b4a1b6a0b1d847032cd783c05b4d5975fb6455fd
[xonotic/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 "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         // NOTE: this is consistent to AngleVectors applied to AnglesFromVectors
202         if (forward[0] == 0 && forward[1] == 0)
203         {
204                 if(forward[2] > 0)
205                 {
206                         VectorSet(right, 0, -1, 0);
207                         VectorSet(up, -1, 0, 0);
208                 }
209                 else
210                 {
211                         VectorSet(right, 0, -1, 0);
212                         VectorSet(up, 1, 0, 0);
213                 }
214         }
215         else
216         {
217                 right[0] = forward[1];
218                 right[1] = -forward[0];
219                 right[2] = 0;
220                 VectorNormalize(right);
221
222                 up[0] = (-forward[2]*forward[0]);
223                 up[1] = (-forward[2]*forward[1]);
224                 up[2] = (forward[0]*forward[0] + forward[1]*forward[1]);
225                 VectorNormalize(up);
226         }
227 }
228
229 void VectorVectorsDouble(const double *forward, double *right, double *up)
230 {
231         if (forward[0] == 0 && forward[1] == 0)
232         {
233                 if(forward[2] > 0)
234                 {
235                         VectorSet(right, 0, -1, 0);
236                         VectorSet(up, -1, 0, 0);
237                 }
238                 else
239                 {
240                         VectorSet(right, 0, -1, 0);
241                         VectorSet(up, 1, 0, 0);
242                 }
243         }
244         else
245         {
246                 right[0] = forward[1];
247                 right[1] = -forward[0];
248                 right[2] = 0;
249                 VectorNormalize(right);
250
251                 up[0] = (-forward[2]*forward[0]);
252                 up[1] = (-forward[2]*forward[1]);
253                 up[2] = (forward[0]*forward[0] + forward[1]*forward[1]);
254                 VectorNormalize(up);
255         }
256 }
257
258 void RotatePointAroundVector( vec3_t dst, const vec3_t dir, const vec3_t point, float degrees )
259 {
260         float t0, t1;
261         float angle, c, s;
262         vec3_t vr, vu, vf;
263
264         angle = DEG2RAD(degrees);
265         c = cos(angle);
266         s = sin(angle);
267         VectorCopy(dir, vf);
268         VectorVectors(vf, vr, vu);
269
270         t0 = vr[0] *  c + vu[0] * -s;
271         t1 = vr[0] *  s + vu[0] *  c;
272         dst[0] = (t0 * vr[0] + t1 * vu[0] + vf[0] * vf[0]) * point[0]
273                + (t0 * vr[1] + t1 * vu[1] + vf[0] * vf[1]) * point[1]
274                + (t0 * vr[2] + t1 * vu[2] + vf[0] * vf[2]) * point[2];
275
276         t0 = vr[1] *  c + vu[1] * -s;
277         t1 = vr[1] *  s + vu[1] *  c;
278         dst[1] = (t0 * vr[0] + t1 * vu[0] + vf[1] * vf[0]) * point[0]
279                + (t0 * vr[1] + t1 * vu[1] + vf[1] * vf[1]) * point[1]
280                + (t0 * vr[2] + t1 * vu[2] + vf[1] * vf[2]) * point[2];
281
282         t0 = vr[2] *  c + vu[2] * -s;
283         t1 = vr[2] *  s + vu[2] *  c;
284         dst[2] = (t0 * vr[0] + t1 * vu[0] + vf[2] * vf[0]) * point[0]
285                + (t0 * vr[1] + t1 * vu[1] + vf[2] * vf[1]) * point[1]
286                + (t0 * vr[2] + t1 * vu[2] + vf[2] * vf[2]) * point[2];
287 }
288
289 /*-----------------------------------------------------------------*/
290
291 // returns the smallest integer greater than or equal to "value", or 0 if "value" is too big
292 unsigned int CeilPowerOf2(unsigned int value)
293 {
294         unsigned int ceilvalue;
295
296         if (value > (1U << (sizeof(int) * 8 - 1)))
297                 return 0;
298
299         ceilvalue = 1;
300         while (ceilvalue < value)
301                 ceilvalue <<= 1;
302
303         return ceilvalue;
304 }
305
306
307 /*-----------------------------------------------------------------*/
308
309
310 void PlaneClassify(mplane_t *p)
311 {
312         // for optimized plane comparisons
313         if (p->normal[0] == 1)
314                 p->type = 0;
315         else if (p->normal[1] == 1)
316                 p->type = 1;
317         else if (p->normal[2] == 1)
318                 p->type = 2;
319         else
320                 p->type = 3;
321         // for BoxOnPlaneSide
322         p->signbits = 0;
323         if (p->normal[0] < 0) // 1
324                 p->signbits |= 1;
325         if (p->normal[1] < 0) // 2
326                 p->signbits |= 2;
327         if (p->normal[2] < 0) // 4
328                 p->signbits |= 4;
329 }
330
331 int BoxOnPlaneSide(const vec3_t emins, const vec3_t emaxs, const mplane_t *p)
332 {
333         if (p->type < 3)
334                 return ((emaxs[p->type] >= p->dist) | ((emins[p->type] < p->dist) << 1));
335         switch(p->signbits)
336         {
337         default:
338         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));
339         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));
340         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));
341         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));
342         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));
