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 <math.h>
  23 #include "quakedef.h"
  24
  25 vec3_t vec3_origin = {0,0,0};
  26 float ixtable[4096];
  27
  28 /*-----------------------------------------------------------------*/
  29
  30 float m_bytenormals[NUMVERTEXNORMALS][3] =
  31 {
  32 {-0.525731, 0.000000, 0.850651}, {-0.442863, 0.238856, 0.864188},
  33 {-0.295242, 0.000000, 0.955423}, {-0.309017, 0.500000, 0.809017},
  34 {-0.162460, 0.262866, 0.951056}, {0.000000, 0.000000, 1.000000},
  35 {0.000000, 0.850651, 0.525731}, {-0.147621, 0.716567, 0.681718},
  36 {0.147621, 0.716567, 0.681718}, {0.000000, 0.525731, 0.850651},
  37 {0.309017, 0.500000, 0.809017}, {0.525731, 0.000000, 0.850651},
  38 {0.295242, 0.000000, 0.955423}, {0.442863, 0.238856, 0.864188},
  39 {0.162460, 0.262866, 0.951056}, {-0.681718, 0.147621, 0.716567},
  40 {-0.809017, 0.309017, 0.500000}, {-0.587785, 0.425325, 0.688191},
  41 {-0.850651, 0.525731, 0.000000}, {-0.864188, 0.442863, 0.238856},
  42 {-0.716567, 0.681718, 0.147621}, {-0.688191, 0.587785, 0.425325},
  43 {-0.500000, 0.809017, 0.309017}, {-0.238856, 0.864188, 0.442863},
  44 {-0.425325, 0.688191, 0.587785}, {-0.716567, 0.681718, -0.147621},
  45 {-0.500000, 0.809017, -0.309017}, {-0.525731, 0.850651, 0.000000},
  46 {0.000000, 0.850651, -0.525731}, {-0.238856, 0.864188, -0.442863},
  47 {0.000000, 0.955423, -0.295242}, {-0.262866, 0.951056, -0.162460},
  48 {0.000000, 1.000000, 0.000000}, {0.000000, 0.955423, 0.295242},
  49 {-0.262866, 0.951056, 0.162460}, {0.238856, 0.864188, 0.442863},
  50 {0.262866, 0.951056, 0.162460}, {0.500000, 0.809017, 0.309017},
  51 {0.238856, 0.864188, -0.442863}, {0.262866, 0.951056, -0.162460},
  52 {0.500000, 0.809017, -0.309017}, {0.850651, 0.525731, 0.000000},
  53 {0.716567, 0.681718, 0.147621}, {0.716567, 0.681718, -0.147621},
  54 {0.525731, 0.850651, 0.000000}, {0.425325, 0.688191, 0.587785},
  55 {0.864188, 0.442863, 0.238856}, {0.688191, 0.587785, 0.425325},
  56 {0.809017, 0.309017, 0.500000}, {0.681718, 0.147621, 0.716567},
  57 {0.587785, 0.425325, 0.688191}, {0.955423, 0.295242, 0.000000},
  58 {1.000000, 0.000000, 0.000000}, {0.951056, 0.162460, 0.262866},
  59 {0.850651, -0.525731, 0.000000}, {0.955423, -0.295242, 0.000000},
  60 {0.864188, -0.442863, 0.238856}, {0.951056, -0.162460, 0.262866},
  61 {0.809017, -0.309017, 0.500000}, {0.681718, -0.147621, 0.716567},
  62 {0.850651, 0.000000, 0.525731}, {0.864188, 0.442863, -0.238856},
  63 {0.809017, 0.309017, -0.500000}, {0.951056, 0.162460, -0.262866},
  64 {0.525731, 0.000000, -0.850651}, {0.681718, 0.147621, -0.716567},
  65 {0.681718, -0.147621, -0.716567}, {0.850651, 0.000000, -0.525731},
  66 {0.809017, -0.309017, -0.500000}, {0.864188, -0.442863, -0.238856},
  67 {0.951056, -0.162460, -0.262866}, {0.147621, 0.716567, -0.681718},
  68 {0.309017, 0.500000, -0.809017}, {0.425325, 0.688191, -0.587785},
  69 {0.442863, 0.238856, -0.864188}, {0.587785, 0.425325, -0.688191},
  70 {0.688191, 0.587785, -0.425325}, {-0.147621, 0.716567, -0.681718},
