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 {-0.525731f, 0.000000f, 0.850651f}, {-0.442863f, 0.238856f, 0.864188f},
34 {-0.295242f, 0.000000f, 0.955423f}, {-0.309017f, 0.500000f, 0.809017f},
35 {-0.162460f, 0.262866f, 0.951056f}, {0.000000f, 0.000000f, 1.000000f},
36 {0.000000f, 0.850651f, 0.525731f}, {-0.147621f, 0.716567f, 0.681718f},
37 {0.147621f, 0.716567f, 0.681718f}, {0.000000f, 0.525731f, 0.850651f},
38 {0.309017f, 0.500000f, 0.809017f}, {0.525731f, 0.000000f, 0.850651f},
39 {0.295242f, 0.000000f, 0.955423f}, {0.442863f, 0.238856f, 0.864188f},
40 {0.162460f, 0.262866f, 0.951056f}, {-0.681718f, 0.147621f, 0.716567f},
41 {-0.809017f, 0.309017f, 0.500000f}, {-0.587785f, 0.425325f, 0.688191f},
42 {-0.850651f, 0.525731f, 0.000000f}, {-0.864188f, 0.442863f, 0.238856f},
43 {-0.716567f, 0.681718f, 0.147621f}, {-0.688191f, 0.587785f, 0.425325f},
44 {-0.500000f, 0.809017f, 0.309017f}, {-0.238856f, 0.864188f, 0.442863f},
45 {-0.425325f, 0.688191f, 0.587785f}, {-0.716567f, 0.681718f, -0.147621f},
46 {-0.500000f, 0.809017f, -0.309017f}, {-0.525731f, 0.850651f, 0.000000f},
47 {0.000000f, 0.850651f, -0.525731f}, {-0.238856f, 0.864188f, -0.442863f},
48 {0.000000f, 0.955423f, -0.295242f}, {-0.262866f, 0.951056f, -0.162460f},
49 {0.000000f, 1.000000f, 0.000000f}, {0.000000f, 0.955423f, 0.295242f},
50 {-0.262866f, 0.951056f, 0.162460f}, {0.238856f, 0.864188f, 0.442863f},
51 {0.262866f, 0.951056f, 0.162460f}, {0.500000f, 0.809017f, 0.309017f},
52 {0.238856f, 0.864188f, -0.442863f}, {0.262866f, 0.951056f, -0.162460f},
53 {0.500000f, 0.809017f, -0.309017f}, {0.850651f, 0.525731f, 0.000000f},
54 {0.716567f, 0.681718f, 0.147621f}, {0.716567f, 0.681718f, -0.147621f},
55 {0.525731f, 0.850651f, 0.000000f}, {0.425325f, 0.688191f, 0.587785f},
56 {0.864188f, 0.442863f, 0.238856f}, {0.688191f, 0.587785f, 0.425325f},
57 {0.809017f, 0.309017f, 0.500000f}, {0.681718f, 0.147621f, 0.716567f},
58 {0.587785f, 0.425325f, 0.688191f}, {0.955423f, 0.295242f, 0.000000f},
59 {1.000000f, 0.000000f, 0.000000f}, {0.951056f, 0.162460f, 0.262866f},
60 {0.850651f, -0.525731f, 0.000000f}, {0.955423f, -0.295242f, 0.000000f},
61 {0.864188f, -0.442863f, 0.238856f}, {0.951056f, -0.162460f, 0.262866f},
62 {0.809017f, -0.309017f, 0.500000f}, {0.681718f, -0.147621f, 0.716567f},
63 {0.850651f, 0.000000f, 0.525731f}, {0.864188f, 0.442863f, -0.238856f},
64 {0.809017f, 0.309017f, -0.500000f}, {0.951056f, 0.162460f, -0.262866f},
65 {0.525731f, 0.000000f, -0.850651f}, {0.681718f, 0.147621f, -0.716567f},
66 {0.681718f, -0.147621f, -0.716567f}, {0.850651f, 0.000000f, -0.525731f},
67 {0.809017f, -0.309017f, -0.500000f}, {0.864188f, -0.442863f, -0.238856f},
68 {0.951056f, -0.162460f, -0.262866f}, {0.147621f, 0.716567f, -0.681718f},
69 {0.309017f, 0.500000f, -0.809017f}, {0.425325f, 0.688191f, -0.587785f},
70 {0.442863f, 0.238856f, -0.864188f}, {0.587785f, 0.425325f, -0.688191f},