343         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));
344         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));
345         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));
346         }
347 }
348
349 #if 0
350 int BoxOnPlaneSide_Separate(const vec3_t emins, const vec3_t emaxs, const vec3_t normal, const vec_t dist)
351 {
352         switch((normal[0] < 0) | ((normal[1] < 0) << 1) | ((normal[2] < 0) << 2))
353         {
354         default:
355         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));
356         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));
357         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));
358         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));
359         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));
360         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));
361         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));
362         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));
363         }
364 }
365 #endif
366
367 void BoxPlaneCorners(const vec3_t emins, const vec3_t emaxs, const mplane_t *p, vec3_t outnear, vec3_t outfar)
368 {
369         if (p->type < 3)
370         {
371                 outnear[0] = outnear[1] = outnear[2] = outfar[0] = outfar[1] = outfar[2] = 0;
372                 outnear[p->type] = emins[p->type];
373                 outfar[p->type] = emaxs[p->type];
374                 return;
375         }
376         switch(p->signbits)
377         {
378         default:
379         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;
380         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;
381         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;
382         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;
383         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;
384         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;
385         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;
386         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;
387         }
388 }
389
390 void BoxPlaneCorners_Separate(const vec3_t emins, const vec3_t emaxs, const vec3_t normal, vec3_t outnear, vec3_t outfar)
391 {
392         switch((normal[0] < 0) | ((normal[1] < 0) << 1) | ((normal[2] < 0) << 2))
393         {
394         default:
395         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;
396         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;
397         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;
398         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;
399         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;
400         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;
401         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;
402         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;
403         }
404 }
405
406 void BoxPlaneCornerDistances(const vec3_t emins, const vec3_t emaxs, const mplane_t *p, vec_t *outneardist, vec_t *outfardist)
407 {
408         if (p->type < 3)
409         {
410                 *outneardist = emins[p->type] - p->dist;
411                 *outfardist = emaxs[p->type] - p->dist;
412                 return;
413         }
414         switch(p->signbits)
415         {
416         default:
417         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;
418         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;
419         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;
420         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;
421         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;
422         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;
423         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;
424         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;
425         }
426 }
427
428 void BoxPlaneCornerDistances_Separate(const vec3_t emins, const vec3_t emaxs, const vec3_t normal, vec_t *outneardist, vec_t *outfardist)
429 {
430         switch((normal[0] < 0) | ((normal[1] < 0) << 1) | ((normal[2] < 0) << 2))
431         {
432         default:
433         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;
434         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;
435         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;
436         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;
437         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;
438         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;
439         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;
440         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;
441         }
442 }
443
444 void AngleVectors (const vec3_t angles, vec3_t forward, vec3_t right, vec3_t up)
445 {
446         double angle, sr, sp, sy, cr, cp, cy;
447
448         angle = angles[YAW] * (M_PI*2 / 360);
449         sy = sin(angle);
450         cy = cos(angle);
451         angle = angles[PITCH] * (M_PI*2 / 360);
452         sp = sin(angle);
453         cp = cos(angle);
454         if (forward)
455         {
456                 forward[0] = cp*cy;
457                 forward[1] = cp*sy;
458                 forward[2] = -sp;
459         }
460         if (right || up)
461         {
462                 if (angles[ROLL])
463                 {
