2 Copyright (C) 1996-1997 Id Software, Inc.
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.
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.
13 See the GNU General Public License for more details.
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.
20 // mathlib.c -- math primitives
26 vec3_t vec3_origin = {0,0,0};
29 /*-----------------------------------------------------------------*/
31 float m_bytenormals[NUMVERTEXNORMALS][3] =
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},
117 unsigned char NormalToByte(const vec3_t n)
120 float bestdistance, distance;
123 bestdistance = DotProduct (n, m_bytenormals[0]);
124 for (i = 1;i < NUMVERTEXNORMALS;i++)
126 distance = DotProduct (n, m_bytenormals[i]);
127 if (distance > bestdistance)
129 bestdistance = distance;
136 // note: uses byte partly to force unsigned for the validity check
137 void ByteToNormal(unsigned char num, vec3_t n)
139 if (num < NUMVERTEXNORMALS)
140 VectorCopy(m_bytenormals[num], n);
142 VectorClear(n); // FIXME: complain?
145 // assumes "src" is normalized
146 void PerpendicularVector( vec3_t dst, const vec3_t src )
148 // LordHavoc: optimized to death and beyond
162 minelem = fabs(src[0]);
163 if (fabs(src[1]) < minelem)
166 minelem = fabs(src[1]);
168 if (fabs(src[2]) < minelem)
172 dst[0] -= src[pos] * src[0];
173 dst[1] -= src[pos] * src[1];
174 dst[2] -= src[pos] * src[2];
176 // normalize the result
177 VectorNormalize(dst);
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)
201 // NOTE: this is consistent to AngleVectors applied to AnglesFromVectors
202 if (forward[0] == 0 && forward[1] == 0)
206 VectorSet(right, 0, -1, 0);
207 VectorSet(up, -1, 0, 0);
211 VectorSet(right, 0, -1, 0);
212 VectorSet(up, 1, 0, 0);
217 right[0] = forward[1];
218 right[1] = -forward[0];
220 VectorNormalize(right);
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]);
229 void VectorVectorsDouble(const double *forward, double *right, double *up)
231 if (forward[0] == 0 && forward[1] == 0)
235 VectorSet(right, 0, -1, 0);
236 VectorSet(up, -1, 0, 0);
240 VectorSet(right, 0, -1, 0);
241 VectorSet(up, 1, 0, 0);
246 right[0] = forward[1];
247 right[1] = -forward[0];
249 VectorNormalize(right);
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]);
258 void RotatePointAroundVector( vec3_t dst, const vec3_t dir, const vec3_t point, float degrees )
264 angle = DEG2RAD(degrees);
268 VectorVectors(vf, vr, vu);
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];
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];
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];
289 /*-----------------------------------------------------------------*/
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)
294 unsigned int ceilvalue;
296 if (value > (1U << (sizeof(int) * 8 - 1)))
300 while (ceilvalue < value)
307 /*-----------------------------------------------------------------*/
310 void PlaneClassify(mplane_t *p)
312 // for optimized plane comparisons
313 if (p->normal[0] == 1)
315 else if (p->normal[1] == 1)
317 else if (p->normal[2] == 1)
321 // for BoxOnPlaneSide
323 if (p->normal[0] < 0) // 1
325 if (p->normal[1] < 0) // 2
327 if (p->normal[2] < 0) // 4
331 int BoxOnPlaneSide(const vec3_t emins, const vec3_t emaxs, const mplane_t *p)
334 return ((emaxs[p->type] >= p->dist) | ((emins[p->type] < p->dist) << 1));
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));
350 int BoxOnPlaneSide_Separate(const vec3_t emins, const vec3_t emaxs, const vec3_t normal, const vec_t dist)
352 switch((normal[0] < 0) | ((normal[1] < 0) << 1) | ((normal[2] < 0) << 2))