71 {0.688191f, 0.587785f, -0.425325f}, {-0.147621f, 0.716567f, -0.681718f},
72 {-0.309017f, 0.500000f, -0.809017f}, {0.000000f, 0.525731f, -0.850651f},
73 {-0.525731f, 0.000000f, -0.850651f}, {-0.442863f, 0.238856f, -0.864188f},
74 {-0.295242f, 0.000000f, -0.955423f}, {-0.162460f, 0.262866f, -0.951056f},
75 {0.000000f, 0.000000f, -1.000000f}, {0.295242f, 0.000000f, -0.955423f},
76 {0.162460f, 0.262866f, -0.951056f}, {-0.442863f, -0.238856f, -0.864188f},
77 {-0.309017f, -0.500000f, -0.809017f}, {-0.162460f, -0.262866f, -0.951056f},
78 {0.000000f, -0.850651f, -0.525731f}, {-0.147621f, -0.716567f, -0.681718f},
79 {0.147621f, -0.716567f, -0.681718f}, {0.000000f, -0.525731f, -0.850651f},
80 {0.309017f, -0.500000f, -0.809017f}, {0.442863f, -0.238856f, -0.864188f},
81 {0.162460f, -0.262866f, -0.951056f}, {0.238856f, -0.864188f, -0.442863f},
82 {0.500000f, -0.809017f, -0.309017f}, {0.425325f, -0.688191f, -0.587785f},
83 {0.716567f, -0.681718f, -0.147621f}, {0.688191f, -0.587785f, -0.425325f},
84 {0.587785f, -0.425325f, -0.688191f}, {0.000000f, -0.955423f, -0.295242f},
85 {0.000000f, -1.000000f, 0.000000f}, {0.262866f, -0.951056f, -0.162460f},
86 {0.000000f, -0.850651f, 0.525731f}, {0.000000f, -0.955423f, 0.295242f},
87 {0.238856f, -0.864188f, 0.442863f}, {0.262866f, -0.951056f, 0.162460f},
88 {0.500000f, -0.809017f, 0.309017f}, {0.716567f, -0.681718f, 0.147621f},
89 {0.525731f, -0.850651f, 0.000000f}, {-0.238856f, -0.864188f, -0.442863f},
90 {-0.500000f, -0.809017f, -0.309017f}, {-0.262866f, -0.951056f, -0.162460f},
91 {-0.850651f, -0.525731f, 0.000000f}, {-0.716567f, -0.681718f, -0.147621f},
92 {-0.716567f, -0.681718f, 0.147621f}, {-0.525731f, -0.850651f, 0.000000f},
93 {-0.500000f, -0.809017f, 0.309017f}, {-0.238856f, -0.864188f, 0.442863f},
94 {-0.262866f, -0.951056f, 0.162460f}, {-0.864188f, -0.442863f, 0.238856f},
95 {-0.809017f, -0.309017f, 0.500000f}, {-0.688191f, -0.587785f, 0.425325f},
96 {-0.681718f, -0.147621f, 0.716567f}, {-0.442863f, -0.238856f, 0.864188f},
97 {-0.587785f, -0.425325f, 0.688191f}, {-0.309017f, -0.500000f, 0.809017f},
98 {-0.147621f, -0.716567f, 0.681718f}, {-0.425325f, -0.688191f, 0.587785f},
99 {-0.162460f, -0.262866f, 0.951056f}, {0.442863f, -0.238856f, 0.864188f},
100 {0.162460f, -0.262866f, 0.951056f}, {0.309017f, -0.500000f, 0.809017f},
101 {0.147621f, -0.716567f, 0.681718f}, {0.000000f, -0.525731f, 0.850651f},
102 {0.425325f, -0.688191f, 0.587785f}, {0.587785f, -0.425325f, 0.688191f},
103 {0.688191f, -0.587785f, 0.425325f}, {-0.955423f, 0.295242f, 0.000000f},
104 {-0.951056f, 0.162460f, 0.262866f}, {-1.000000f, 0.000000f, 0.000000f},
105 {-0.850651f, 0.000000f, 0.525731f}, {-0.955423f, -0.295242f, 0.000000f},
106 {-0.951056f, -0.162460f, 0.262866f}, {-0.864188f, 0.442863f, -0.238856f},
107 {-0.951056f, 0.162460f, -0.262866f}, {-0.809017f, 0.309017f, -0.500000f},
108 {-0.864188f, -0.442863f, -0.238856f}, {-0.951056f, -0.162460f, -0.262866f},
