sy = sin(angle);
 478         cy = cos(angle);
 479         angle = angles[PITCH] * (M_PI*2 / 360);
 480         sp = sin(angle);
 481         cp = cos(angle);
 482         if (forward)
 483         {
 484                 forward[0] = cp*cy;
 485                 forward[1] = cp*sy;
 486                 forward[2] = -sp;
 487         }
 488         if (left || up)
 489         {
 490                 if (angles[ROLL])
 491                 {
 492                         angle = angles[ROLL] * (M_PI*2 / 360);
 493                         sr = sin(angle);
 494                         cr = cos(angle);
 495                         if (left)
 496                         {
 497                                 left[0] = sr*sp*cy+cr*-sy;
 498                                 left[1] = sr*sp*sy+cr*cy;
 499                                 left[2] = sr*cp;
 500                         }
 501                         if (up)
 502                         {
 503                                 up[0] = cr*sp*cy+-sr*-sy;
 504                                 up[1] = cr*sp*sy+-sr*cy;
 505                                 up[2] = cr*cp;
 506                         }
 507                 }
 508                 else
 509                 {
 510                         if (left)
 511                         {
 512                                 left[0] = -sy;
 513                                 left[1] = cy;
 514                                 left[2] = 0;
 515                         }
 516                         if (up)
 517                         {
 518                                 up[0] = sp*cy;
 519                                 up[1] = sp*sy;
 520                                 up[2] = cp;
 521                         }
 522                 }
 523         }
 524 }
 525
 526 // LordHavoc: calculates pitch/yaw/roll angles from forward and up vectors
 527 void AnglesFromVectors (vec3_t angles, const vec3_t forward, const vec3_t up, qboolean flippitch)
 528 {
 529         if (forward[0] == 0 && forward[1] == 0)
 530         {
 531                 if(forward[2] > 0)
 532                 {
 533                         angles[PITCH] = -M_PI * 0.5;
 534                         angles[YAW] = up ? atan2(-up[1], -up[0]) : 0;
 535                 }
 536                 else
 537                 {
 538                         angles[PITCH] = M_PI * 0.5;
 539                         angles[YAW] = up ? atan2(up[1], up[0]) : 0;
 540                 }
 541                 angles[ROLL] = 0;
 542         }
 543         else
 544         {
 545                 angles[YAW] = atan2(forward[1], forward[0]);
 546                 angles[PITCH] = -atan2(forward[2], sqrt(forward[0]*forward[0] + forward[1]*forward[1]));
 547                 if (up)
 548                 {
 549                         vec_t cp = cos(angles[PITCH]), sp = sin(angles[PITCH]);
 550                         vec_t cy = cos(angles[YAW]), sy = sin(angles[YAW]);
 551                         vec3_t tleft, tup;
 552                         tleft[0] = -sy;
 553                         tleft[1] = cy;
 554                         tleft[2] = 0;
 555                         tup[0] = sp*cy;
 556                         tup[1] = sp*sy;
 557                         tup[2] = cp;
 558                         angles[ROLL] = -atan2(DotProduct(up, tleft), DotProduct(up, tup));
 559                 }
 560                 else
 561                         angles[ROLL] = 0;
 562         }
 563
 564         // now convert radians to degrees, and make all values positive
 565         VectorScale(angles, 180.0 / M_PI, angles);
 566         if (flippitch)
 567                 angles[PITCH] *= -1;
 568         if (angles[PITCH] < 0) angles[PITCH] += 360;
 569         if (angles[YAW] < 0) angles[YAW] += 360;
 570         if (angles[ROLL] < 0) angles[ROLL] += 360;
 571
 572 #if 0
 573 {
 574         // debugging code
 575         vec3_t tforward, tleft, tup, nforward, nup;
 576         VectorCopy(forward, nforward);
 577         VectorNormalize(nforward);
 578         if (up)
 579         {
 580                 VectorCopy(up, nup);
 581                 VectorNormalize(nup);
 582                 AngleVectors(angles, tforward, tleft, tup);
 583                 if (VectorDistance(tforward, nforward) > 0.01 || VectorDistance(tup, nup) > 0.01)
 584                 {
 585                         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]);
 586                         Con_Printf("^3But that is '%f %f %f', '%f %f %f'\n", tforward[0], tforward[1], tforward[2], tup[0], tup[1], tup[2]);
 587                 }
 588         }
 589         else
 590         {
 591                 AngleVectors(angles, tforward, tleft, tup);
 592                 if (VectorDistance(tforward, nforward) > 0.01)
 593                 {
 594                         Con_Printf("vectoangles('%f %f %f') = %f %f %f\n", nforward[0], nforward[1], nforward[2], angles[0], angles[1], angles[2]);
 595                         Con_Printf("^3But that is '%f %f %f'\n", tforward[0], tforward[1], tforward[2]);
 596                 }
 597         }
 598 }
 599 #endif
 600 }
 601
 602 #if 0
 603 void AngleMatrix (const vec3_t angles, const vec3_t translate, vec_t matrix[][4])
 604 {
 605         double angle, sr, sp, sy, cr, cp, cy;
 606
 607         angle = angles[YAW] * (M_PI*2 / 360);
 608         sy = sin(angle);
 609         cy = cos(angle);
 610         angle = angles[PITCH] * (M_PI*2 / 360);
 611         sp = sin(angle);
 612         cp = cos(angle);
 613         angle = angles[ROLL] * (M_PI*2 / 360);
 614         sr = sin(angle);
 615         cr = cos(angle);
 616         matrix[0][0] = cp*cy;
 617         matrix[0][1] = sr*sp*cy+cr*-sy;
 618         matrix[0][2] = cr*sp*cy+-sr*-sy;
