/* =========================================================================== Copyright (C) 1999-2005 Id Software, Inc. Copyright (C) 2002-2021 Q3Rally Team (Per Thormann - q3rally@gmail.com) This file is part of q3rally source code. q3rally source code 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. q3rally source code 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 q3rally; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =========================================================================== */ // // q_math.c -- stateless support routines that are included in each code module // Some of the vector functions are static inline in q_shared.h. q3asm // doesn't understand static functions though, so we only want them in // one file. That's what this is about. #ifdef Q3_VM #define __Q3_VM_MATH #endif #include "q_shared.h" vec3_t vec3_origin = {0,0,0}; vec3_t axisDefault[3] = { { 1, 0, 0 }, { 0, 1, 0 }, { 0, 0, 1 } }; vec4_t colorBlack = {0, 0, 0, 1}; vec4_t colorRed = {1, 0, 0, 1}; vec4_t colorGreen = {0, 1, 0, 1}; vec4_t colorBlue = {0, 0, 1, 1}; vec4_t colorYellow = {1, 1, 0, 1}; vec4_t colorMagenta= {1, 0, 1, 1}; vec4_t colorCyan = {0, 1, 1, 1}; vec4_t colorWhite = {1, 1, 1, 1}; vec4_t colorLtGrey = {0.75, 0.75, 0.75, 1}; vec4_t colorMdGrey = {0.5, 0.5, 0.5, 1}; vec4_t colorDkGrey = {0.25, 0.25, 0.25, 1}; vec4_t g_color_table[8] = { {0.0, 0.0, 0.0, 1.0}, {1.0, 0.0, 0.0, 1.0}, {0.0, 1.0, 0.0, 1.0}, {1.0, 1.0, 0.0, 1.0}, {0.0, 0.0, 1.0, 1.0}, {0.0, 1.0, 1.0, 1.0}, {1.0, 0.0, 1.0, 1.0}, {1.0, 1.0, 1.0, 1.0}, }; vec3_t bytedirs[NUMVERTEXNORMALS] = { {-0.525731f, 0.000000f, 0.850651f}, {-0.442863f, 0.238856f, 0.864188f}, {-0.295242f, 0.000000f, 0.955423f}, {-0.309017f, 0.500000f, 0.809017f}, {-0.162460f, 0.262866f, 0.951056f}, {0.000000f, 0.000000f, 1.000000f}, {0.000000f, 0.850651f, 0.525731f}, {-0.147621f, 0.716567f, 0.681718f}, {0.147621f, 0.716567f, 0.681718f}, {0.000000f, 0.525731f, 0.850651f}, {0.309017f, 0.500000f, 0.809017f}, {0.525731f, 0.000000f, 0.850651f}, {0.295242f, 0.000000f, 0.955423f}, {0.442863f, 0.238856f, 0.864188f}, {0.162460f, 0.262866f, 0.951056f}, {-0.681718f, 0.147621f, 0.716567f}, {-0.809017f, 0.309017f, 0.500000f},{-0.587785f, 0.425325f, 0.688191f}, {-0.850651f, 0.525731f, 0.000000f},{-0.864188f, 0.442863f, 0.238856f}, {-0.716567f, 0.681718f, 0.147621f},{-0.688191f, 0.587785f, 0.425325f}, {-0.500000f, 0.809017f, 0.309017f}, {-0.238856f, 0.864188f, 0.442863f}, {-0.425325f, 0.688191f, 0.587785f}, {-0.716567f, 0.681718f, -0.147621f}, {-0.500000f, 0.809017f, -0.309017f}, {-0.525731f, 0.850651f, 0.000000f}, {0.000000f, 0.850651f, -0.525731f}, {-0.238856f, 0.864188f, -0.442863f}, {0.000000f, 0.955423f, -0.295242f}, {-0.262866f, 0.951056f, -0.162460f}, {0.000000f, 1.000000f, 0.000000f}, {0.000000f, 0.955423f, 0.295242f}, {-0.262866f, 0.951056f, 0.162460f}, {0.238856f, 0.864188f, 0.442863f}, {0.262866f, 0.951056f, 0.162460f}, {0.500000f, 0.809017f, 0.309017f}, {0.238856f, 0.864188f, -0.442863f},{0.262866f, 0.951056f, -0.162460f}, {0.500000f, 0.809017f, -0.309017f},{0.850651f, 0.525731f, 0.000000f}, {0.716567f, 0.681718f, 0.147621f}, {0.716567f, 0.681718f, -0.147621f}, {0.525731f, 0.850651f, 0.000000f}, {0.425325f, 0.688191f, 0.587785f}, {0.864188f, 0.442863f, 0.238856f}, {0.688191f, 0.587785f, 0.425325f}, {0.809017f, 0.309017f, 0.500000f}, {0.681718f, 0.147621f, 0.716567f}, {0.587785f, 0.425325f, 0.688191f}, {0.955423f, 0.295242f, 0.000000f}, {1.000000f, 0.000000f, 0.000000f}, {0.951056f, 0.162460f, 0.262866f}, {0.850651f, -0.525731f, 0.000000f},{0.955423f, -0.295242f, 0.000000f}, {0.864188f, -0.442863f, 0.238856f}, {0.951056f, -0.162460f, 0.262866f}, {0.809017f, -0.309017f, 0.500000f}, {0.681718f, -0.147621f, 0.716567f}, {0.850651f, 0.000000f, 0.525731f}, {0.864188f, 0.442863f, -0.238856f}, {0.809017f, 0.309017f, -0.500000f}, {0.951056f, 0.162460f, -0.262866f}, {0.525731f, 0.000000f, -0.850651f}, {0.681718f, 0.147621f, -0.716567f}, {0.681718f, -0.147621f, -0.716567f},{0.850651f, 0.000000f, -0.525731f}, {0.809017f, -0.309017f, -0.500000f}, {0.864188f, -0.442863f, -0.238856f}, {0.951056f, -0.162460f, -0.262866f}, {0.147621f, 0.716567f, -0.681718f}, {0.309017f, 0.500000f, -0.809017f}, {0.425325f, 0.688191f, -0.587785f}, {0.442863f, 0.238856f, -0.864188f}, {0.587785f, 