/* Copyright (C) 1996-1997 Id Software, Inc. This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. */ // mathlib.c -- math primitives #include #include "quakedef.h" vec3_t vec3_origin = {0,0,0}; float ixtable[4096]; /*-----------------------------------------------------------------*/ float m_bytenormals[NUMVERTEXNORMALS][3] = { {-0.525731, 0.000000, 0.850651}, {-0.442863, 0.238856, 0.864188}, {-0.295242, 0.000000, 0.955423}, {-0.309017, 0.500000, 0.809017}, {-0.162460, 0.262866, 0.951056}, {0.000000, 0.000000, 1.000000}, {0.000000, 0.850651, 0.525731}, {-0.147621, 0.716567, 0.681718}, {0.147621, 0.716567, 0.681718}, {0.000000, 0.525731, 0.850651}, {0.309017, 0.500000, 0.809017}, {0.525731, 0.000000, 0.850651}, {0.295242, 0.000000, 0.955423}, {0.442863, 0.238856, 0.864188}, {0.162460, 0.262866, 0.951056}, {-0.681718, 0.147621, 0.716567}, {-0.809017, 0.309017, 0.500000}, {-0.587785, 0.425325, 0.688191}, {-0.850651, 0.525731, 0.000000}, {-0.864188, 0.442863, 0.238856}, {-0.716567, 0.681718, 0.147621}, {-0.688191, 0.587785, 0.425325}, {-0.500000, 0.809017, 0.309017}, {-0.238856, 0.864188, 0.442863}, {-0.425325, 0.688191, 0.587785}, {-0.716567, 0.681718, -0.147621}, {-0.500000, 0.809017, -0.309017}, {-0.525731, 0.850651, 0.000000}, {0.000000, 0.850651, -0.525731}, {-0.238856, 0.864188, -0.442863}, {0.000000, 0.955423, -0.295242}, {-0.262866, 0.951056, -0.162460}, {0.000000, 1.000000, 0.000000}, {0.000000, 0.955423, 0.295242}, {-0.262866, 0.951056, 0.162460}, {0.238856, 0.864188, 0.442863}, {0.262866, 0.951056, 0.162460}, {0.500000, 0.809017, 0.309017}, {0.238856, 0.864188, -0.442863}, {0.262866, 0.951056, -0.162460}, {0.500000, 0.809017, -0.309017}, {0.850651, 0.525731, 0.000000}, {0.716567, 0.681718, 0.147621}, {0.716567, 0.681718, -0.147621}, {0.525731, 0.850651, 0.000000}, {0.425325, 0.688191, 0.587785}, {0.864188, 0.442863, 0.238856}, {0.688191, 0.587785, 0.425325}, {0.809017, 0.309017, 0.500000}, {0.681718, 0.147621, 0.716567}, {0.587785, 0.425325, 0.688191}, {0.955423, 0.295242, 0.000000}, {1.000000, 0.000000, 0.000000}, {0.951056, 0.162460, 0.262866}, {0.850651, -0.525731, 0.000000}, {0.955423, -0.295242, 0.000000}, {0.864188, -0.442863, 0.238856}, {0.951056, -0.162460, 0.262866}, {0.809017, -0.309017, 0.500000}, {0.681718, -0.147621, 0.716567}, {0.850651, 0.000000, 0.525731}, {0.864188, 0.442863, -0.238856}, {0.809017, 0.309017, -0.500000}, {0.951056, 0.162460, -0.262866}, {0.525731, 0.000000, -0.850651}, {0.681718, 0.147621, -0.716567}, {0.681718, -0.147621, -0.716567}, {0.850651, 0.000000, -0.525731}, {0.809017, -0.309017, -0.500000}, {0.864188, -0.442863, -0.238856}, {0.951056, -0.162460, -0.262866}, {0.147621, 0.716567, -0.681718}, {0.309017, 0.500000, -0.809017}, {0.425325, 0.688191, -0.587785}, {0.442863, 0.238856, -0.864188}, {0.587785, 0.425325, -0.688191}, {0.688191, 0.587785, -0.425325}, {-0.147621, 0.716567, -0.681718}, {-0.309017, 0.500000, -0.809017}, {0.000000, 0.525731, -0.850651}, {-0.525731, 0.000000, -0.850651}, {-0.442863, 0.238856, -0.864188}, {-0.295242, 0.000000, -0.955423}, {-0.162460, 0.262866, -0.951056}, {0.000000, 0.000000, -1.000000}, {0.295242, 0.000000, -0.955423}, {0.162460, 0.262866, -0.951056}, {-0.442863, -0.238856, -0.864188}, {-0.309017, -0.500000, -0.809017}, {-0.162460, -0.262866, -0.951056}, {0.000000, -0.850651, -0.525731}, {-0.147621, -0.716567, -0.681718}, {0.147621, -0.716567, -0.681718}, {0.000000, -0.525731, -0.850651}, {0.309017, -0.500000, -0.809017}, {0.442863, -0.238856, -0.864188}, {0.162460, -0.262866, -0.951056}, {0.238856, -0.864188, -0.442863}, {0.500000, -0.809017, -0.309017}, {0.425325, -0.688191, -0.587785}, {0.716567, -0.681718, -0.147621}, {0.688191, -0.587785, -0.425325}, {0.587785, -0.425325, -0.688191}, {0.000000, -0.955423, -0.295242}, {0.000000, -1.000000, 