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