vertex arrays renamed to varray_ and exposed to rest of engine
[divverent/darkplaces.git] / 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