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 void Sys_Error (char *error, ...);
  26
  27 vec3_t vec3_origin = {0,0,0};
  28 float ixtable[4096];
  29
  30 /*-----------------------------------------------------------------*/
  31
  32 float m_bytenormals[NUMVERTEXNORMALS][3] =
  33 {
  34 {-0.525731, 0.000000, 0.850651}, {-0.442863, 0.238856, 0.864188},
  35 {-0.295242, 0.000000, 0.955423}, {-0.309017, 0.500000, 0.809017},
  36 {-0.162460, 0.262866, 0.951056}, {0.000000, 0.000000, 1.000000},
  37 {0.000000, 0.850651, 0.525731}, {-0.147621, 0.716567, 0.681718},
  38 {0.147621, 0.716567, 0.681718}, {0.000000, 0.525731, 0.850651},
  39 {0.309017, 0.500000, 0.809017}, {0.525731, 0.000000, 0.850651},
  40 {0.295242, 0.000000, 0.955423}, {0.442863, 0.238856, 0.864188},
  41 {0.162460, 0.262866, 0.951056}, {-0.681718, 0.147621, 0.716567},
  42 {-0.809017, 0.309017, 0.500000}, {-0.587785, 0.425325, 0.688191},
  43 {-0.850651, 0.525731, 0.000000}, {-0.864188, 0.442863, 0.238856},
  44 {-0.716567, 0.681718, 0.147621}, {-0.688191, 0.587785, 0.425325},
  45 {-0.500000, 0.809017, 0.309017}, {-0.238856, 0.864188, 0.442863},
  46 {-0.425325, 0.688191, 0.587785}, {-0.716567, 0.681718, -0.147621},
  47 {-0.500000, 0.809017, -0.309017}, {-0.525731, 0.850651, 0.000000},
  48 {0.000000, 0.850651, -0.525731}, {-0.238856, 0.864188, -0.442863},
  49 {0.000000, 0.955423, -0.295242}, {-0.262866, 0.951056, -0.162460},
  50 {0.000000, 1.000000, 0.000000}, {0.000000, 0.955423, 0.295242},
  51 {-0.262866, 0.951056, 0.162460}, {0.238856, 0.864188, 0.442863},
  52 {0.262866, 0.951056, 0.162460}, {0.500000, 0.809017, 0.309017},
  53 {0.238856, 0.864188, -0.442863}, {0.262866, 0.951056, -0.162460},
  54 {0.500000, 0.809017, -0.309017}, {0.850651, 0.525731, 0.000000},
  55 {0.716567, 0.681718, 0.147621}, {0.716567, 0.681718, -0.147621},
  56 {0.525731, 0.850651, 0.000000}, {0.425325, 0.688191, 0.587785},
  57 {0.864188, 0.442863, 0.238856}, {0.688191, 0.587785, 0.425325},
  58 {0.809017, 0.309017, 0.500000}, {0.681718, 0.147621, 0.716567},
  59 {0.587785, 0.425325, 0.688191}, {0.955423, 0.295242, 0.000000},
  60 {1.000000, 0.000000, 0.000000}, {0.951056, 0.162460, 0.262866},
  61 {0.850651, -0.525731, 0.000000}, {0.955423, -0.295242, 0.000000},
  62 {0.864188, -0.442863, 0.238856}, {0.951056, -0.162460, 0.262866},
  63 {0.809017, -0.309017, 0.500000}, {0.681718, -0.147621, 0.716567},
  64 {0.850651, 0.000000, 0.525731}, {0.864188, 0.442863, -0.238856},
  65 {0.809017, 0.309017, -0.500000}, {0.951056, 0.162460, -0.262866},
  66 {0.525731, 0.000000, -0.850651}, {0.681718, 0.147621, -0.716567},
  67 {0.681718, -0.147621, -0.716567}, {0.850651, 0.000000, -0.525731},
  68 {0.809017, -0.309017, -0.500000}, {0.864188, -0.442863, -0.238856},
  69 {0.951056, -0.162460, -0.262866}, {0.147621, 0.716567, -0.681718},