0.000000}, {0.262866, -0.951056, -0.162460}, {0.000000, -0.850651, 0.525731}, {0.000000, -0.955423, 0.295242}, {0.238856, -0.864188, 0.442863}, {0.262866, -0.951056, 0.162460}, {0.500000, -0.809017, 0.309017}, {0.716567, -0.681718, 0.147621}, {0.525731, -0.850651, 0.000000}, {-0.238856, -0.864188, -0.442863}, {-0.500000, -0.809017, -0.309017}, {-0.262866, -0.951056, -0.162460}, {-0.850651, -0.525731, 0.000000}, {-0.716567, -0.681718, -0.147621}, {-0.716567, -0.681718, 0.147621}, {-0.525731, -0.850651, 0.000000}, {-0.500000, -0.809017, 0.309017}, {-0.238856, -0.864188, 0.442863}, {-0.262866, -0.951056, 0.162460}, {-0.864188, -0.442863, 0.238856}, {-0.809017, -0.309017, 0.500000}, {-0.688191, -0.587785, 0.425325}, {-0.681718, -0.147621, 0.716567}, {-0.442863, -0.238856, 0.864188}, {-0.587785, -0.425325, 0.688191}, {-0.309017, -0.500000, 0.809017}, {-0.147621, -0.716567, 0.681718}, {-0.425325, -0.688191, 0.587785}, {-0.162460, -0.262866, 0.951056}, {0.442863, -0.238856, 0.864188}, {0.162460, -0.262866, 0.951056}, {0.309017, -0.500000, 0.809017}, {0.147621, -0.716567, 0.681718}, {0.000000, -0.525731, 0.850651}, {0.425325, -0.688191, 0.587785}, {0.587785, -0.425325, 0.688191}, {0.688191, -0.587785, 0.425325}, {-0.955423, 0.295242, 0.000000}, {-0.951056, 0.162460, 0.262866}, {-1.000000, 0.000000, 0.000000}, {-0.850651, 0.000000, 0.525731}, {-0.955423, -0.295242, 0.000000}, {-0.951056, -0.162460, 0.262866}, {-0.864188, 0.442863, -0.238856}, {-0.951056, 0.162460, -0.262866}, {-0.809017, 0.309017, -0.500000}, {-0.864188, -0.442863, -0.238856}, {-0.951056, -0.162460, -0.262866}, {-0.809017, -0.309017, -0.500000}, {-0.681718, 0.147621, -0.716567}, {-0.681718, -0.147621, -0.716567}, {-0.850651, 0.000000, -0.525731}, {-0.688191, 0.587785, -0.425325}, {-0.587785, 0.425325, -0.688191}, {-0.425325, 0.688191, -0.587785}, {-0.425325, -0.688191, -0.587785}, {-0.587785, -0.425325, -0.688191}, {-0.688191, -0.587785, -0.425325}, }; #if 0 qbyte NormalToByte(const vec3_t n) { int i, best; float bestdistance, distance; best = 0; bestdistance = DotProduct (n, m_bytenormals[0]); for (i = 1;i < NUMVERTEXNORMALS;i++) { distance = DotProduct (n, m_bytenormals[i]); if (distance > bestdistance) { bestdistance = distance; best = i; } } return best; } // note: uses byte partly to force unsigned for the validity check void ByteToNormal(qbyte num, vec3_t n) { if (num < NUMVERTEXNORMALS) VectorCopy(m_bytenormals[num], n); else VectorClear(n); // FIXME: complain? } float Q_RSqrt(float number) { float y; if (number == 0.0f) return 0.0f; *((int *)&y) = 0x5f3759df - ((* (int *) &number) >> 1); return y * (1.5f - (number * 0.5f * y * y)); } // assumes "src" is normalized void PerpendicularVector( vec3_t dst, const vec3_t src ) { // LordHavoc: optimized to death and beyond int pos; float minelem; if (src[0]) { dst[0] = 0; if (src[1]) { dst[1] = 0; if (src[2]) { dst[2] = 0; pos = 0; minelem = fabs(src[0]); if (fabs(src[1]) < minelem) { pos = 1; minelem = fabs(src[1]); } if (fabs(src[2]) < minelem) pos = 2; dst[pos] = 1; dst[0] -= src[pos] * src[0]; dst[1] -= src[pos] * src[1]; dst[2] -= src[pos] * src[2]; // normalize the result VectorNormalize(dst); } else dst[2] = 1; } else { dst[1] = 1; dst[2] = 0; } } else { dst[0] = 1; dst[1] = 0; dst[2] = 0; } } #endif // LordHavoc: like AngleVectors, but taking a forward vector instead of angles, useful! void VectorVectors(const vec3_t forward, vec3_t right, vec3_t up) { float d; right[0] = forward[2]; right[1] = -forward[0]; right[2] = forward[1]; d = DotProduct(forward, right); VectorMA(right, -d, forward, right); VectorNormalizeFast(right); CrossProduct(right, forward, up); } void