109 {-0.809017f, -0.309017f, -0.500000f}, {-0.681718f, 0.147621f, -0.716567f},
110 {-0.681718f, -0.147621f, -0.716567f}, {-0.850651f, 0.000000f, -0.525731f},
111 {-0.688191f, 0.587785f, -0.425325f}, {-0.587785f, 0.425325f, -0.688191f},
112 {-0.425325f, 0.688191f, -0.587785f}, {-0.425325f, -0.688191f, -0.587785f},
113 {-0.587785f, -0.425325f, -0.688191f}, {-0.688191f, -0.587785f, -0.425325f},
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, double maxShearAngle)
554 double angle, sr, sy, cr, cy;
555 double sxx, sxz, szx, szz;
556 double cosMaxShearAngle = cos(maxShearAngle * (M_PI*2 / 360));
557 double tanMaxShearAngle = tan(maxShearAngle * (M_PI*2 / 360));
559 angle = angles[YAW] * (M_PI*2 / 360);
562 angle = angles[PITCH] * (M_PI*2 / 360);
564 // We will calculate a shear matrix pitch = [[sxx sxz][szx szz]].
566 if (fabs(cos(angle)) > cosMaxShearAngle)
568 // Pure shear. Keep the original sign of the coefficients.
573 // Covering angle per screen coordinate:
574 // d/dt arctan((sxz + t*szz) / (sxx + t*szx)) @ t=0
575 // d_angle = det(S) / (sxx*sxx + szx*szx)
576 // = 1 / (1 + tan^2 angle)
581 // A mix of shear and rotation. Implementation-wise, we're
582 // looking at a capsule, and making the screen surface
583 // tangential to it... and if we get here, we're looking at the
584 // two half-spheres of the capsule (and the cylinder part is
586 double x, y, h, t, d, f;
587 h = tanMaxShearAngle;
590 t = h * fabs(y) + sqrt(1 - (h * x) * (h * x));
592 sxz = y * t - h * (y > 0 ? 1.0 : -1.0);
595 // BUT: keep the amount of a sphere we see in pitch direction
597 // Covering angle per screen coordinate:
598 // d_angle = det(S) / (sxx*sxx + szx*szx)
599 d = (sxx * szz - sxz * szx) / (sxx * sxx + szx * szx);
600 f = cosMaxShearAngle * cosMaxShearAngle / d;
615 angle = angles[ROLL] * (M_PI*2 / 360);
620 left[0] = sr*sxz*cy+cr*-sy;
621 left[1] = sr*sxz*sy+cr*cy;
626 up[0] = cr*sxz*cy+-sr*-sy;
627 up[1] = cr*sxz*sy+-sr*cy;
649 // LordHavoc: calculates pitch/yaw/roll angles from forward and up vectors
650 void AnglesFromVectors (vec3_t angles, const vec3_t forward, const vec3_t up, qboolean flippitch)
652 if (forward[0] == 0 && forward[1] == 0)
656 angles[PITCH] = -M_PI * 0.5;
657 angles[YAW] = up ? atan2(-up[1], -up[0]) : 0;
661 angles[PITCH] = M_PI * 0.5;
662 angles[YAW] = up ? atan2(up[1], up[0]) : 0;
668 angles[YAW] = atan2(forward[1], forward[0]);
669 angles[PITCH] = -atan2(forward[2], sqrt(forward[0]*forward[0] + forward[1]*forward[1]));
670 // note: we know that angles[PITCH] is in ]-pi/2..pi/2[ due to atan2(anything, positive)
673 vec_t cp = cos(angles[PITCH]), sp = sin(angles[PITCH]);
674 // note: we know cp > 0, due to the range angles[pitch] is in
675 vec_t cy = cos(angles[YAW]), sy = sin(angles[YAW]);
683 angles[ROLL] = -atan2(DotProduct(up, tleft), DotProduct(up, tup));
684 // for up == '0 0 1', this is
685 // angles[ROLL] = -atan2(0, cp);
691 // so no up vector is equivalent to '1 0 0'!