  70 {0.309017, 0.500000, -0.809017}, {0.425325, 0.688191, -0.587785},
  71 {0.442863, 0.238856, -0.864188}, {0.587785, 0.425325, -0.688191},
  72 {0.688191, 0.587785, -0.425325}, {-0.147621, 0.716567, -0.681718},
  73 {-0.309017, 0.500000, -0.809017}, {0.000000, 0.525731, -0.850651},
  74 {-0.525731, 0.000000, -0.850651}, {-0.442863, 0.238856, -0.864188},
  75 {-0.295242, 0.000000, -0.955423}, {-0.162460, 0.262866, -0.951056},
  76 {0.000000, 0.000000, -1.000000}, {0.295242, 0.000000, -0.955423},
  77 {0.162460, 0.262866, -0.951056}, {-0.442863, -0.238856, -0.864188},
  78 {-0.309017, -0.500000, -0.809017}, {-0.162460, -0.262866, -0.951056},
  79 {0.000000, -0.850651, -0.525731}, {-0.147621, -0.716567, -0.681718},
  80 {0.147621, -0.716567, -0.681718}, {0.000000, -0.525731, -0.850651},
  81 {0.309017, -0.500000, -0.809017}, {0.442863, -0.238856, -0.864188},
  82 {0.162460, -0.262866, -0.951056}, {0.238856, -0.864188, -0.442863},
  83 {0.500000, -0.809017, -0.309017}, {0.425325, -0.688191, -0.587785},
  84 {0.716567, -0.681718, -0.147621}, {0.688191, -0.587785, -0.425325},
  85 {0.587785, -0.425325, -0.688191}, {0.000000, -0.955423, -0.295242},
  86 {0.000000, -1.000000, 0.000000}, {0.262866, -0.951056, -0.162460},
  87 {0.000000, -0.850651, 0.525731}, {0.000000, -0.955423, 0.295242},
  88 {0.238856, -0.864188, 0.442863}, {0.262866, -0.951056, 0.162460},
  89 {0.500000, -0.809017, 0.309017}, {0.716567, -0.681718, 0.147621},
  90 {0.525731, -0.850651, 0.000000}, {-0.238856, -0.864188, -0.442863},
  91 {-0.500000, -0.809017, -0.309017}, {-0.262866, -0.951056, -0.162460},
  92 {-0.850651, -0.525731, 0.000000}, {-0.716567, -0.681718, -0.147621},
  93 {-0.716567, -0.681718, 0.147621}, {-0.525731, -0.850651, 0.000000},
  94 {-0.500000, -0.809017, 0.309017}, {-0.238856, -0.864188, 0.442863},
  95 {-0.262866, -0.951056, 0.162460}, {-0.864188, -0.442863, 0.238856},
  96 {-0.809017, -0.309017, 0.500000}, {-0.688191, -0.587785, 0.425325},
  97 {-0.681718, -0.147621, 0.716567}, {-0.442863, -0.238856, 0.864188},
  98 {-0.587785, -0.425325, 0.688191}, {-0.309017, -0.500000, 0.809017},
  99 {-0.147621, -0.716567, 0.681718}, {-0.425325, -0.688191, 0.587785},
 100 {-0.162460, -0.262866, 0.951056}, {0.442863, -0.238856, 0.864188},
 101 {0.162460, -0.262866, 0.951056}, {0.309017, -0.500000, 0.809017},
 102 {0.147621, -0.716567, 0.681718}, {0.000000, -0.525731, 0.850651},
 103 {0.425325, -0.688191, 0.587785}, {0.587785, -0.425325, 0.688191},
 104 {0.688191, -0.587785, 0.425325}, {-0.955423, 0.295242, 0.000000},
 105 {-0.951056, 0.162460, 0.262866}, {-1.000000, 0.000000, 0.000000},
 106 {-0.850651, 0.000000, 0.525731}, {-0.955423, -0.295242, 0.000000},
 107 {-0.951056, -0.162460, 0.262866}, {-0.864188, 0.442863, -0.238856},
 108 {-0.951056, 0.162460, -0.262866}, {-0.809017, 0.309017, -0.500000},