0.425325f, -0.688191f}, {0.688191f, 0.587785f, -0.425325f}, {-0.147621f, 0.716567f, -0.681718f}, {-0.309017f, 0.500000f, -0.809017f}, {0.000000f, 0.525731f, -0.850651f}, {-0.525731f, 0.000000f, -0.850651f}, {-0.442863f, 0.238856f, -0.864188f}, {-0.295242f, 0.000000f, -0.955423f}, {-0.162460f, 0.262866f, -0.951056f}, {0.000000f, 0.000000f, -1.000000f}, {0.295242f, 0.000000f, -0.955423f}, {0.162460f, 0.262866f, -0.951056f}, {-0.442863f, -0.238856f, -0.864188f}, {-0.309017f, -0.500000f, -0.809017f}, {-0.162460f, -0.262866f, -0.951056f}, {0.000000f, -0.850651f, -0.525731f}, {-0.147621f, -0.716567f, -0.681718f}, {0.147621f, -0.716567f, -0.681718f}, {0.000000f, -0.525731f, -0.850651f}, {0.309017f, -0.500000f, -0.809017f}, {0.442863f, -0.238856f, -0.864188f}, {0.162460f, -0.262866f, -0.951056f}, {0.238856f, -0.864188f, -0.442863f}, {0.500000f, -0.809017f, -0.309017f}, {0.425325f, -0.688191f, -0.587785f}, {0.716567f, -0.681718f, -0.147621f}, {0.688191f, -0.587785f, -0.425325f}, {0.587785f, -0.425325f, -0.688191f}, {0.000000f, -0.955423f, -0.295242f}, {0.000000f, -1.000000f, 0.000000f}, {0.262866f, -0.951056f, -0.162460f}, {0.000000f, -0.850651f, 0.525731f}, {0.000000f, -0.955423f, 0.295242f}, {0.238856f, -0.864188f, 0.442863f}, {0.262866f, -0.951056f, 0.162460f}, {0.500000f, -0.809017f, 0.309017f}, {0.716567f, -0.681718f, 0.147621f}, {0.525731f, -0.850651f, 0.000000f}, {-0.238856f, -0.864188f, -0.442863f}, {-0.500000f, -0.809017f, -0.309017f}, {-0.262866f, -0.951056f, -0.162460f}, {-0.850651f, -0.525731f, 0.000000f}, {-0.716567f, -0.681718f, -0.147621f}, {-0.716567f, -0.681718f, 0.147621f}, {-0.525731f, -0.850651f, 0.000000f}, {-0.500000f, -0.809017f, 0.309017f}, {-0.238856f, -0.864188f, 0.442863f}, {-0.262866f, -0.951056f, 0.162460f}, {-0.864188f, -0.442863f, 0.238856f}, {-0.809017f, -0.309017f, 0.500000f}, {-0.688191f, -0.587785f, 0.425325f}, {-0.681718f, -0.147621f, 0.716567f}, {-0.442863f, -0.238856f, 0.864188f}, {-0.587785f, -0.425325f, 0.688191f}, {-0.309017f, -0.500000f, 0.809017f}, {-0.147621f, -0.716567f, 0.681718f}, {-0.425325f, -0.688191f, 0.587785f}, {-0.162460f, -0.262866f, 0.951056f}, {0.442863f, -0.238856f, 0.864188f}, {0.162460f, -0.262866f, 0.951056f}, {0.309017f, -0.500000f, 0.809017f}, {0.147621f, -0.716567f, 0.681718f}, {0.000000f, -0.525731f, 0.850651f}, {0.425325f, -0.688191f, 0.587785f}, {0.587785f, -0.425325f, 0.688191f}, {0.688191f, -0.587785f, 0.425325f}, {-0.955423f, 0.295242f, 0.000000f}, {-0.951056f, 0.162460f, 0.262866f}, {-1.000000f, 0.000000f, 0.000000f}, {-0.850651f, 0.000000f, 0.525731f}, {-0.955423f, -0.295242f, 0.000000f}, {-0.951056f, -0.162460f, 0.262866f}, {-0.864188f, 0.442863f, -0.238856f}, {-0.951056f, 0.162460f, -0.262866f}, {-0.809017f, 0.309017f, -0.500000f}, {-0.864188f, -0.442863f, -0.238856f}, {-0.951056f, -0.162460f, -0.262866f}, {-0.809017f, -0.309017f, -0.500000f}, {-0.681718f, 0.147621f, -0.716567f}, {-0.681718f, -0.147621f, -0.716567f}, {-0.850651f, 0.000000f, -0.525731f}, {-0.688191f, 0.587785f, -0.425325f}, {-0.587785f, 0.425325f, -0.688191f}, {-0.425325f, 0.688191f, -0.587785f}, {-0.425325f, -0.688191f, -0.587785f}, {-0.587785f, -0.425325f, -0.688191f}, {-0.688191f, -0.587785f, -0.425325f} }; //============================================================== int Q_rand( int *seed ) { *seed = (69069U * *seed + 1U); return *seed; } float Q_random( int *seed ) { return ( Q_rand( seed ) & 0xffff ) / (float)0x10000; } float Q_crandom( int *seed ) { return 2.0 * ( Q_random( seed ) - 0.5 ); } //======================================================= signed char ClampChar( int i ) { if ( i < -128 ) { return -128; } if ( i > 127 ) { return 127; } return i; } signed short ClampShort( int i ) { if ( i < -32768 ) { return -32768; } if ( i > 0x7fff ) { return 0x7fff; } return i; } // this isn't a real cheap function to call! int DirToByte( vec3_t dir ) { int i, best; float d, bestd; if ( !dir ) { return 0; } bestd = 0; best = 0; for (i=0 ; i bestd) { bestd = d; best = i; } } return best; } void ByteToDir( int b, vec3_t dir ) { if ( b < 0 || b >= NUMVERTEXNORMALS ) { VectorCopy( vec3_origin, dir ); return; } VectorCopy (bytedirs[b], dir); } unsigned ColorBytes3 (float r, float g, float b) { unsigned i; ( (byte *)&i )[0] = r * 255; ( (byte *)&i )[1] = g * 255; ( (byte *)&i )[2] = b * 255; return i; } unsigned ColorBytes4 (float r, float g, float b, float a) { unsigned i; ( (byte *)&i )[0] = r * 255; ( (byte *)&i )[1] = g * 255; ( (byte *)&i )[2] = b * 255; ( (byte *)&i )[3] = a * 255; return i; } float NormalizeColor( const vec3_t in, vec3_t out ) { float max; max = in[0]; if ( in[1] > max ) { max = in[1]; } if ( in[2] > max ) { max = in[2]; } if ( !max ) { VectorClear( out ); } else { out[0] = in[0] / max; out[1] = in[1] / max; out[2] = in[2] / max; } return max; } /* ===================== PlaneFromPoints Returns false if the triangle is degenrate. The normal will point out of the clock for clockwise ordered points ===================== */ qboolean PlaneFromPoints( vec4_t plane, const vec3_t a, const vec3_t b, const vec3_t c ) { vec3_t d1, d2; VectorSubtract( b, a, d1 ); VectorSubtract( c, a, d2 ); CrossProduct( d2, d1, plane ); if ( VectorNormalize( plane ) == 0 ) { return qfalse; } plane[3] = DotProduct( a, plane ); return qtrue; } /* =============== RotatePointAroundVector This is not implemented very well... =============== */ void RotatePointAroundVector( vec3_t dst, const vec3_t dir, const vec3_t point, float degrees ) { float m[3][3]; float im[3][3]; float zrot[3][3]; float tmpmat[3][3]; float rot[3][3]; int i; vec3_t vr, vup, vf; float rad; vf[0] = dir[0]; vf[1] = dir[1]; vf[2] = dir[2]; PerpendicularVector( vr, dir ); CrossProduct( vr, vf, vup ); m[0][0] = vr[0]; m[1][0] = vr[1]; m[2][0] = vr[2]; m[0][1] = vup[0]; m[1][1] = vup[1]; m[2][1] = vup[2]; m[0][2] = vf[0]; m[1][2] = vf[1]; m[2][2] = vf[2]; memcpy( im, m, sizeof( im ) ); im[0][1] = m[1][0]; im[0][2] = m[2][0]; im[1][0] = m[0][1]; im[1][2] = m[2][1]; im[2][0] = m[0][2]; im[2][1] = m[1][2]; memset( zrot, 0, sizeof( zrot ) ); zrot[0][0] = zrot[1][1] = zrot[2][2] = 1.0F; rad = DEG2RAD( degrees ); zrot[0][0] = cos( rad ); zrot[0][1] = sin( rad ); zrot[1][0] = -sin( rad ); zrot[1][1] = cos( rad ); MatrixMultiply( m, zrot, tmpmat ); MatrixMultiply( tmpmat, im, rot ); for ( i = 0; i < 3; i++ ) { dst[i] = rot[i][0] * point[0] + rot[i][1] * point[1] + rot[i][2] * point[2]; } } /* =============== RotateAroundDirection =============== */ void RotateAroundDirection( vec3_t axis[3], float yaw ) { // create an arbitrary axis[1] PerpendicularVector( axis[1], axis[0] ); // rotate it around axis[0] by yaw if ( yaw ) { vec3_t temp; VectorCopy( axis[1], temp ); RotatePointAroundVector( axis[1], axis[0], temp, yaw ); } // cross to get axis[2] CrossProduct( axis[0], axis[1], axis[2] ); } void vectoangles( const vec3_t value1, vec3_t angles ) { float forward; float yaw, pitch; if ( value1[1] == 0 && value1[0] == 0 ) { yaw = 0; if ( value1[2] > 0 ) { pitch = 90; } else { pitch = 270; } } else { if ( value1[0] ) { // STONELANCE // yaw = ( atan2 ( value1[1], value1[0] ) * 180 / M_PI ); yaw = ( atan2 ( value1[1], value1[0] ) * M_180_PI ); // END } else if ( value1[1] > 0 ) { yaw = 90; } else { yaw = 270; } if ( yaw < 0 ) { yaw += 360; } forward = sqrt ( value1[0]*value1[0] + value1[1]*value1[1] ); // STONELANCE // pitch = ( atan2(value1[2], forward) * 180 / M_PI ); pitch = ( atan2(value1[2], forward) * M_180_PI ); // END if ( pitch < 0 ) { pitch += 360; } } angles[PITCH] = -pitch; angles[YAW] = yaw; angles[ROLL] = 0; } /* ================= AnglesToAxis ================= */ void AnglesToAxis( const vec3_t angles, vec3_t axis[3] ) { vec3_t right; // angle vectors returns "right" instead of "y axis" AngleVectors( angles, axis[0], right, axis[2] ); VectorSubtract( vec3_origin, right, axis[1] ); } void AxisClear( vec3_t axis[3] ) { axis[0][0] = 1; axis[0][1] = 0; axis[0][2] = 0; axis[1][0] = 0; axis[1][1] = 1; axis[1][2] = 0; axis[2][0] = 0; axis[2][1] = 0; axis[2][2] = 1; } void AxisCopy( vec3_t in[3], vec3_t out[3] ) { VectorCopy( in[0], out[0] ); VectorCopy( in[1], out[1] ); VectorCopy( in[2], out[2] ); } void ProjectPointOnPlane( vec3_t dst, const vec3_t p, const vec3_t normal ) { float d; vec3_t n; float inv_denom; inv_denom = DotProduct( normal, normal ); #ifndef Q3_VM assert( Q_fabs(inv_denom) != 0.0f ); // zero vectors get here #endif inv_denom = 1.0f / inv_denom; d = DotProduct( normal, p ) * inv_denom; n[0] = normal[0] * inv_denom; n[1] = normal[1] * inv_denom; n[2] = normal[2] * inv_denom; dst[0] = p[0] - d * n[0]; dst[1] = p[1] - d * n[1]; dst[2] = p[2] - d * n[2]; } /* ================ MakeNormalVectors Given a normalized forward vector, create two other perpendicular vectors ================ */ void MakeNormalVectors( const vec3_t forward, vec3_t right, vec3_t up) { float d; // this rotate and negate guarantees a vector // not colinear with the original right[1] = -forward[0]; right[2] = forward[1]; right[0] = forward[2]; d = DotProduct (right, forward); VectorMA (right, -d, forward, right); VectorNormalize (right); CrossProduct (right, forward, up); } void VectorRotate( vec3_t in, vec3_t matrix[3], vec3_t out ) { out[0] = DotProduct( in, matrix[0] ); out[1] = DotProduct( in, matrix[1] ); out[2] = DotProduct( in, matrix[2] ); } //============================================================================ #if !idppc /* ** float q_rsqrt( float number ) */ float Q_rsqrt( float number ) { floatint_t t; float x2, y; const float threehalfs = 1.5F; x2 = number * 0.5F; t.f = number; t.i = 0x5f3759df - ( t.i >> 1 ); // what the fuck? y = t.f; y = y * ( threehalfs - ( x2 * y * y ) ); // 1st iteration // y = y * ( threehalfs - ( x2 * y * y ) ); // 2nd iteration, this can be removed return y; } float Q_fabs( float f ) { floatint_t fi; fi.f = f; fi.i &= 0x7FFFFFFF; return fi.f; } #endif //============================================================ /* =============== LerpAngle =============== */ float LerpAngle (float from, float to, float frac) { float a; if ( to - from > 180 ) { to -= 360; } if ( to - from < -180 ) { to += 360; } a = from + frac * (to - from); return a; } /* ================= AngleSubtract Always returns a value from -180 to 180 ================= */ float AngleSubtract( float a1, float a2 ) { float a; a = a1 - a2; while ( a > 180 ) { a -= 360; } while ( a < -180 ) { a += 360; } return a; } void AnglesSubtract( vec3_t v1, vec3_t v2, vec3_t v3 ) { v3[0] = AngleSubtract( v1[0], v2[0] ); v3[1] = AngleSubtract( v1[1], v2[1] ); v3[2] = AngleSubtract( v1[2], v2[2] ); } float AngleMod(float a) { a = (360.0/65536) * ((int)(a*(65536/360.0)) & 65535); return a; } /* ================= AngleNormalize360 returns angle normalized to the range [0 <= angle < 360] ================= */ float AngleNormalize360 ( float angle ) { return (360.0 / 65536) * ((int)(angle * (65536 / 360.0)) & 65535); } /* ================= AngleNormalize180 returns angle normalized to the range [-180 < angle <= 180] ================= */ float AngleNormalize180 ( float angle ) { angle = AngleNormalize360( angle ); if ( angle > 180.0 ) { angle -= 360.0; } return angle; } /* ================= AngleDelta returns the normalized delta from angle1 to angle2 ================= */ float AngleDelta ( float angle1, float angle2 ) { return AngleNormalize180( angle1 - angle2 ); } //============================================================ /* ================= SetPlaneSignbits ================= */ void SetPlaneSignbits (cplane_t *out) { int bits, j; // for fast box on planeside test bits = 0; for (j=0 ; j<3 ; j++) { if (out->normal[j] < 0) { bits |= 1<signbits = bits; } /* ================== BoxOnPlaneSide Returns 1, 2, or 1 + 2 ================== */ int BoxOnPlaneSide(vec3_t emins, vec3_t emaxs, struct cplane_s *p) { float dist[2]; int sides, b, i; // fast axial cases if (p->type < 3) { if (p->dist <= emins[p->type]) return 1; if (p->dist >= emaxs[p->type]) return 2; return 3; } // general case dist[0] = dist[1] = 0; if (p->signbits < 8) // >= 8: default case is original code (dist[0]=dist[1]=0) { for (i=0 ; i<3 ; i++) { b = (p->signbits >> i) & 1; dist[ b] += p->normal[i]*emaxs[i]; dist[!b] += p->normal[i]*emins[i]; } } sides = 0; if (dist[0] >= p->dist) sides = 1; if (dist[1] < p->dist) sides |= 2; return sides; } /* ================= RadiusFromBounds ================= */ float RadiusFromBounds( const vec3_t mins, const vec3_t maxs ) { int i; vec3_t corner; float a, b; for (i=0 ; i<3 ; i++) { a = fabs( mins[i] ); b = fabs( maxs[i] ); corner[i] = a > b ? a : b; } return VectorLength (corner); } void ClearBounds( vec3_t mins, vec3_t maxs ) { mins[0] = mins[1] = mins[2] = 99999; maxs[0] = maxs[1] = maxs[2] = -99999; } void AddPointToBounds( const vec3_t v, vec3_t mins, vec3_t maxs ) { if ( v[0] < mins[0] ) { mins[0] = v[0]; } if ( v[0] > maxs[0]) { maxs[0] = v[0]; } if ( v[1] < mins[1] ) { mins[1] = v[1]; } if ( v[1] > maxs[1]) { maxs[1] = v[1]; } if ( v[2] < mins[2] ) { mins[2] = v[2]; } if ( v[2] > maxs[2]) { maxs[2] = v[2]; } } qboolean BoundsIntersect(const vec3_t mins, const vec3_t maxs, const vec3_t mins2, const vec3_t maxs2) { if ( maxs[0] < mins2[0] || maxs[1] < mins2[1] || maxs[2] < mins2[2] || mins[0] > maxs2[0] || mins[1] > maxs2[1] || mins[2] > maxs2[2]) { return qfalse; } return qtrue; } qboolean BoundsIntersectSphere(const vec3_t mins, const vec3_t maxs, const vec3_t origin, vec_t radius) { if ( origin[0] - radius > maxs[0] || origin[0] + radius < mins[0] || origin[1] - radius > maxs[1] || origin[1] + radius < mins[1] || origin[2] - radius > maxs[2] || origin[2] + radius < mins[2]) { return qfalse; } return qtrue; } qboolean BoundsIntersectPoint(const vec3_t mins, const vec3_t maxs, const vec3_t origin) { if ( origin[0] > maxs[0] || origin[0] < mins[0] || origin[1] > maxs[1] || origin[1] < mins[1] || origin[2] > maxs[2] || origin[2] < mins[2]) { return qfalse; } return qtrue; } vec_t VectorNormalize( vec3_t v ) { // NOTE: TTimo - Apple G4 altivec source uses double? float length, ilength; length = v[0]*v[0] + v[1]*v[1] + v[2]*v[2]; if ( length ) { /* writing it this way allows gcc to recognize that rsqrt can be used */ ilength = 1/(float)sqrt (length); /* sqrt(length) = length * (1 / sqrt(length)) */ length *= ilength; v[0] *= ilength; v[1] *= ilength; v[2] *= ilength; } return length; } vec_t VectorNormalize2( const vec3_t v, vec3_t out) { float length, ilength; length = v[0]*v[0] + v[1]*v[1] + v[2]*v[2]; if (length) { /* writing it this way allows gcc to recognize that rsqrt can be used */ ilength = 1/(float)sqrt (length); /* sqrt(length) = length * (1 / sqrt(length)) */ length *= ilength; out[0] = v[0]*ilength; out[1] = v[1]*ilength; out[2] = v[2]*ilength; } else { VectorClear( out ); } return length; } void _VectorMA( const vec3_t veca, float scale, const vec3_t vecb, vec3_t vecc) { vecc[0] = veca[0] + scale*vecb[0]; vecc[1] = veca[1] + scale*vecb[1]; vecc[2] = veca[2] + scale*vecb[2]; } vec_t _DotProduct( const vec3_t v1, const vec3_t v2 ) { return v1[0]*v2[0] + v1[1]*v2[1] + v1[2]*v2[2]; } void _VectorSubtract( const vec3_t veca, const vec3_t vecb, vec3_t out ) { out[0] = veca[0]-vecb[0]; out[1] = veca[1]-vecb[1]; out[2] = veca[2]-vecb[2]; } void _VectorAdd( const vec3_t veca, const vec3_t vecb, vec3_t out ) { out[0] = veca[0]+vecb[0]; out[1] = veca[1]+vecb[1]; out[2] = veca[2]+vecb[2]; } void _VectorCopy( const vec3_t in, vec3_t out ) { out[0] = in[0]; out[1] = in[1]; out[2] = in[2]; } void _VectorScale( const vec3_t in, vec_t scale, vec3_t out ) { out[0] = in[0]*scale; out[1] = in[1]*scale; out[2] = in[2]*scale; } void Vector4Scale( const vec4_t in, vec_t scale, vec4_t out ) { out[0] = in[0]*scale; out[1] = in[1]*scale; out[2] = in[2]*scale; out[3] = in[3]*scale; } int Q_log2( int val ) { int answer; answer = 0; while ( ( val>>=1 ) != 0 ) { answer++; } return answer; } /* ================= PlaneTypeForNormal ================= */ /* int PlaneTypeForNormal (vec3_t normal) { if ( normal[0] == 1.0 ) return PLANE_X; if ( normal[1] == 1.0 ) return PLANE_Y; if ( normal[2] == 1.0 ) return PLANE_Z; return PLANE_NON_AXIAL; } */ // STONELANCE /* ================================================================================ VectorNAN ================================================================================ */ qboolean VectorNAN( const vec3_t vec ){ if (IS_NAN(vec[0]) || IS_NAN(vec[1]) || IS_NAN(vec[2])){ return qtrue; } return qfalse; } /* ================ MatrixMultiply ================ */ void MatrixMultiply( float in1[3][3], float in2[3][3], float out[3][3]) { if( in1 == out || in2 == out ) { float temp[3][3]; temp[0][0] = in1[0][0] * in2[0][0] + in1[0][1] * in2[1][0] + in1[0][2] * in2[2][0]; temp[0][1] = in1[0][0] * in2[0][1] + in1[0][1] * in2[1][1] + in1[0][2] * in2[2][1]; temp[0][2] = in1[0][0] * in2[0][2] + in1[0][1] * in2[1][2] + in1[0][2] * in2[2][2]; temp[1][0] = in1[1][0] * in2[0][0] + in1[1][1] * in2[1][0] + in1[1][2] * in2[2][0]; temp[1][1] = in1[1][0] * in2[0][1] + in1[1][1] * in2[1][1] + in1[1][2] * in2[2][1]; temp[1][2] = in1[1][0] * in2[0][2] + in1[1][1] * in2[1][2] + in1[1][2] * in2[2][2]; temp[2][0] = in1[2][0] * in2[0][0] + in1[2][1] * in2[1][0] + in1[2][2] * in2[2][0]; temp[2][1] = in1[2][0] * in2[0][1] + in1[2][1] * in2[1][1] + in1[2][2] * in2[2][1]; temp[2][2] = in1[2][0] * in2[0][2] + in1[2][1] * in2[1][2] + in1[2][2] * in2[2][2]; out[0][0] = temp[0][0]; out[0][1] = temp[0][1]; out[0][2] = temp[0][2]; out[1][0] = temp[1][0]; out[1][1] = temp[1][1]; out[1][2] = temp[1][2]; out[2][0] = temp[2][0]; out[2][1] = temp[2][1]; out[2][2] = temp[2][2]; } else { out[0][0] = in1[0][0] * in2[0][0] + in1[0][1] * in2[1][0] + in1[0][2] * in2[2][0]; out[0][1] = in1[0][0] * in2[0][1] + in1[0][1] * in2[1][1] + in1[0][2] * in2[2][1]; out[0][2] = in1[0][0] * in2[0][2] + in1[0][1] * in2[1][2] + in1[0][2] * in2[2][2]; out[1][0] = in1[1][0] * in2[0][0] + in1[1][1] * in2[1][0] + in1[1][2] * in2[2][0]; out[1][1] = in1[1][0] * in2[0][1] + in1[1][1] * in2[1][1] + in1[1][2] * in2[2][1]; out[1][2] = in1[1][0] * in2[0][2] + in1[1][1] * in2[1][2] + in1[1][2] * in2[2][2]; out[2][0] = in1[2][0] * in2[0][0] + in1[2][1] * in2[1][0] + in1[2][2] * in2[2][0]; out[2][1] = in1[2][0] * in2[0][1] + in1[2][1] * in2[1][1] + in1[2][2] * in2[2][1]; out[2][2] = in1[2][0] * in2[0][2] + in1[2][1] * in2[1][2] + in1[2][2] * in2[2][2]; } } /* ================ MatrixTranspose Cant do MatrixTranspose(m, m); ================ */ void MatrixTranspose( float in[3][3], float out[3][3] ) { out[0][0] = in[0][0]; out[0][1] = in[1][0]; out[0][2] = in[2][0]; out[1][0] = in[0][1]; out[1][1] = in[1][1]; out[1][2] = in[2][1]; out[2][0] = in[0][2]; out[2][1] = in[1][2]; out[2][2] = in[2][2]; } /* ================ MatrixAdd ================ */ void MatrixAdd( float in1[3][3], float in2[3][3], float out[3][3] ) { out[0][0] = in1[0][0] + in2[0][0]; out[0][1] = in1[0][1] + in2[0][1]; out[0][2] = in1[0][2] + in2[0][2]; out[1][0] = in1[1][0] + in2[1][0]; out[1][1] = in1[1][1] + in2[1][1]; out[1][2] = in1[1][2] + in2[1][2]; out[2][0] = in1[2][0] + in2[2][0]; out[2][1] = in1[2][1] + in2[2][1]; out[2][2] = in1[2][2] + in2[2][2]; } /* ================ MatrixScale ================ */ void MatrixScale( float in[3][3], float s, float out[3][3] ) { out[0][0] = in[0][0] * s; out[0][1] = in[0][1] * s; out[0][2] = in[0][2] * s; out[1][0] = in[1][0] * s; out[1][1] = in[1][1] * s; out[1][2] = in[1][2] * s; out[2][0] = in[2][0] * s; out[2][1] = in[2][1] * s; out[2][2] = in[2][2] * s; } /* ================ AnglesToOrientation Converts car angles to an orientation matrix ================ */ void AnglesToOrientation( const vec3_t angles, float t[3][3] ) { float angle; static float sr, sp, sy, cr, cp, cy; // static to help MS compiler fp bugs angle = angles[YAW] * M_PI_180; sy = sin(angle); cy = cos(angle); angle = angles[PITCH] * M_PI_180; sp = sin(angle); cp = cos(angle); angle = angles[ROLL] * M_PI_180; sr = sin(angle); cr = cos(angle); t[0][0] = (-1*sr*sp*cy+-1*cr*-sy); t[1][0] = (-1*sr*sp*sy+-1*cr*cy); t[2][0] = -1*sr*cp; t[0][1] = cp*cy; t[1][1] = cp*sy; t[2][1] = -sp; t[0][2] = (cr*sp*cy+-sr*-sy); t[1][2] = (cr*sp*sy+-sr*cy); t[2][2] = cr*cp; } /* ================ OrientationToVectors Converts orientation matrix to angle vectors ================ */ void OrientationToVectors( float t[3][3], vec3_t forward, vec3_t right, vec3_t up ) { right[0] = t[0][0]; right[1] = t[1][0]; right[2] = t[2][0]; forward[0] = t[0][1]; forward[1] = t[1][1]; forward[2] = t[2][1]; up[0] = t[0][2]; up[1] = t[1][2]; up[2] = t[2][2]; // VectorNormalize(right); // VectorNormalize(forward); // VectorNormalize(up); } /* ================ AnglesToDeltaAngles Converts orientation matrix to car angles ================ */ void AnglesToDeltaAngles( vec3_t angles, const vec3_t w, vec3_t deltaAngles ) { /* float cr, cy; float sr, sy; float aaa; sy = sin( angles[YAW] * M_180_PI ); cy = cos( angles[YAW] * M_180_PI ); sr = sin( angles[ROLL] * M_180_PI ); cr = cos( angles[ROLL] * M_180_PI ); // [ dpsi dtheta dphi ]T = M-1(theta,phi) * Omega // // M-1(theta,phi) = [ cos(phi)/cos(theta) sin(phi)/cos(theta) 0 ] // [ -sin(phi) cos(phi) 0 ] // [ cos(phi)*sin(theta)/cos(theta) sin(phi)*sin(theta)/cos(theta) 1 ] aaa = ( cr + sr ) / cy; delta_angles[0] = ( aaa ) * w[0]; delta_angles[1] = ( cr - sr ) * w[1]; delta_angles[2] = ( aaa * sy + 1 ) * w[2]; */ float c1, c2, c3, s1, s2, s3; float p, sp; c1 = cos( angles[0] * M_PI_180 ); c2 = cos( angles[1] * M_PI_180 ); c3 = cos( angles[2] * M_PI_180 ); s1 = sin( angles[0] * M_PI_180 ); s2 = sin( angles[1] * M_PI_180 ); s3 = sin( angles[2] * M_PI_180 ); p = 2.0f * Q_acos( c1*c2*c3 - s1*s2*s3 ); sp = p / sin( p / 2.0f ) ; deltaAngles[0] = (c1*s2*c3 + s1*c2*c3) * sp * M_180_PI; deltaAngles[1] = (s1*s2*c3 + c1*s2*s3) * sp * M_180_PI; deltaAngles[2] = (c1*c2*s3 + s1*s2*c3) * sp * M_180_PI; } /* ================ OrientationToDeltaAngles Converts orientation matrix to car angles ================ */ void OrientationToDeltaAngles( float t[3][3], const vec3_t w, vec3_t delta_angles ) { // vec3_t forward, right, up; // float cp, as; // OrientationToVectors(t, forward, right, up); /* forward[0] = -w[2] * t[1][1] + w[1] * t[1][2]; forward[1] = w[2] * t[1][0] + w[0] * t[1][2]; forward[2] = -w[1] * t[1][0] + w[0] * t[1][1]; up[2] = -w[1] * t[2][0] + w[0] * t[2][1]; right[2] = -w[1] * t[0][0] + w[0] * t[0][1]; delta_angles[PITCH] = Q_asin( -forward[2] ) * M_180_PI; if (up[2] < 0.0f) delta_angles[PITCH] = 180 - delta_angles[PITCH]; cp = cos( delta_angles[PITCH] * M_PI_180 ); if (cp){ // fix small floating point errors that would cause it to // have asin() of a number > 1.00 as = forward[1] / cp > 1.00f ? 1.00f : forward[1] / cp; as = as < -1.00f ? -1.00f : as; delta_angles[YAW] = Q_asin(as) * M_180_PI; if (forward[0] < 0.0f) delta_angles[YAW] = 180 - delta_angles[YAW]; if (up[2] < 0.0f) delta_angles[YAW] = 180 - delta_angles[YAW]; as = -right[2] / cp > 1.00f ? 1.00f : -right[2] / cp; as = as < -1.00f ? -1.00f : as; delta_angles[ROLL] = Q_asin(as) * M_180_PI; } else { delta_angles[YAW]=0; delta_angles[ROLL]=0; } // we still want yaw to be facing the front of the car so spin yaw // 180 and adjust pitch and roll to keep car in the same position if (fabs(delta_angles[PITCH]) > 90){ delta_angles[YAW] += 180; delta_angles[PITCH] = 180 - delta_angles[PITCH]; delta_angles[ROLL] += 180; } */ } /* ================ OrientationToAngles Converts orientation matrix to car angles ================ */ void OrientationToAngles( float t[3][3], vec3_t angles ) { vec3_t forward, right, up; float cp, as; OrientationToVectors(t, forward, right, up); angles[PITCH] = Q_asin(-forward[2]) * M_180_PI; if (up[2] < 0.0f) angles[PITCH] = 180 - angles[PITCH]; cp = cos(angles[PITCH] * M_PI_180 ); if (cp){ // fix small floating point errors that would cause it to // have asin() of a number > 1.00 as = forward[1] / cp > 1.00f ? 1.00f : forward[1] / cp; as = as < -1.00f ? -1.00f : as; angles[YAW] = Q_asin(as) * M_180_PI; if (forward[0] < 0.0f) angles[YAW] = 180 - angles[YAW]; if (up[2] < 0.0f) angles[YAW] = 180 - angles[YAW]; as = -right[2] / cp > 1.00f ? 1.00f : -right[2] / cp; as = as < -1.00f ? -1.00f : as; angles[ROLL] = Q_asin(as) * M_180_PI; } else { angles[YAW]=0; angles[ROLL]=0; } // we still want yaw to be facing the front of the car so spin yaw // 180 and adjust pitch and roll to keep car in the same position if (fabs(angles[PITCH]) > 90){ angles[YAW] += 180; angles[PITCH] = 180 - angles[PITCH]; angles[ROLL] += 180; } } /* ================ OrthonormalizeOrientation Normalizes orientation matrix ================ */ void OrthonormalizeOrientation( float t[3][3] ){ vec3_t x, y, z; VectorSet(x, t[0][0], t[1][0], t[2][0]); VectorSet(y, t[0][1], t[1][1], t[2][1]); // FIXME: check for 0 length? VectorNormalize(x); CrossProduct(x, y, z); VectorNormalize(z); CrossProduct(z, x, y); VectorNormalize(y); t[0][0] = x[0]; t[0][1] = y[0]; t[0][2] = z[0]; t[1][0] = x[1]; t[1][1] = y[1]; t[1][2] = z[1]; t[2][0] = x[2]; t[2][1] = y[2]; t[2][2] = z[2]; } /* ================ QuaternionLengthSquared Returns the DotProduct(q, q) ================ */ float QuaternionLengthSquared( const vec4_t q ){ return q[0]*q[0] + q[1]*q[1] + q[2]*q[2] + q[3]*q[3]; } /* ================ QuaternionLength Returns the sqrt( DotProduct(q, q) ) ================ */ float QuaternionLength( const vec4_t q ){ return sqrt( q[0]*q[0] + q[1]*q[1] + q[2]*q[2] + q[3]*q[3] ); } /* ================ QuaternionFastNormalize Normalizes quat avoiding a sqrt returns squared length of quaternion; Quaternion function code from racer ================ */ float QuaternionFastNormalize( vec4_t quat ) { // Check if quaternion needs normalizing float len = QuaternionLengthSquared( quat ); if ( len == 0.0f ) { // TODO: Make w 0 instead