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));
367 void BoxPlaneCorners(const vec3_t emins, const vec3_t emaxs, const mplane_t *p, vec3_t outnear, vec3_t outfar)
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];
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;
390 void BoxPlaneCorners_Separate(const vec3_t emins, const vec3_t emaxs, const vec3_t normal, vec3_t outnear, vec3_t outfar)
392 switch((normal[0] < 0) | ((normal[1] < 0) << 1) | ((normal[2] < 0) << 2))
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;
406 void BoxPlaneCornerDistances(const vec3_t emins, const vec3_t emaxs, const mplane_t *p, vec_t *outneardist, vec_t *outfardist)
410 *outneardist = emins[p->type] - p->dist;
411 *outfardist = emaxs[p->type] - p->dist;
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;
428 void BoxPlaneCornerDistances_Separate(const vec3_t emins, const vec3_t emaxs, const vec3_t normal, vec_t *outneardist, vec_t *outfardist)
430 switch((normal[0] < 0) | ((normal[1] < 0) << 1) | ((normal[2] < 0) << 2))
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;
444 void AngleVectors (const vec3_t angles, vec3_t forward, vec3_t right, vec3_t up)
446 double angle, sr, sp, sy, cr, cp, cy;
448 angle = angles[YAW] * (M_PI*2 / 360);
451 angle = angles[PITCH] * (M_PI*2 / 360);
464 angle = angles[ROLL] * (M_PI*2 / 360);
469 right[0] = -1*(sr*sp*cy+cr*-sy);
470 right[1] = -1*(sr*sp*sy+cr*cy);
471 right[2] = -1*(sr*cp);
475 up[0] = (cr*sp*cy+-sr*-sy);
476 up[1] = (cr*sp*sy+-sr*cy);
498 void AngleVectorsFLU (const vec3_t angles, vec3_t forward, vec3_t left, vec3_t up)
500 double angle, sr, sp, sy, cr, cp, cy;
502 angle = angles[YAW] * (M_PI*2 / 360);
505 angle = angles[PITCH] * (M_PI*2 / 360);
518 angle = angles[ROLL] * (M_PI*2 / 360);
523 left[0] = sr*sp*cy+cr*-sy;
524 left[1] = sr*sp*sy+cr*cy;
529 up[0] = cr*sp*cy+-sr*-sy;
530 up[1] = cr*sp*sy+-sr*cy;
552 void AngleVectorsDuke3DFLU (const vec3_t angles, vec3_t forward, vec3_t left, vec3_t up)
554 double angle, sr, tp, sy, cr, sgnp, cy;
556 angle = angles[YAW] * (M_PI*2 / 360);
559 angle = ANGLEMOD(angles[PITCH]);
560 // Avoid hitting tan(M_PI/2 * (2n+1))...
561 // TODO shouldn't this be a cvar?
562 // |pitch| <= 90 degrees.
563 if (angle <= 90 && angle > 80)
565 if (angle >= 270 && angle < 280)
567 // |pitch| > 90 degrees.
568 if (angle > 90 && angle < 100)
570 if (angle < 270 && angle > 260)
572 // Flip the view when "turning over".
573 sgnp = (angle > 90) && (angle < 270) ? -1.0 : 1.0;
574 angle *= (M_PI*2 / 360);
578 forward[0] = cy*sgnp;
579 forward[1] = sy*sgnp;
586 angle = angles[ROLL] * (M_PI*2 / 360);
620 // LordHavoc: calculates pitch/yaw/roll angles from forward and up vectors
621 void AnglesFromVectors (vec3_t angles, const vec3_t forward, const vec3_t up, qboolean flippitch)
623 if (forward[0] == 0 && forward[1] == 0)
627 angles[PITCH] = -M_PI * 0.5;
628 angles[YAW] = up ? atan2(-up[1], -up[0]) : 0;
632 angles[PITCH] = M_PI * 0.5;
633 angles[YAW] = up ? atan2(up[1], up[0]) : 0;
639 angles[YAW] = atan2(forward[1], forward[0]);
640 angles[PITCH] = -atan2(forward[2], sqrt(forward[0]*forward[0] + forward[1]*forward[1]));
641 // note: we know that angles[PITCH] is in ]-pi/2..pi/2[ due to atan2(anything, positive)
644 vec_t cp = cos(angles[PITCH]), sp = sin(angles[PITCH]);
645 // note: we know cp > 0, due to the range angles[pitch] is in
646 vec_t cy = cos(angles[YAW]), sy = sin(angles[YAW]);
654 angles[ROLL] = -atan2(DotProduct(up, tleft), DotProduct(up, tup));
655 // for up == '0 0 1', this is
656 // angles[ROLL] = -atan2(0, cp);
662 // so no up vector is equivalent to '1 0 0'!