 109 {-0.864188, -0.442863, -0.238856}, {-0.951056, -0.162460, -0.262866},
 110 {-0.809017, -0.309017, -0.500000}, {-0.681718, 0.147621, -0.716567},
 111 {-0.681718, -0.147621, -0.716567}, {-0.850651, 0.000000, -0.525731},
 112 {-0.688191, 0.587785, -0.425325}, {-0.587785, 0.425325, -0.688191},
 113 {-0.425325, 0.688191, -0.587785}, {-0.425325, -0.688191, -0.587785},
 114 {-0.587785, -0.425325, -0.688191}, {-0.688191, -0.587785, -0.425325},
 115 };
 116
 117 qbyte 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(qbyte 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 float Q_RSqrt(float number)
 146 {
 147         float y;
 148
 149         if (number == 0.0f)
 150                 return 0.0f;
 151
 152         *((int *)&y) = 0x5f3759df - ((* (int *) &number) >> 1);
 153         return y * (1.5f - (number * 0.5f * y * y));
 154 }
 155
 156
 157 // assumes "src" is normalized
 158 void PerpendicularVector( vec3_t dst, const vec3_t src )
 159 {
 160         // LordHavoc: optimized to death and beyond
 161         int     pos;
 162         float minelem;
 163
 164         if (src[0])
 165         {
 166                 dst[0] = 0;
 167                 if (src[1])
 168                 {
 169                         dst[1] = 0;
 170                         if (src[2])
 171                         {
 172                                 dst[2] = 0;
 173                                 pos = 0;
 174                                 minelem = fabs(src[0]);
 175                                 if (fabs(src[1]) < minelem)
 176                                 {
 177                                         pos = 1;
 178                                         minelem = fabs(src[1]);
 179                                 }
 180                                 if (fabs(src[2]) < minelem)
 181                                         pos = 2;
 182
 183                                 dst[pos] = 1;
 184                                 dst[0] -= src[pos] * src[0];
 185                                 dst[1] -= src[pos] * src[1];
 186                                 dst[2] -= src[pos] * src[2];
 187
 188                                 // normalize the result
 189                                 VectorNormalize(dst);
 190                         }
 191                         else
 192                                 dst[2] = 1;
 193                 }
 194                 else
 195                 {
 196                         dst[1] = 1;
 197                         dst[2] = 0;
 198                 }
 199         }
 200         else
 201         {
 202                 dst[0] = 1;
 203                 dst[1] = 0;
 204                 dst[2] = 0;
 205         }
 206 }
 207
 208
 209 // LordHavoc: like AngleVectors, but taking a forward vector instead of angles, useful!