  71 {-0.309017, 0.500000, -0.809017}, {0.000000, 0.525731, -0.850651},
  72 {-0.525731, 0.000000, -0.850651}, {-0.442863, 0.238856, -0.864188},
  73 {-0.295242, 0.000000, -0.955423}, {-0.162460, 0.262866, -0.951056},
  74 {0.000000, 0.000000, -1.000000}, {0.295242, 0.000000, -0.955423},
  75 {0.162460, 0.262866, -0.951056}, {-0.442863, -0.238856, -0.864188},
  76 {-0.309017, -0.500000, -0.809017}, {-0.162460, -0.262866, -0.951056},
  77 {0.000000, -0.850651, -0.525731}, {-0.147621, -0.716567, -0.681718},
  78 {0.147621, -0.716567, -0.681718}, {0.000000, -0.525731, -0.850651},
  79 {0.309017, -0.500000, -0.809017}, {0.442863, -0.238856, -0.864188},
  80 {0.162460, -0.262866, -0.951056}, {0.238856, -0.864188, -0.442863},
  81 {0.500000, -0.809017, -0.309017}, {0.425325, -0.688191, -0.587785},
  82 {0.716567, -0.681718, -0.147621}, {0.688191, -0.587785, -0.425325},
  83 {0.587785, -0.425325, -0.688191}, {0.000000, -0.955423, -0.295242},
  84 {0.000000, -1.000000, 0.000000}, {0.262866, -0.951056, -0.162460},
  85 {0.000000, -0.850651, 0.525731}, {0.000000, -0.955423, 0.295242},
  86 {0.238856, -0.864188, 0.442863}, {0.262866, -0.951056, 0.162460},
  87 {0.500000, -0.809017, 0.309017}, {0.716567, -0.681718, 0.147621},
  88 {0.525731, -0.850651, 0.000000}, {-0.238856, -0.864188, -0.442863},
  89 {-0.500000, -0.809017, -0.309017}, {-0.262866, -0.951056, -0.162460},
  90 {-0.850651, -0.525731, 0.000000}, {-0.716567, -0.681718, -0.147621},
  91 {-0.716567, -0.681718, 0.147621}, {-0.525731, -0.850651, 0.000000},
  92 {-0.500000, -0.809017, 0.309017}, {-0.238856, -0.864188, 0.442863},
  93 {-0.262866, -0.951056, 0.162460}, {-0.864188, -0.442863, 0.238856},
  94 {-0.809017, -0.309017, 0.500000}, {-0.688191, -0.587785, 0.425325},
  95 {-0.681718, -0.147621, 0.716567}, {-0.442863, -0.238856, 0.864188},
  96 {-0.587785, -0.425325, 0.688191}, {-0.309017, -0.500000, 0.809017},
  97 {-0.147621, -0.716567, 0.681718}, {-0.425325, -0.688191, 0.587785},
  98 {-0.162460, -0.262866, 0.951056}, {0.442863, -0.238856, 0.864188},
  99 {0.162460, -0.262866, 0.951056}, {0.309017, -0.500000, 0.809017},
 100 {0.147621, -0.716567, 0.681718}, {0.000000, -0.525731, 0.850651},
 101 {0.425325, -0.688191, 0.587785}, {0.587785, -0.425325, 0.688191},
 102 {0.688191, -0.587785, 0.425325}, {-0.955423, 0.295242, 0.000000},
 103 {-0.951056, 0.162460, 0.262866}, {-1.000000, 0.000000, 0.000000},
 104 {-0.850651, 0.000000, 0.525731}, {-0.955423, -0.295242, 0.000000},
 105 {-0.951056, -0.162460, 0.262866}, {-0.864188, 0.442863, -0.238856},
 106 {-0.951056, 0.162460, -0.262866}, {-0.809017, 0.309017, -0.500000},
 107 {-0.864188, -0.442863, -0.238856}, {-0.951056, -0.162460, -0.262866},
 108 {-0.809017, -0.309017, -0.500000}, {-0.681718, 0.147621, -0.716567},
 109 {-0.681718, -0.147621, -0.716567}, {-0.850651, 0.000000, -0.525731},
 110 {-0.688191, 0.587785, -0.425325}, {-0.587785, 0.425325, -0.688191},
 111 {-0.425325, 0.688191, -0.587785}, {-0.425325, -0.688191, -0.587785},
 112 {-0.587785, -0.425325, -0.688191}, {-0.688191, -0.587785, -0.425325},
 113 };
 114
 115 qbyte NormalToByte(const vec3_t n)