665 // now convert radians to degrees, and make all values positive
666 VectorScale(angles, 180.0 / M_PI, angles);
669 if (angles[PITCH] < 0) angles[PITCH] += 360;
670 if (angles[YAW] < 0) angles[YAW] += 360;
671 if (angles[ROLL] < 0) angles[ROLL] += 360;
676 vec3_t tforward, tleft, tup, nforward, nup;
677 VectorCopy(forward, nforward);
678 VectorNormalize(nforward);
682 VectorNormalize(nup);
683 AngleVectors(angles, tforward, tleft, tup);
684 if (VectorDistance(tforward, nforward) > 0.01 || VectorDistance(tup, nup) > 0.01)
686 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]);
687 Con_Printf("^3But that is '%f %f %f', '%f %f %f'\n", tforward[0], tforward[1], tforward[2], tup[0], tup[1], tup[2]);
692 AngleVectors(angles, tforward, tleft, tup);
693 if (VectorDistance(tforward, nforward) > 0.01)
695 Con_Printf("vectoangles('%f %f %f') = %f %f %f\n", nforward[0], nforward[1], nforward[2], angles[0], angles[1], angles[2]);
696 Con_Printf("^3But that is '%f %f %f'\n", tforward[0], tforward[1], tforward[2]);
704 void AngleMatrix (const vec3_t angles, const vec3_t translate, vec_t matrix[][4])
706 double angle, sr, sp, sy, cr, cp, cy;
708 angle = angles[YAW] * (M_PI*2 / 360);
711 angle = angles[PITCH] * (M_PI*2 / 360);
714 angle = angles[ROLL] * (M_PI*2 / 360);
717 matrix[0][0] = cp*cy;
718 matrix[0][1] = sr*sp*cy+cr*-sy;
719 matrix[0][2] = cr*sp*cy+-sr*-sy;
720 matrix[0][3] = translate[0];
721 matrix[1][0] = cp*sy;
722 matrix[1][1] = sr*sp*sy+cr*cy;
723 matrix[1][2] = cr*sp*sy+-sr*cy;
724 matrix[1][3] = translate[1];
726 matrix[2][1] = sr*cp;
727 matrix[2][2] = cr*cp;
728 matrix[2][3] = translate[2];
733 // LordHavoc: renamed this to Length, and made the normal one a #define
734 float VectorNormalizeLength (vec3_t v)
736 float length, ilength;
738 length = v[0]*v[0] + v[1]*v[1] + v[2]*v[2];
739 length = sqrt (length);
759 void R_ConcatRotations (const float in1[3*3], const float in2[3*3], float out[3*3])
761 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];
762 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];
763 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];
764 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];
765 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];
766 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];
767 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];
768 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];
769 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];
778 void R_ConcatTransforms (const float in1[3*4], const float in2[3*4], float out[3*4])
780 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];
781 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];
782 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];
783 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];
784 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];
785 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];
786 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];
787 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];
788 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];
789 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];
790 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];
791 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];
794 float RadiusFromBounds (const vec3_t mins, const vec3_t maxs)
797 VectorMultiply(mins, mins, m1);
798 VectorMultiply(maxs, maxs, m2);
799 return sqrt(max(m1[0], m2[0]) + max(m1[1], m2[1]) + max(m1[2], m2[2]));
802 float RadiusFromBoundsAndOrigin (const vec3_t mins, const vec3_t maxs, const vec3_t origin)
805 VectorSubtract(mins, origin, m1);VectorMultiply(m1, m1, m1);
806 VectorSubtract(maxs, origin, m2);VectorMultiply(m2, m2, m2);
807 return sqrt(max(m1[0], m2[0]) + max(m1[1], m2[1]) + max(m1[2], m2[2]));
810 void Mathlib_Init(void)
814 // LordHavoc: setup 1.0f / N table for quick recipricols of integers
816 for (a = 1;a < 4096;a++)
817 ixtable[a] = 1.0f / a;
820 #include "matrixlib.h"
822 void Matrix4x4_Print(const matrix4x4_t *in)
824 Con_Printf("%f %f %f %f\n%f %f %f %f\n%f %f %f %f\n%f %f %f %f\n"
825 , in->m[0][0], in->m[0][1], in->m[0][2], in->m[0][3]
826 , in->m[1][0], in->m[1][1], in->m[1][2], in->m[1][3]
827 , in->m[2][0], in->m[2][1], in->m[2][2], in->m[2][3]
828 , in->m[3][0], in->m[3][1], in->m[3][2], in->m[3][3]);
831 int Math_atov(const char *s, prvm_vec3_t out)
837 for (i = 0;i < 3;i++)
839 while (*s == ' ' || *s == '\t')
842 if (out[i] == 0 && *s != '-' && *s != '+' && (*s < '0' || *s > '9'))
843 break; // not a number
844 while (*s && *s != ' ' && *s !='\t' && *s != '\'')
852 void BoxFromPoints(vec3_t mins, vec3_t maxs, int numpoints, vec_t *point3f)
855 VectorCopy(point3f, mins);
856 VectorCopy(point3f, maxs);
857 for (i = 1, point3f += 3;i < numpoints;i++, point3f += 3)
859 mins[0] = min(mins[0], point3f[0]);maxs[0] = max(maxs[0], point3f[0]);
860 mins[1] = min(mins[1], point3f[1]);maxs[1] = max(maxs[1], point3f[1]);
861 mins[2] = min(mins[2], point3f[2]);maxs[2] = max(maxs[2], point3f[2]);
865 // LordHavoc: this has to be done right or you get severe precision breakdown
866 int LoopingFrameNumberFromDouble(double t, int loopframes)
869 return (int)(t - floor(t/loopframes)*loopframes);