694 // now convert radians to degrees, and make all values positive
695 VectorScale(angles, 180.0 / M_PI, angles);
698 if (angles[PITCH] < 0) angles[PITCH] += 360;
699 if (angles[YAW] < 0) angles[YAW] += 360;
700 if (angles[ROLL] < 0) angles[ROLL] += 360;
705 vec3_t tforward, tleft, tup, nforward, nup;
706 VectorCopy(forward, nforward);
707 VectorNormalize(nforward);
711 VectorNormalize(nup);
712 AngleVectors(angles, tforward, tleft, tup);
713 if (VectorDistance(tforward, nforward) > 0.01 || VectorDistance(tup, nup) > 0.01)
715 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]);
716 Con_Printf("^3But that is '%f %f %f', '%f %f %f'\n", tforward[0], tforward[1], tforward[2], tup[0], tup[1], tup[2]);
721 AngleVectors(angles, tforward, tleft, tup);
722 if (VectorDistance(tforward, nforward) > 0.01)
724 Con_Printf("vectoangles('%f %f %f') = %f %f %f\n", nforward[0], nforward[1], nforward[2], angles[0], angles[1], angles[2]);
725 Con_Printf("^3But that is '%f %f %f'\n", tforward[0], tforward[1], tforward[2]);
733 void AngleMatrix (const vec3_t angles, const vec3_t translate, vec_t matrix[][4])
735 double angle, sr, sp, sy, cr, cp, cy;
737 angle = angles[YAW] * (M_PI*2 / 360);
740 angle = angles[PITCH] * (M_PI*2 / 360);
743 angle = angles[ROLL] * (M_PI*2 / 360);
746 matrix[0][0] = cp*cy;
747 matrix[0][1] = sr*sp*cy+cr*-sy;
748 matrix[0][2] = cr*sp*cy+-sr*-sy;
749 matrix[0][3] = translate[0];
750 matrix[1][0] = cp*sy;
751 matrix[1][1] = sr*sp*sy+cr*cy;
752 matrix[1][2] = cr*sp*sy+-sr*cy;
753 matrix[1][3] = translate[1];
755 matrix[2][1] = sr*cp;
756 matrix[2][2] = cr*cp;
757 matrix[2][3] = translate[2];
762 // LordHavoc: renamed this to Length, and made the normal one a #define
763 float VectorNormalizeLength (vec3_t v)
765 float length, ilength;
767 length = v[0]*v[0] + v[1]*v[1] + v[2]*v[2];
768 length = sqrt (length);
788 void R_ConcatRotations (const float in1[3*3], const float in2[3*3], float out[3*3])
790 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];
791 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];
792 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];
793 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];
794 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];
795 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];
796 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];
797 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];
798 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];
807 void R_ConcatTransforms (const float in1[3*4], const float in2[3*4], float out[3*4])
809 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];
810 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];
811 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];
812 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];
813 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];
814 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];
815 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];
816 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];
817 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];
818 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];
819 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];
820 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];
823 float RadiusFromBounds (const vec3_t mins, const vec3_t maxs)
826 VectorMultiply(mins, mins, m1);
827 VectorMultiply(maxs, maxs, m2);
828 return sqrt(max(m1[0], m2[0]) + max(m1[1], m2[1]) + max(m1[2], m2[2]));