 116 {
 117         int i, best;
 118         float bestdistance, distance;
 119
 120         best = 0;
 121         bestdistance = DotProduct (n, m_bytenormals[0]);
 122         for (i = 1;i < NUMVERTEXNORMALS;i++)
 123         {
 124                 distance = DotProduct (n, m_bytenormals[i]);
 125                 if (distance > bestdistance)
 126                 {
 127                         bestdistance = distance;
 128                         best = i;
 129                 }
 130         }
 131         return best;
 132 }
 133
 134 // note: uses byte partly to force unsigned for the validity check
 135 void ByteToNormal(qbyte num, vec3_t n)
 136 {
 137         if (num < NUMVERTEXNORMALS)
 138                 VectorCopy(m_bytenormals[num], n);
 139         else
 140                 VectorClear(n); // FIXME: complain?
 141 }
 142
 143 float Q_RSqrt(float number)
 144 {
 145         float y;
 146
 147         if (number == 0.0f)
 148                 return 0.0f;
 149
 150         *((int *)&y) = 0x5f3759df - ((* (int *) &number) >> 1);
 151         return y * (1.5f - (number * 0.5f * y * y));
 152 }
 153
 154
 155 // assumes "src" is normalized
 156 void PerpendicularVector( vec3_t dst, const vec3_t src )
 157 {
 158         // LordHavoc: optimized to death and beyond
 159         int pos;
 160         float minelem;
 161
 162         if (src[0])
 163         {
 164                 dst[0] = 0;
 165                 if (src[1])
 166                 {
 167                         dst[1] = 0;
 168                         if (src[2])
 169                         {
 170                                 dst[2] = 0;
 171                                 pos = 0;
 172                                 minelem = fabs(src[0]);
 173                                 if (fabs(src[1]) < minelem)
 174                                 {
 175                                         pos = 1;
 176                                         minelem = fabs(src[1]);
 177                                 }
 178                                 if (fabs(src[2]) < minelem)
 179                                         pos = 2;
 180
 181                                 dst[pos] = 1;
 182                                 dst[0] -= src[pos] * src[0];
 183                                 dst[1] -= src[pos] * src[1];
 184                                 dst[2] -= src[pos] * src[2];
 185
 186                                 // normalize the result
 187                                 VectorNormalize(dst);
 188                         }
 189                         else
 190                                 dst[2] = 1;
 191                 }
 192                 else
 193                 {
 194                         dst[1] = 1;
 195                         dst[2] = 0;
 196                 }
 197         }
 198         else
 199         {
 200                 dst[0] = 1;
 201                 dst[1] = 0;
 202                 dst[2] = 0;
 203         }
 204 }
 205
 206
 207 // LordHavoc: like AngleVectors, but taking a forward vector instead of angles, useful!