 210 void VectorVectors(const vec3_t forward, vec3_t right, vec3_t up)
 211 {
 212         float d;
 213
 214         right[0] = forward[2];
 215         right[1] = -forward[0];
 216         right[2] = forward[1];
 217
 218         d = DotProduct(forward, right);
 219         right[0] -= d * forward[0];
 220         right[1] -= d * forward[1];
 221         right[2] -= d * forward[2];
 222         VectorNormalizeFast(right);
 223         CrossProduct(right, forward, up);
 224 }
 225
 226 void VectorVectorsDouble(const double *forward, double *right, double *up)
 227 {
 228         double d;
 229
 230         right[0] = forward[2];
 231         right[1] = -forward[0];
 232         right[2] = forward[1];
 233
 234         d = DotProduct(forward, right);
 235         right[0] -= d * forward[0];
 236         right[1] -= d * forward[1];
 237         right[2] -= d * forward[2];
 238         VectorNormalize(right);
 239         CrossProduct(right, forward, up);
 240 }
 241
 242 void RotatePointAroundVector( vec3_t dst, const vec3_t dir, const vec3_t point, float degrees )
 243 {
 244         float   t0, t1;
 245         float   angle, c, s;
 246         vec3_t  vr, vu, vf;
 247
 248         angle = DEG2RAD(degrees);
 249
 250         c = cos(angle);
 251         s = sin(angle);
 252
 253         vf[0] = dir[0];
 254         vf[1] = dir[1];
 255         vf[2] = dir[2];
 256
 257         VectorVectors(vf, vr, vu);
 258
 259         t0 = vr[0] *  c + vu[0] * -s;
 260         t1 = vr[0] *  s + vu[0] *  c;
 261         dst[0] = (t0 * vr[0] + t1 * vu[0] + vf[0] * vf[0]) * point[0]
 262                + (t0 * vr[1] + t1 * vu[1] + vf[0] * vf[1]) * point[1]
 263                + (t0 * vr[2] + t1 * vu[2] + vf[0] * vf[2]) * point[2];
 264
 265         t0 = vr[1] *  c + vu[1] * -s;
 266         t1 = vr[1] *  s + vu[1] *  c;
 267         dst[1] = (t0 * vr[0] + t1 * vu[0] + vf[1] * vf[0]) * point[0]
 268                + (t0 * vr[1] + t1 * vu[1] + vf[1] * vf[1]) * point[1]
 269                + (t0 * vr[2] + t1 * vu[2] + vf[1] * vf[2]) * point[2];
 270
 271         t0 = vr[2] *  c + vu[2] * -s;
 272         t1 = vr[2] *  s + vu[2] *  c;
 273         dst[2] = (t0 * vr[0] + t1 * vu[0] + vf[2] * vf[0]) * point[0]
 274                + (t0 * vr[1] + t1 * vu[1] + vf[2] * vf[1]) * point[1]
 275                + (t0 * vr[2] + t1 * vu[2] + vf[2] * vf[2]) * point[2];
 276 }
 277
 278 /*-----------------------------------------------------------------*/
 279
 280
 281 // LordHavoc note 1:
 282 // BoxOnPlaneSide did a switch on a 'signbits' value and had optimized
 283 // assembly in an attempt to accelerate it further, very inefficient
 284 // considering that signbits of the frustum planes only changed each
 285 // frame, and the world planes changed only at load time.
 286 // So, to optimize it further I took the obvious route of storing a function
 287 // pointer in the plane struct itself, and shrunk each of the individual
 288 // cases to a single return statement.
 289 // LordHavoc note 2:
 290 // realized axial cases would be a nice speedup for world geometry, although
 291 // never useful for the frustum planes.
