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