 208 void VectorVectors(const vec3_t forward, vec3_t right, vec3_t up)
 209 {
 210         float d;
 211
 212         right[0] = forward[2];
 213         right[1] = -forward[0];
 214         right[2] = forward[1];
 215
 216         d = DotProduct(forward, right);
 217         right[0] -= d * forward[0];
 218         right[1] -= d * forward[1];
 219         right[2] -= d * forward[2];
 220         VectorNormalizeFast(right);
 221         CrossProduct(right, forward, up);
 222 }
 223
 224 void VectorVectorsDouble(const double *forward, double *right, double *up)
 225 {
 226         double d;
 227
 228         right[0] = forward[2];
 229         right[1] = -forward[0];
 230         right[2] = forward[1];
 231
 232         d = DotProduct(forward, right);
 233         right[0] -= d * forward[0];
 234         right[1] -= d * forward[1];
 235         right[2] -= d * forward[2];
 236         VectorNormalize(right);
 237         CrossProduct(right, forward, up);
 238 }
 239
 240 void RotatePointAroundVector( vec3_t dst, const vec3_t dir, const vec3_t point, float degrees )
 241 {
 242         float t0, t1;
 243         float angle, c, s;
 244         vec3_t vr, vu, vf;
 245
 246         angle = DEG2RAD(degrees);
 247
 248         c = cos(angle);
 249         s = sin(angle);
 250
 251         vf[0] = dir[0];
 252         vf[1] = dir[1];
 253         vf[2] = dir[2];
 254
 255         VectorVectors(vf, vr, vu);
 256
 257         t0 = vr[0] *  c + vu[0] * -s;
 258         t1 = vr[0] *  s + vu[0] *  c;
 259         dst[0] = (t0 * vr[0] + t1 * vu[0] + vf[0] * vf[0]) * point[0]
 260                + (t0 * vr[1] + t1 * vu[1] + vf[0] * vf[1]) * point[1]
 261                + (t0 * vr[2] + t1 * vu[2] + vf[0] * vf[2]) * point[2];
 262
 263         t0 = vr[1] *  c + vu[1] * -s;
 264         t1 = vr[1] *  s + vu[1] *  c;
 265         dst[1] = (t0 * vr[0] + t1 * vu[0] + vf[1] * vf[0]) * point[0]
 266                + (t0 * vr[1] + t1 * vu[1] + vf[1] * vf[1]) * point[1]
 267                + (t0 * vr[2] + t1 * vu[2] + vf[1] * vf[2]) * point[2];
 268
 269         t0 = vr[2] *  c + vu[2] * -s;
 270         t1 = vr[2] *  s + vu[2] *  c;
 271         dst[2] = (t0 * vr[0] + t1 * vu[0] + vf[2] * vf[0]) * point[0]
 272                + (t0 * vr[1] + t1 * vu[1] + vf[2] * vf[1]) * point[1]
 273                + (t0 * vr[2] + t1 * vu[2] + vf[2] * vf[2]) * point[2];
 274 }
 275
 276 /*-----------------------------------------------------------------*/
 277
 278
 279 // LordHavoc note 1:
 280 // BoxOnPlaneSide did a switch on a 'signbits' value and had optimized
 281 // assembly in an attempt to accelerate it further, very inefficient
 282 // considering that signbits of the frustum planes only changed each
 283 // frame, and the world planes changed only at load time.
 284 // So, to optimize it further I took the obvious route of storing a function
 285 // pointer in the plane struct itself, and shrunk each of the individual
 286 // cases to a single return statement.
 287 // LordHavoc note 2:
 288 // realized axial cases would be a nice speedup for world geometry, although
 289 // never useful for the frustum planes.
 290 int BoxOnPlaneSideX (vec3_t emins, vec3_t emaxs, mplane_t *p) {return p->dist <= emins[0] ? 1 : (p->dist >= emaxs[0] ? 2 : 3);}
 291 int BoxOnPlaneSideY (vec3_t emins, vec3_t emaxs, mplane_t *p) {return p->dist <= emins[1] ? 1 : (p->dist >= emaxs[1] ? 2 : 3);}
 292 int BoxOnPlaneSideZ (vec3_t emins, vec3_t emaxs, mplane_t *p) {return p->dist <= emins[2] ? 1 : (p->dist >= emaxs[2] ? 2 : 3);}
 293 int BoxOnPlaneSide0 (vec3_t emins, vec3_t emaxs, mplane_t *p) {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));}
 294 int BoxOnPlaneSide1 (vec3_t emins, vec3_t emaxs, mplane_t *p) {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));}
 295 int BoxOnPlaneSide2 (vec3_t emins, vec3_t emaxs, mplane_t *p) {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));}
 296 int BoxOnPlaneSide3 (vec3_t emins, vec3_t emaxs, mplane_t *p) {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));}
 297 int BoxOnPlaneSide4 (vec3_t emins, vec3_t emaxs, mplane_t *p) {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));}
 298 int BoxOnPlaneSide5 (vec3_t emins, vec3_t emaxs, mplane_t *p) {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));}
 299 int BoxOnPlaneSide6 (vec3_t emins, vec3_t emaxs, mplane_t *p) {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));}