464                         angle = angles[ROLL] * (M_PI*2 / 360);
465                         sr = sin(angle);
466                         cr = cos(angle);
467                         if (right)
468                         {
469                                 right[0] = -1*(sr*sp*cy+cr*-sy);
470                                 right[1] = -1*(sr*sp*sy+cr*cy);
471                                 right[2] = -1*(sr*cp);
472                         }
473                         if (up)
474                         {
475                                 up[0] = (cr*sp*cy+-sr*-sy);
476                                 up[1] = (cr*sp*sy+-sr*cy);
477                                 up[2] = cr*cp;
478                         }
479                 }
480                 else
481                 {
482                         if (right)
483                         {
484                                 right[0] = sy;
485                                 right[1] = -cy;
486                                 right[2] = 0;
487                         }
488                         if (up)
489                         {
490                                 up[0] = (sp*cy);
491                                 up[1] = (sp*sy);
492                                 up[2] = cp;
493                         }
494                 }
495         }
496 }
497
498 void AngleVectorsFLU (const vec3_t angles, vec3_t forward, vec3_t left, vec3_t up)
499 {
500         double angle, sr, sp, sy, cr, cp, cy;
501
502         angle = angles[YAW] * (M_PI*2 / 360);
503         sy = sin(angle);
504         cy = cos(angle);
505         angle = angles[PITCH] * (M_PI*2 / 360);
506         sp = sin(angle);
507         cp = cos(angle);
508         if (forward)
509         {
510                 forward[0] = cp*cy;
511                 forward[1] = cp*sy;
512                 forward[2] = -sp;
513         }
514         if (left || up)
515         {
516                 if (angles[ROLL])
517                 {
518                         angle = angles[ROLL] * (M_PI*2 / 360);
519                         sr = sin(angle);
520                         cr = cos(angle);
521                         if (left)
522                         {
523                                 left[0] = sr*sp*cy+cr*-sy;
524                                 left[1] = sr*sp*sy+cr*cy;
525                                 left[2] = sr*cp;
526                         }
527                         if (up)
528                         {
529                                 up[0] = cr*sp*cy+-sr*-sy;
530                                 up[1] = cr*sp*sy+-sr*cy;
531                                 up[2] = cr*cp;
532                         }
533                 }
534                 else
535                 {
536                         if (left)
537                         {
538                                 left[0] = -sy;
539                                 left[1] = cy;
540                                 left[2] = 0;
541                         }
542                         if (up)
543                         {
544                                 up[0] = sp*cy;
545                                 up[1] = sp*sy;
546                                 up[2] = cp;
547                         }
548                 }
549         }
550 }
551
552 // LordHavoc: calculates pitch/yaw/roll angles from forward and up vectors
553 void AnglesFromVectors (vec3_t angles, const vec3_t forward, const vec3_t up, qboolean flippitch)
554 {
555         if (forward[0] == 0 && forward[1] == 0)
556         {
557                 if(forward[2] > 0)
558                 {
559                         angles[PITCH] = -M_PI * 0.5;
560                         angles[YAW] = up ? atan2(-up[1], -up[0]) : 0;
561                 }
562                 else
563                 {
564                         angles[PITCH] = M_PI * 0.5;
565                         angles[YAW] = up ? atan2(up[1], up[0]) : 0;
566                 }
567                 angles[ROLL] = 0;
568         }
569         else
570         {
571                 angles[YAW] = atan2(forward[1], forward[0]);
572                 angles[PITCH] = -atan2(forward[2], sqrt(forward[0]*forward[0] + forward[1]*forward[1]));
573                 // note: we know that angles[PITCH] is in ]-pi/2..pi/2[ due to atan2(anything, positive)
574                 if (up)
575                 {
576                         vec_t cp = cos(angles[PITCH]), sp = sin(angles[PITCH]);
577                         // note: we know cp > 0, due to the range angles[pitch] is in
578                         vec_t cy = cos(angles[YAW]), sy = sin(angles[YAW]);
579                         vec3_t tleft, tup;
580                         tleft[0] = -sy;
581                         tleft[1] = cy;
582                         tleft[2] = 0;
583                         tup[0] = sp*cy;
584                         tup[1] = sp*sy;
585                         tup[2] = cp;
586                         angles[ROLL] = -atan2(DotProduct(up, tleft), DotProduct(up, tup));
587                         // for up == '0 0 1', this is
588                         // angles[ROLL] = -atan2(0, cp);
589                         // which is 0
590                 }
591                 else
592                         angles[ROLL] = 0;
593
594                 // so no up vector is equivalent to '1 0 0'!