 292 int BoxOnPlaneSideX (vec3_t emins, vec3_t emaxs, mplane_t *p) {return p->dist <= emins[0] ? 1 : (p->dist >= emaxs[0] ? 2 : 3);}
 293 int BoxOnPlaneSideY (vec3_t emins, vec3_t emaxs, mplane_t *p) {return p->dist <= emins[1] ? 1 : (p->dist >= emaxs[1] ? 2 : 3);}
 294 int BoxOnPlaneSideZ (vec3_t emins, vec3_t emaxs, mplane_t *p) {return p->dist <= emins[2] ? 1 : (p->dist >= emaxs[2] ? 2 : 3);}
 295 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));}
 296 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));}
 297 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));}
 298 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));}
 299 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));}
 300 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));}
 301 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));}
 302 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));}
 303
 304 void BoxOnPlaneSideClassify(mplane_t *p)
 305 {
 306         switch(p->type)
 307         {
 308         case 0: // x axis
 309                 p->BoxOnPlaneSideFunc = BoxOnPlaneSideX;
 310                 break;
 311         case 1: // y axis
 312                 p->BoxOnPlaneSideFunc = BoxOnPlaneSideY;
 313                 break;
 314         case 2: // z axis
 315                 p->BoxOnPlaneSideFunc = BoxOnPlaneSideZ;
 316                 break;
 317         default:
 318                 if (p->normal[2] < 0) // 4
 319                 {
 320                         if (p->normal[1] < 0) // 2
 321                         {
 322                                 if (p->normal[0] < 0) // 1
 323                                         p->BoxOnPlaneSideFunc = BoxOnPlaneSide7;
 324                                 else
 325                                         p->BoxOnPlaneSideFunc = BoxOnPlaneSide6;
 326                         }
 327                         else
 328                         {
 329                                 if (p->normal[0] < 0) // 1
 330                                         p->BoxOnPlaneSideFunc = BoxOnPlaneSide5;
 331                                 else
 332                                         p->BoxOnPlaneSideFunc = BoxOnPlaneSide4;
 333                         }
 334                 }
 335                 else
 336                 {
 337                         if (p->normal[1] < 0) // 2
 338                         {
 339                                 if (p->normal[0] < 0) // 1
 340                                         p->BoxOnPlaneSideFunc = BoxOnPlaneSide3;
 341                                 else
 342                                         p->BoxOnPlaneSideFunc = BoxOnPlaneSide2;
 343                         }
 344                         else
 345                         {
 346                                 if (p->normal[0] < 0) // 1
 347                                         p->BoxOnPlaneSideFunc = BoxOnPlaneSide1;
 348                                 else
 349                                         p->BoxOnPlaneSideFunc = BoxOnPlaneSide0;
 350                         }
 351                 }
 352                 break;
 353         }
 354 }
 355
 356 void PlaneClassify(mplane_t *p)
 357 {
 358         if (p->normal[0] == 1)
 359                 p->type = 0;
 360         else if (p->normal[1] == 1)
 361                 p->type = 1;
 362         else if (p->normal[2] == 1)
 363                 p->type = 2;
 364         else
 365                 p->type = 3;
 366         BoxOnPlaneSideClassify(p);
 367 }
 368
 369 void AngleVectors (const vec3_t angles, vec3_t forward, vec3_t right, vec3_t up)
 370 {
 371         double angle, sr, sp, sy, cr, cp, cy;
 372
 373         angle = angles[YAW] * (M_PI*2 / 360);
 374         sy = sin(angle);
 375         cy = cos(angle);
 376         angle = angles[PITCH] * (M_PI*2 / 360);
 377         sp = sin(angle);
 378         cp = cos(angle);
 379         if (forward)
 380         {
 381                 forward[0] = cp*cy;
 382                 forward[1] = cp*sy;
 383                 forward[2] = -sp;
 384         }
 385         if (right || up)
 386         {
 387                 angle = angles[ROLL] * (M_PI*2 / 360);
 388                 sr = sin(angle);
 389                 cr = cos(angle);
 390                 if (right)
 391                 {
 392                         right[0] = -1*(sr*sp*cy+cr*-sy);
 393                         right[1] = -1*(sr*sp*sy+cr*cy);
 394                         right[2] = -1*(sr*cp);
 395                 }
 396                 if (up)
 397                 {
 398                         up[0] = (cr*sp*cy+-sr*-sy);
 399                         up[1] = (cr*sp*sy+-sr*cy);
 400                         up[2] = cr*cp;
 401                 }
 402         }
 403 }
 404
 405 void AngleVectorsFLU (const vec3_t angles, vec3_t forward, vec3_t left, vec3_t up)