 300 int BoxOnPlaneSide7 (vec3_t emins, vec3_t emaxs, mplane_t *p) {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));}
 301
 302 void BoxOnPlaneSideClassify(mplane_t *p)
 303 {
 304         switch(p->type)
 305         {
 306         case 0: // x axis
 307                 p->BoxOnPlaneSideFunc = BoxOnPlaneSideX;
 308                 break;
 309         case 1: // y axis
 310                 p->BoxOnPlaneSideFunc = BoxOnPlaneSideY;
 311                 break;
 312         case 2: // z axis
 313                 p->BoxOnPlaneSideFunc = BoxOnPlaneSideZ;
 314                 break;
 315         default:
 316                 if (p->normal[2] < 0) // 4
 317                 {
 318                         if (p->normal[1] < 0) // 2
 319                         {
 320                                 if (p->normal[0] < 0) // 1
 321                                         p->BoxOnPlaneSideFunc = BoxOnPlaneSide7;
 322                                 else
 323                                         p->BoxOnPlaneSideFunc = BoxOnPlaneSide6;
 324                         }
 325                         else
 326                         {
 327                                 if (p->normal[0] < 0) // 1
 328                                         p->BoxOnPlaneSideFunc = BoxOnPlaneSide5;
 329                                 else
 330                                         p->BoxOnPlaneSideFunc = BoxOnPlaneSide4;
 331                         }
 332                 }
 333                 else
 334                 {
 335                         if (p->normal[1] < 0) // 2
 336                         {
 337                                 if (p->normal[0] < 0) // 1
 338                                         p->BoxOnPlaneSideFunc = BoxOnPlaneSide3;
 339                                 else
 340                                         p->BoxOnPlaneSideFunc = BoxOnPlaneSide2;
 341                         }
 342                         else
 343                         {
 344                                 if (p->normal[0] < 0) // 1
 345                                         p->BoxOnPlaneSideFunc = BoxOnPlaneSide1;
 346                                 else
 347                                         p->BoxOnPlaneSideFunc = BoxOnPlaneSide0;
 348                         }
 349                 }
 350                 break;
 351         }
 352 }
 353
 354 void PlaneClassify(mplane_t *p)
 355 {
 356         if (p->normal[0] == 1)
 357                 p->type = 0;
 358         else if (p->normal[1] == 1)
 359                 p->type = 1;
 360         else if (p->normal[2] == 1)
 361                 p->type = 2;
 362         else
 363                 p->type = 3;
 364         BoxOnPlaneSideClassify(p);
 365 }
 366
 367 void AngleVectors (const vec3_t angles, vec3_t forward, vec3_t right, vec3_t up)
 368 {
 369         double angle, sr, sp, sy, cr, cp, cy;
 370
 371         angle = angles[YAW] * (M_PI*2 / 360);
 372         sy = sin(angle);
 373         cy = cos(angle);
 374         angle = angles[PITCH] * (M_PI*2 / 360);
 375         sp = sin(angle);
 376         cp = cos(angle);
 377         if (forward)
 378         {
 379                 forward[0] = cp*cy;
 380                 forward[1] = cp*sy;
 381                 forward[2] = -sp;
 382         }
 383         if (right || up)
 384         {
 385                 angle = angles[ROLL] * (M_PI*2 / 360);
 386                 sr = sin(angle);
 387                 cr = cos(angle);
 388                 if (right)
 389                 {
 390                         right[0] = -1*(sr*sp*cy+cr*-sy);
 391                         right[1] = -1*(sr*sp*sy+cr*cy);
 392                         right[2] = -1*(sr*cp);
 393                 }
 394                 if (up)
 395                 {
 396                         up[0] = (cr*sp*cy+-sr*-sy);
 397                         up[1] = (cr*sp*sy+-sr*cy);
 398                         up[2] = cr*cp;
 399                 }
 400         }
 401 }
 402
 403 void AngleVectorsFLU (const vec3_t angles, vec3_t forward, vec3_t left, vec3_t up)
 404 {
 405         double angle, sr, sp, sy, cr, cp, cy;
 406
 407         angle = angles[YAW] * (M_PI*2 / 360);
 408         sy = sin(angle);
 409         cy = cos(angle);
 410         angle = angles[PITCH] * (M_PI*2 / 360);
 411         sp = sin(angle);
 412         cp = cos(angle);
 413         if (forward)
 414         {