595         }
596
597         // now convert radians to degrees, and make all values positive
598         VectorScale(angles, 180.0 / M_PI, angles);
599         if (flippitch)
600                 angles[PITCH] *= -1;
601         if (angles[PITCH] < 0) angles[PITCH] += 360;
602         if (angles[YAW] < 0) angles[YAW] += 360;
603         if (angles[ROLL] < 0) angles[ROLL] += 360;
604
605 #if 0
606 {
607         // debugging code
608         vec3_t tforward, tleft, tup, nforward, nup;
609         VectorCopy(forward, nforward);
610         VectorNormalize(nforward);
611         if (up)
612         {
613                 VectorCopy(up, nup);
614                 VectorNormalize(nup);
615                 AngleVectors(angles, tforward, tleft, tup);
616                 if (VectorDistance(tforward, nforward) > 0.01 || VectorDistance(tup, nup) > 0.01)
617                 {
618                         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]);
619                         Con_Printf("^3But that is '%f %f %f', '%f %f %f'\n", tforward[0], tforward[1], tforward[2], tup[0], tup[1], tup[2]);
620                 }
621         }
622         else
623         {
624                 AngleVectors(angles, tforward, tleft, tup);
625                 if (VectorDistance(tforward, nforward) > 0.01)
626                 {
627                         Con_Printf("vectoangles('%f %f %f') = %f %f %f\n", nforward[0], nforward[1], nforward[2], angles[0], angles[1], angles[2]);
628                         Con_Printf("^3But that is '%f %f %f'\n", tforward[0], tforward[1], tforward[2]);
629                 }
630         }
631 }
632 #endif
633 }
634
635 #if 0
636 void AngleMatrix (const vec3_t angles, const vec3_t translate, vec_t matrix[][4])
637 {
638         double angle, sr, sp, sy, cr, cp, cy;
639
640         angle = angles[YAW] * (M_PI*2 / 360);
641         sy = sin(angle);
642         cy = cos(angle);
643         angle = angles[PITCH] * (M_PI*2 / 360);
644         sp = sin(angle);
645         cp = cos(angle);
646         angle = angles[ROLL] * (M_PI*2 / 360);
647         sr = sin(angle);
648         cr = cos(angle);
649         matrix[0][0] = cp*cy;
650         matrix[0][1] = sr*sp*cy+cr*-sy;
651         matrix[0][2] = cr*sp*cy+-sr*-sy;
652         matrix[0][3] = translate[0];
653         matrix[1][0] = cp*sy;
654         matrix[1][1] = sr*sp*sy+cr*cy;
655         matrix[1][2] = cr*sp*sy+-sr*cy;
656         matrix[1][3] = translate[1];
657         matrix[2][0] = -sp;
658         matrix[2][1] = sr*cp;
659         matrix[2][2] = cr*cp;
660         matrix[2][3] = translate[2];
661 }
662 #endif
663
664
665 // LordHavoc: renamed this to Length, and made the normal one a #define
666 float VectorNormalizeLength (vec3_t v)
667 {
668         float length, ilength;
669
670         length = v[0]*v[0] + v[1]*v[1] + v[2]*v[2];
671         length = sqrt (length);
672
673         if (length)
674         {
675                 ilength = 1/length;
676                 v[0] *= ilength;
677                 v[1] *= ilength;
678                 v[2] *= ilength;
679         }
680
681         return length;
682
683 }
684
685
686 /*
687 ================
688 R_ConcatRotations
689 ================
690 */
691 void R_ConcatRotations (const float in1[3*3], const float in2[3*3], float out[3*3])
692 {
693         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];
694         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];
695         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];
696         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];
697         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];
698         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];
699         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];
700         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];
701         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];