831 float RadiusFromBoundsAndOrigin (const vec3_t mins, const vec3_t maxs, const vec3_t origin)
834 VectorSubtract(mins, origin, m1);VectorMultiply(m1, m1, m1);
835 VectorSubtract(maxs, origin, m2);VectorMultiply(m2, m2, m2);
836 return sqrt(max(m1[0], m2[0]) + max(m1[1], m2[1]) + max(m1[2], m2[2]));
839 void Mathlib_Init(void)
843 // LordHavoc: setup 1.0f / N table for quick recipricols of integers
845 for (a = 1;a < 4096;a++)
846 ixtable[a] = 1.0f / a;
849 #include "matrixlib.h"
851 void Matrix4x4_Print(const matrix4x4_t *in)
853 Con_Printf("%f %f %f %f\n%f %f %f %f\n%f %f %f %f\n%f %f %f %f\n"
854 , in->m[0][0], in->m[0][1], in->m[0][2], in->m[0][3]
855 , in->m[1][0], in->m[1][1], in->m[1][2], in->m[1][3]
856 , in->m[2][0], in->m[2][1], in->m[2][2], in->m[2][3]
857 , in->m[3][0], in->m[3][1], in->m[3][2], in->m[3][3]);
860 int Math_atov(const char *s, prvm_vec3_t out)
866 for (i = 0;i < 3;i++)
868 while (*s == ' ' || *s == '\t')
871 if (out[i] == 0 && *s != '-' && *s != '+' && (*s < '0' || *s > '9'))
872 break; // not a number
873 while (*s && *s != ' ' && *s !='\t' && *s != '\'')
881 void BoxFromPoints(vec3_t mins, vec3_t maxs, int numpoints, vec_t *point3f)
884 VectorCopy(point3f, mins);
885 VectorCopy(point3f, maxs);
886 for (i = 1, point3f += 3;i < numpoints;i++, point3f += 3)
888 mins[0] = min(mins[0], point3f[0]);maxs[0] = max(maxs[0], point3f[0]);
889 mins[1] = min(mins[1], point3f[1]);maxs[1] = max(maxs[1], point3f[1]);
890 mins[2] = min(mins[2], point3f[2]);maxs[2] = max(maxs[2], point3f[2]);
894 // LordHavoc: this has to be done right or you get severe precision breakdown
895 int LoopingFrameNumberFromDouble(double t, int loopframes)
898 return (int)(t - floor(t/loopframes)*loopframes);
903 static unsigned int mul_Lecuyer[4] = { 0x12e15e35, 0xb500f16e, 0x2e714eb2, 0xb37916a5 };
905 static void mul128(unsigned int a[], unsigned int b[], unsigned int dest[4])
907 unsigned long long t[4];
913 // this is complicated because C doesn't have a way to make use of the
914 // cpu status carry flag, so we do it all in reverse order from what
915 // would otherwise make sense, and have to make multiple passes...
916 t[3] += t[2] >> 32; t[2] &= 0xffffffff;
917 t[2] += t[1] >> 32; t[1] &= 0xffffffff;
918 t[1] += t[0] >> 32; t[0] &= 0xffffffff;
920 t[3] += t[2] >> 32; t[2] &= 0xffffffff;
921 t[2] += t[1] >> 32; t[1] &= 0xffffffff;
923 t[3] += t[2] >> 32; t[2] &= 0xffffffff;
925 dest[0] = t[0] & 0xffffffff;
926 dest[1] = t[1] & 0xffffffff;
927 dest[2] = t[2] & 0xffffffff;
928 dest[3] = t[3] & 0xffffffff;
931 void Math_RandomSeed_Reset(randomseed_t *r)
939 void Math_RandomSeed_FromInt(randomseed_t *r, unsigned int n)
941 // if the entire s[] is zero the algorithm would break completely, so make sure it isn't zero by putting a 1 here
948 unsigned long long Math_rand64(randomseed_t *r)
951 mul128(r->s, mul_Lecuyer, o);
956 return ((unsigned long long)o[3] << 32) + o[2];
959 float Math_randomf(randomseed_t *r)
961 unsigned long long n = Math_rand64(r);
962 return n * (0.25f / 0x80000000 / 0x80000000);
965 float Math_crandomf(randomseed_t *r)
967 // do this with a signed number and double the result, so we make use of all parts of the cow
968 long long n = (long long)Math_rand64(r);
969 return n * (0.5f / 0x80000000 / 0x80000000);
972 float Math_randomrangef(randomseed_t *r, float minf, float maxf)
974 return Math_randomf(r) * (maxf - minf) + minf;
977 int Math_randomrangei(randomseed_t *r, int mini, int maxi)
979 unsigned long long n = Math_rand64(r);
980 return (int)(((n >> 33) * (maxi - mini) + mini) >> 31);