 415                 forward[0] = cp*cy;
 416                 forward[1] = cp*sy;
 417                 forward[2] = -sp;
 418         }
 419         if (left || up)
 420         {
 421                 angle = angles[ROLL] * (M_PI*2 / 360);
 422                 sr = sin(angle);
 423                 cr = cos(angle);
 424                 if (left)
 425                 {
 426                         left[0] = sr*sp*cy+cr*-sy;
 427                         left[1] = sr*sp*sy+cr*cy;
 428                         left[2] = sr*cp;
 429                 }
 430                 if (up)
 431                 {
 432                         up[0] = cr*sp*cy+-sr*-sy;
 433                         up[1] = cr*sp*sy+-sr*cy;
 434                         up[2] = cr*cp;
 435                 }
 436         }
 437 }
 438
 439 void AngleMatrix (const vec3_t angles, const vec3_t translate, vec_t matrix[][4])
 440 {
 441         double angle, sr, sp, sy, cr, cp, cy;
 442
 443         angle = angles[YAW] * (M_PI*2 / 360);
 444         sy = sin(angle);
 445         cy = cos(angle);
 446         angle = angles[PITCH] * (M_PI*2 / 360);
 447         sp = sin(angle);
 448         cp = cos(angle);
 449         angle = angles[ROLL] * (M_PI*2 / 360);
 450         sr = sin(angle);
 451         cr = cos(angle);
 452         matrix[0][0] = cp*cy;
 453         matrix[0][1] = sr*sp*cy+cr*-sy;
 454         matrix[0][2] = cr*sp*cy+-sr*-sy;
 455         matrix[0][3] = translate[0];
 456         matrix[1][0] = cp*sy;
 457         matrix[1][1] = sr*sp*sy+cr*cy;
 458         matrix[1][2] = cr*sp*sy+-sr*cy;
 459         matrix[1][3] = translate[1];
 460         matrix[2][0] = -sp;
 461         matrix[2][1] = sr*cp;
 462         matrix[2][2] = cr*cp;
 463         matrix[2][3] = translate[2];
 464 }
 465
 466
 467 // LordHavoc: renamed this to Length, and made the normal one a #define
 468 float VectorNormalizeLength (vec3_t v)
 469 {
 470         float length, ilength;
 471
 472         length = v[0]*v[0] + v[1]*v[1] + v[2]*v[2];
 473         length = sqrt (length);
 474
 475         if (length)
 476         {
 477                 ilength = 1/length;
 478                 v[0] *= ilength;
 479                 v[1] *= ilength;
 480                 v[2] *= ilength;
 481         }
 482
 483         return length;
 484
 485 }
 486
 487
 488 /*
 489 ================
 490 R_ConcatRotations
 491 ================
 492 */
 493 void R_ConcatRotations (const float in1[3*3], const float in2[3*3], float out[3*3])
 494 {
 495         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];
 496         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];
 497         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];
 498         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];
 499         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];
 500         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];
 501         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];
 502         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];
 503         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];
 504 }
 505
 506
 507 /*
 508 ================
 509 R_ConcatTransforms
 510 ================
 511 */
 512 void R_ConcatTransforms (const float in1[3*4], const float in2[3*4], float out[3*4])
 513 {
 514         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];
 515         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];
 516         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];
 517         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];
 518         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];
 519         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];
 520         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];
 521         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];
 522         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];
 523         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];
 524         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];
 525         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];
 526 }
 527
 528
 529 void Mathlib_Init(void)
 530 {
 531         int a;
 532
 533         // LordHavoc: setup 1.0f / N table for quick recipricols of integers
 534         ixtable[0] = 0;
 535         for (a = 1;a < 4096;a++)
 536                 ixtable[a] = 1.0f / a;
 537 }
 538