 406 {
 407         double angle, sr, sp, sy, cr, cp, cy;
 408
 409         angle = angles[YAW] * (M_PI*2 / 360);
 410         sy = sin(angle);
 411         cy = cos(angle);
 412         angle = angles[PITCH] * (M_PI*2 / 360);
 413         sp = sin(angle);
 414         cp = cos(angle);
 415         if (forward)
 416         {
 417                 forward[0] = cp*cy;
 418                 forward[1] = cp*sy;
 419                 forward[2] = -sp;
 420         }
 421         if (left || up)
 422         {
 423                 angle = angles[ROLL] * (M_PI*2 / 360);
 424                 sr = sin(angle);
 425                 cr = cos(angle);
 426                 if (left)
 427                 {
 428                         left[0] = sr*sp*cy+cr*-sy;
 429                         left[1] = sr*sp*sy+cr*cy;
 430                         left[2] = sr*cp;
 431                 }
 432                 if (up)
 433                 {
 434                         up[0] = cr*sp*cy+-sr*-sy;
 435                         up[1] = cr*sp*sy+-sr*cy;
 436                         up[2] = cr*cp;
 437                 }
 438         }
 439 }
 440
 441 void AngleMatrix (const vec3_t angles, const vec3_t translate, vec_t matrix[][4])
 442 {
 443         double angle, sr, sp, sy, cr, cp, cy;
 444
 445         angle = angles[YAW] * (M_PI*2 / 360);
 446         sy = sin(angle);
 447         cy = cos(angle);
 448         angle = angles[PITCH] * (M_PI*2 / 360);
 449         sp = sin(angle);
 450         cp = cos(angle);
 451         angle = angles[ROLL] * (M_PI*2 / 360);
 452         sr = sin(angle);
 453         cr = cos(angle);
 454         matrix[0][0] = cp*cy;
 455         matrix[0][1] = sr*sp*cy+cr*-sy;
 456         matrix[0][2] = cr*sp*cy+-sr*-sy;
 457         matrix[0][3] = translate[0];
 458         matrix[1][0] = cp*sy;
 459         matrix[1][1] = sr*sp*sy+cr*cy;
 460         matrix[1][2] = cr*sp*sy+-sr*cy;
 461         matrix[1][3] = translate[1];
 462         matrix[2][0] = -sp;
 463         matrix[2][1] = sr*cp;
 464         matrix[2][2] = cr*cp;
 465         matrix[2][3] = translate[2];
 466 }
 467
 468
 469 // LordHavoc: renamed these to Length, and made the normal ones #define
 470 float VectorNormalizeLength (vec3_t v)
 471 {
 472         float   length, ilength;
 473
 474         length = v[0]*v[0] + v[1]*v[1] + v[2]*v[2];
 475         length = sqrt (length);         // FIXME
 476
 477         if (length)
 478         {
 479                 ilength = 1/length;
 480                 v[0] *= ilength;
 481                 v[1] *= ilength;
 482                 v[2] *= ilength;
 483         }
 484
 485         return length;
 486
 487 }
 488
 489
 490 /*
 491 ================
 492 R_ConcatRotations
 493 ================
 494 */
 495 void R_ConcatRotations (const float in1[3*3], const float in2[3*3], float out[3*3])
 496 {
 497         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];
 498         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];
 499         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];
 500         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];
 501         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];
 502         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];
 503         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];
 504         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];
 505         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];
 506 }
 507
 508
 509 /*
 510 ================
 511 R_ConcatTransforms
 512 ================
 513 */
 514 void R_ConcatTransforms (const float in1[3*4], const float in2[3*4], float out[3*4])
 515 {
 516         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];
 517         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];
 518         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];
 519         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];
 520         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];
 521         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];
 522         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];
 523         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];
 524         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];
 525         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];
 526         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];
 527         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];
 528 }
 529
 530
 531 void Mathlib_Init(void)
 532 {
 533         int a;
 534
 535         // LordHavoc: setup 1.0f / N table for quick recipricols of integers
 536         ixtable[0] = 0;
 537         for (a = 1;a < 4096;a++)
 538                 ixtable[a] = 1.0f / a;
 539 }
 540