702 }
703
704
705 /*
706 ================
707 R_ConcatTransforms
708 ================
709 */
710 void R_ConcatTransforms (const float in1[3*4], const float in2[3*4], float out[3*4])
711 {
712         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];
713         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];
714         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];
715         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];
716         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];
717         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];
718         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];
719         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];
720         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];
721         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];
722         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];
723         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];
724 }
725
726 float RadiusFromBounds (const vec3_t mins, const vec3_t maxs)
727 {
728         vec3_t m1, m2;
729         VectorMultiply(mins, mins, m1);
730         VectorMultiply(maxs, maxs, m2);
731         return sqrt(max(m1[0], m2[0]) + max(m1[1], m2[1]) + max(m1[2], m2[2]));
732 }
733
734 float RadiusFromBoundsAndOrigin (const vec3_t mins, const vec3_t maxs, const vec3_t origin)
735 {
736         vec3_t m1, m2;
737         VectorSubtract(mins, origin, m1);VectorMultiply(m1, m1, m1);
738         VectorSubtract(maxs, origin, m2);VectorMultiply(m2, m2, m2);
739         return sqrt(max(m1[0], m2[0]) + max(m1[1], m2[1]) + max(m1[2], m2[2]));
740 }
741
742 void Mathlib_Init(void)
743 {
744         int a;
745
746         // LordHavoc: setup 1.0f / N table for quick recipricols of integers
747         ixtable[0] = 0;
748         for (a = 1;a < 4096;a++)
749                 ixtable[a] = 1.0f / a;
750 }
751
752 #include "matrixlib.h"
753
754 void Matrix4x4_Print(const matrix4x4_t *in)
755 {
756         Con_Printf("%f %f %f %f\n%f %f %f %f\n%f %f %f %f\n%f %f %f %f\n"
757         , in->m[0][0], in->m[0][1], in->m[0][2], in->m[0][3]
758         , in->m[1][0], in->m[1][1], in->m[1][2], in->m[1][3]
759         , in->m[2][0], in->m[2][1], in->m[2][2], in->m[2][3]
760         , in->m[3][0], in->m[3][1], in->m[3][2], in->m[3][3]);
761 }
762
763 int Math_atov(const char *s, vec3_t out)
764 {
765         int i;
766         VectorClear(out);
767         if (*s == '\'')
768                 s++;
769         for (i = 0;i < 3;i++)
770         {
771                 while (*s == ' ' || *s == '\t')
772                         s++;
773                 out[i] = atof (s);
774                 if (out[i] == 0 && *s != '-' && *s != '+' && (*s < '0' || *s > '9'))
775                         break; // not a number
776                 while (*s && *s != ' ' && *s !='\t' && *s != '\'')
777                         s++;
778                 if (*s == '\'')
779                         break;
780         }
781         return i;
782 }
783
784 void BoxFromPoints(vec3_t mins, vec3_t maxs, int numpoints, vec_t *point3f)
785 {
786         int i;
787         VectorCopy(point3f, mins);
788         VectorCopy(point3f, maxs);
789         for (i = 1, point3f += 3;i < numpoints;i++, point3f += 3)
790         {
791                 mins[0] = min(mins[0], point3f[0]);maxs[0] = max(maxs[0], point3f[0]);
792                 mins[1] = min(mins[1], point3f[1]);maxs[1] = max(maxs[1], point3f[1]);
793                 mins[2] = min(mins[2], point3f[2]);maxs[2] = max(maxs[2], point3f[2]);
794         }
795 }
796
797 // LordHavoc: this has to be done right or you get severe precision breakdown
798 int LoopingFrameNumberFromDouble(double t, int loopframes)
799 {
800         if (loopframes)
801                 return (int)(t - floor(t/loopframes)*loopframes);
802         else
803                 return (int)t;
804 }
805