VectorVectorsDouble(const double *forward, double *right, double *up) { double d; right[0] = forward[2]; right[1] = -forward[0]; right[2] = forward[1]; d = DotProduct(forward, right); VectorMA(right, -d, forward, right); VectorNormalize(right); CrossProduct(right, forward, up); } void RotatePointAroundVector( vec3_t dst, const vec3_t dir, const vec3_t point, float degrees ) { float t0, t1; float angle, c, s; vec3_t vr, vu, vf; angle = DEG2RAD(degrees); c = cos(angle); s = sin(angle); VectorCopy(dir, vf); VectorVectors(vf, vr, vu); t0 = vr[0] * c + vu[0] * -s; t1 = vr[0] * s + vu[0] * c; dst[0] = (t0 * vr[0] + t1 * vu[0] + vf[0] * vf[0]) * point[0] + (t0 * vr[1] + t1 * vu[1] + vf[0] * vf[1]) * point[1] + (t0 * vr[2] + t1 * vu[2] + vf[0] * vf[2]) * point[2]; t0 = vr[1] * c + vu[1] * -s; t1 = vr[1] * s + vu[1] * c; dst[1] = (t0 * vr[0] + t1 * vu[0] + vf[1] * vf[0]) * point[0] + (t0 * vr[1] + t1 * vu[1] + vf[1] * vf[1]) * point[1] + (t0 * vr[2] + t1 * vu[2] + vf[1] * vf[2]) * point[2]; t0 = vr[2] * c + vu[2] * -s; t1 = vr[2] * s + vu[2] * c; dst[2] = (t0 * vr[0] + t1 * vu[0] + vf[2] * vf[0]) * point[0] + (t0 * vr[1] + t1 * vu[1] + vf[2] * vf[1]) * point[1] + (t0 * vr[2] + t1 * vu[2] + vf[2] * vf[2]) * point[2]; } /*-----------------------------------------------------------------*/ void PlaneClassify(mplane_t *p) { // for optimized plane comparisons if (p->normal[0] == 1) p->type = 0; else if (p->normal[1] == 1) p->type = 1; else if (p->normal[2] == 1) p->type = 2; else p->type = 3; // for BoxOnPlaneSide p->signbits = 0; if (p->normal[0] < 0) // 1 p->signbits |= 1; if (p->normal[1] < 0) // 2 p->signbits |= 2; if (p->normal[2] < 0) // 4 p->signbits |= 4; } int BoxOnPlaneSide (const vec3_t emins, const vec3_t emaxs, const mplane_t *p) { if (p->type < 3) return ((emaxs[p->type] >= p->dist) | ((emins[p->type] < p->dist) << 1)); switch(p->signbits) { default: 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)); 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)); 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)); 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)); 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)); 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)); 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)); 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)); } } void AngleVectors (const vec3_t angles, vec3_t forward, vec3_t right, vec3_t up) { double angle, sr, sp, sy, cr, cp, cy; angle = angles[YAW] * (M_PI*2 / 360); sy = sin(angle); cy = cos(angle); angle = angles[PITCH] * (M_PI*2 / 360); sp = sin(angle); cp = cos(angle); if (forward) { forward[0] = cp*cy; forward[1] = cp*sy; forward[2] = -sp; } if (right || up) { angle = angles[ROLL] * (M_PI*2 / 360); sr = sin(angle); cr = cos(angle); if (right) { right[0] = -1*(sr*sp*cy+cr*-sy); right[1] = -1*(sr*sp*sy+cr*cy); right[2] = -1*(sr*cp); } if (up) { up[0] = (cr*sp*cy+-sr*-sy); up[1] = (cr*sp*sy+-sr*cy); up[2] = cr*cp; } } } void AngleVectorsFLU (const vec3_t angles, vec3_t forward, vec3_t left, vec3_t up) { double angle, sr, sp, sy, cr, cp, cy; angle = angles[YAW] * (M_PI*2 / 360); sy = sin(angle); cy = cos(angle); angle = angles[PITCH] * (M_PI*2 / 360); sp = sin(angle); cp = cos(angle); if (forward) { forward[0] = cp*cy; forward[1] = cp*sy; forward[2] = -sp; } if (left || up) { angle = angles[ROLL] * (M_PI*2 / 360); sr = sin(angle); cr = cos(angle); if (left) { left[0] = sr*sp*cy+cr*-sy; left[1] = sr*sp*sy+cr*cy; left[2] = sr*cp; } if (up) { up[0] = cr*sp*cy+-sr*-sy; up[1] = cr*sp*sy+-sr*cy; up[2] = cr*cp; } } } #if 0 void AngleMatrix (const vec3_t angles, const vec3_t translate, vec_t matrix[][4]) { double angle, sr, sp, sy, cr, cp, cy; angle = angles[YAW] * (M_PI*2 / 360); sy = sin(angle); cy = cos(angle); angle = angles[PITCH] * (M_PI*2 / 360); sp = sin(angle); cp = cos(angle); angle = angles[ROLL] * (M_PI*2 / 360); sr = sin(angle); cr = cos(angle); matrix[0][0] = cp*cy; matrix[0][1] = sr*sp*cy+cr*-sy; matrix[0][2] = cr*sp*cy+-sr*-sy; matrix[0][3] = translate[0]; matrix[1][0] = cp*sy; matrix[1][1] = sr*sp*sy+cr*cy; matrix[1][2] = cr*sp*sy+-sr*cy; matrix[1][3] = translate[1]; matrix[2][0] = -sp; matrix[2][1] = sr*cp; matrix[2][2] = cr*cp; matrix[2][3] = translate[2]; } #endif // LordHavoc: renamed this to Length, and made the normal one a #define float VectorNormalizeLength (vec3_t v) { float length, ilength; length = v[0]*v[0] + v[1]*v[1] + v[2]*v[2]; length = sqrt (length); if (length) { ilength = 1/length; v[0] *= ilength; v[1] *= ilength; v[2] *= ilength; } return length; } /* ================ R_ConcatRotations ================ */ void R_ConcatRotations (const float in1[3*3], const float in2[3*3], float out[3*3]) { 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]; 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]; 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]; 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]; 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]; 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]; 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]; 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]; 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]; } /* ================ R_ConcatTransforms ================ */ void R_ConcatTransforms (const float in1[3*4], const float in2[3*4], float out[3*4]) { 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]; 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]; 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]; 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]; 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]; 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]; 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]; 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]; 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]; 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]; 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]; 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]; } float RadiusFromBounds (const vec3_t mins, const vec3_t maxs) { vec3_t m1, m2; VectorMultiply(mins, mins, m1); VectorMultiply(maxs, maxs, m2); return sqrt(max(m1[0], m2[0]) + max(m1[1], m2[1]) + max(m1[2], m2[2])); } float RadiusFromBoundsAndOrigin (const vec3_t mins, const vec3_t maxs, const vec3_t origin) { vec3_t m1, m2; VectorSubtract(mins, origin, m1);VectorMultiply(m1, m1, m1); VectorSubtract(maxs, origin, m2);VectorMultiply(m2, m2, m2); return sqrt(max(m1[0], m2[0]) + max(m1[1], m2[1]) + max(m1[2], m2[2])); } void Mathlib_Init(void) { int a; // LordHavoc: setup 1.0f / N table for quick recipricols of integers ixtable[0] = 0; for (a = 1;a < 4096;a++) ixtable[a] = 1.0f / a; } #include "matrixlib.h" void Matrix4x4_Print (const matrix4x4_t *in) { Con_Printf("%f %f %f %f\n%f %f %f %f\n%f %f %f %f\n%f %f %f %f\n" , in->m[0][0], in->m[0][1], in->m[0][2], in->m[0][3] , in->m[1][0], in->m[1][1], in->m[1][2], in->m[1][3] , in->m[2][0], in->m[2][1], in->m[2][2], in->m[2][3] , in->m[3][0], in->m[3][1], in->m[3][2], in->m[3][3]); } int Math_atov(const char *s, vec3_t out) { int i; VectorClear(out); if (*s == '\'') s++; for (i = 0;i < 3;i++) { while (*s == ' ' || *s == '\t') s++; out[i] = atof (s); if (out[i] == 0 && *s != '-' && *s != '+' && (*s < '0' || *s > '9')) break; // not a number while (*s && *s != ' ' && *s !='\t' && *s != '\'') s++; if (*s == '\'') break; } return i; }