 619         matrix[0][3] = translate[0];
 620         matrix[1][0] = cp*sy;
 621         matrix[1][1] = sr*sp*sy+cr*cy;
 622         matrix[1][2] = cr*sp*sy+-sr*cy;
 623         matrix[1][3] = translate[1];
 624         matrix[2][0] = -sp;
 625         matrix[2][1] = sr*cp;
 626         matrix[2][2] = cr*cp;
 627         matrix[2][3] = translate[2];
 628 }
 629 #endif
 630
 631
 632 // LordHavoc: renamed this to Length, and made the normal one a #define
 633 float VectorNormalizeLength (vec3_t v)
 634 {
 635         float length, ilength;
 636
 637         length = v[0]*v[0] + v[1]*v[1] + v[2]*v[2];
 638         length = sqrt (length);
 639
 640         if (length)
 641         {
 642                 ilength = 1/length;
 643                 v[0] *= ilength;
 644                 v[1] *= ilength;
 645                 v[2] *= ilength;
 646         }
 647
 648         return length;
 649
 650 }
 651
 652
 653 /*
 654 ================
 655 R_ConcatRotations
 656 ================
 657 */
 658 void R_ConcatRotations (const float in1[3*3], const float in2[3*3], float out[3*3])
 659 {
 660         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];
 661         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];
 662         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];
 663         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];
 664         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];
 665         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];
 666         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];
 667         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];
 668         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];
 669 }
 670
 671
 672 /*
 673 ================
 674 R_ConcatTransforms
 675 ================
 676 */
 677 void R_ConcatTransforms (const float in1[3*4], const float in2[3*4], float out[3*4])
 678 {
 679         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];
 680         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];
 681         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];
 682         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];
 683         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];
 684         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];
 685         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];
 686         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];
 687         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];
 688         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];
 689         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];
 690         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];
 691 }
 692
 693 float RadiusFromBounds (const vec3_t mins, const vec3_t maxs)
 694 {
 695         vec3_t m1, m2;
 696         VectorMultiply(mins, mins, m1);
 697         VectorMultiply(maxs, maxs, m2);
 698         return sqrt(max(m1[0], m2[0]) + max(m1[1], m2[1]) + max(m1[2], m2[2]));
 699 }
 700
 701 float RadiusFromBoundsAndOrigin (const vec3_t mins, const vec3_t maxs, const vec3_t origin)
 702 {
 703         vec3_t m1, m2;
 704         VectorSubtract(mins, origin, m1);VectorMultiply(m1, m1, m1);
 705         VectorSubtract(maxs, origin, m2);VectorMultiply(m2, m2, m2);
 706         return sqrt(max(m1[0], m2[0]) + max(m1[1], m2[1]) + max(m1[2], m2[2]));
 707 }
 708
 709 void Mathlib_Init(void)
 710 {
 711         int a;
 712
 713         // LordHavoc: setup 1.0f / N table for quick recipricols of integers
 714         ixtable[0] = 0;
 715         for (a = 1;a < 4096;a++)
 716                 ixtable[a] = 1.0f / a;
 717 }
 718
 719 #include "matrixlib.h"
 720
 721 void Matrix4x4_Print(const matrix4x4_t *in)
 722 {
 723         Con_Printf("%f %f %f %f\n%f %f %f %f\n%f %f %f %f\n%f %f %f %f\n"
 724         , in->m[0][0], in->m[0][1], in->m[0][2], in->m[0][3]
 725         , in->m[1][0], in->m[1][1], in->m[1][2], in->m[1][3]
 726         , in->m[2][0], in->m[2][1], in->m[2][2], in->m[2][3]
 727         , in->m[3][0], in->m[3][1], in->m[3][2], in->m[3][3]);
 728 }
 729
 730 int Math_atov(const char *s, vec3_t out)
 731 {
 732         int i;
 733         VectorClear(out);
 734         if (*s == '\'')
 735                 s++;
 736         for (i = 0;i < 3;i++)
 737         {
 738                 while (*s == ' ' || *s == '\t')
 739                         s++;
 740                 out[i] = atof (s);
 741                 if (out[i] == 0 && *s != '-' && *s != '+' && (*s < '0' || *s > '9'))
 742                         break; // not a number
 743                 while (*s && *s != ' ' && *s !='\t' && *s != '\'')
 744                         s++;
 745                 if (*s == '\'')
 746                         break;
 747         }
 748         return i;
 749 }
 750
 751 void BoxFromPoints(vec3_t mins, vec3_t maxs, int numpoints, vec_t *point3f)
 752 {
 753         int i;
 754         VectorCopy(point3f, mins);
 755         VectorCopy(point3f, maxs);
 756         for (i = 1, point3f += 3;i < numpoints;i++, point3f += 3)
 757         {
 758                 mins[0] = min(mins[0], point3f[0]);maxs[0] = max(maxs[0], point3f[0]);
 759                 mins[1] = min(mins[1], point3f[1]);maxs[1] = max(maxs[1], point3f[1]);
 760                 mins[2] = min(mins[2], point3f[2]);maxs[2] = max(maxs[2], point3f[2]);
 761         }
 762 }
 763
 764 // LordHavoc: this has to be done right or you get severe precision breakdown
 765 int LoopingFrameNumberFromDouble(double t, int loopframes)
 766 {
 767         if (loopframes)
 768                 return (int)(t - floor(t/loopframes)*loopframes);
 769         else
 770                 return (int)t;
 771 }
 772