of this? quat[3] = 1.0f; quat[0] = quat[1] = quat[2] = 0.0f; } else if( len < 0.9999f || len > 1.0001f ) { // Push quat back to 1.0 (avoid a sqrt()) float n = ( len + 1.0f ) / ( 2.0f * len ); quat[0] *= n; quat[1] *= n; quat[2] *= n; quat[3] *= n; } return len; } /* ================ QuaternionNormalize Normalizes a quat using the normal sqrt method returns length of quaternion; Quaternion function code from racer ================ */ float QuaternionNormalize( vec4_t quat ) { float tmp, len; len = QuaternionLength( quat ); if ( len == 0.0f ) { // TODO: Make w 0 instead of this? quat[3] = 1.0f; quat[0] = quat[1] = quat[2] = 0.0f; return len; } tmp = 1.0f / len; quat[3] *= tmp; quat[0] *= tmp; quat[1] *= tmp; quat[2] *= tmp; return len; } /* ================ QuaternionMultiply Multiplies two quaternions together Quaternion function code from skwid ================ */ void QuaternionMultiply(const vec4_t in1, const vec4_t in2, vec4_t out){ /* // from racer w = in1[3] * in2[3] - in1[0] * in2[0] - in1[1] * in2[1] - in1[2] * in2[2]; x = in1[3] * in2[0] + in1[0] * in2[3] + in1[1] * in2[2] - in1[2] * in2[1]; y = in1[3] * in2[1] - in1[0] * in2[2] + in1[1] * in2[3] + in1[2] * in2[0]; z = in1[3] * in2[2] + in1[0] * in2[1] - in1[1] * in2[0] + in1[2] * in2[3]; */ /* this crap doesnt work float A, B, C, D, E, F, G, H; A = (q1[3] + q1[0]) * (q2[3] + q2[0]); B = (q1[2] - q1[1]) * (q2[1] - q2[2]); C = (q1[3] - q1[0]) * (q2[1] + q2[2]); D = (q1[1] + q1[2]) * (q2[3] - q2[0]); E = (q1[0] + q1[2]) * (q2[0] + q2[1]); F = (q1[0] - q1[2]) * (q2[0] - q2[1]); G = (q1[3] + q1[1]) * (q2[3] - q2[2]); H = (q1[3] - q1[1]) * (q2[3] + q2[2]); res[0] = A - (E + F + G + H)/2; res[1] = C + (E - F + G - H)/2; res[2] = D + (E - F - G + H)/2; res[3] = B + (-E - F + G + H) /2; */ vec3_t temp; // in case of mulp(a, b, a) temp[0] = (in1[1] * in2[2] - in1[2] * in2[1]) + in2[3] * in1[0] + in1[3] * in2[0]; temp[1] = (in1[2] * in2[0] - in1[0] * in2[2]) + in2[3] * in1[1] + in1[3] * in2[1]; temp[2] = (in1[0] * in2[1] - in1[1] * in2[0]) + in2[3] * in1[2] + in1[3] * in2[2]; out[3] = in1[3] * in2[3] - (in1[0] * in2[0] + in1[1] * in2[1] + in1[2] * in2[2]); out[0] = temp[0]; out[1] = temp[1]; out[2] = temp[2]; } /* ================ QuaternionRotate Rotates quat by the amount specified in w*time w in body coords Note: out cannot be the same as quat ================ */ void QuaternionRotate( const vec4_t quat, const vec3_t w, const float time, vec4_t out){ vec3_t tempVec; // divide by 2.0f is part of quaternion derivative calculation VectorScale( w, time / 2.0f, tempVec ); out[0] = quat[0] + ( quat[3]*tempVec[0] - quat[2]*tempVec[1] + quat[1]*tempVec[2] ); out[1] = quat[1] + ( quat[2]*tempVec[0] + quat[3]*tempVec[1] - quat[0]*tempVec[2] ); out[2] = quat[2] + (-quat[1]*tempVec[0] + quat[0]*tempVec[1] + quat[3]*tempVec[2] ); out[3] = quat[3] + (-quat[0]*tempVec[0] - quat[1]*tempVec[1] - quat[2]*tempVec[2] ); } /* ================ QuaternionSLERP 4D Spherically lerps from one quarternion to another. 'from' and 'to' need to be normalized t = fraction of move from start quarternion to end quarternion [0 .. 1] ================ */ void QuaternionSLERP(const vec4_t from, const vec4_t to, float t, vec4_t res){ /* // from racer float theta, costheta, w1, w2, sintheta; costheta = from[0] * to[0] + from[1] * to[1] + from[2] * to[2] + from[3] * to[3]; // OPTIMIZE: If costheta was squared then i could use the sin(t)^2 = 1-cos(t)^s // Is sintheta ever negative? If not then sin(t)^2 > 0 == sin(t) > 0 theta = Q_acos( costheta ); sintheta = sin( theta ); if( sintheta > 0.0f ) { w1 = sin( (1.0f - t) * theta ) / sintheta; w2 = sin( t * theta ) / sintheta; } else { // They're the same quaternion, so who cares? w1 = 1.0f; w2 = 0.0f; } res[0] = w1 * from[0] + w2 * to[0]; res[1] = w1 * from[1] + w2 * to[1]; res[2] = w1 * from[2] + w2 * to[2]; res[3] = w1 * from[3] + w2 * to[3]; */ /* // Quaternion function from 'Rotating Objects Using Quaternions' by Nick Bobick vec4_t to1; double omega, cosom, sinom, scale0, scale1; // calc cosine cosom = from[0] * to[0] + from[1] * to[1] + from[2] * to[2] + from[3] * to[3]; // adjust signs (if necessary) if ( cosom < 0.0 ){ cosom = -cosom; to1[0] = -to[0]; to1[1] = -to[1]; to1[2] = -to[2]; to1[3] = -to[3]; } else { to1[0] = to[0]; to1[1] = to[1]; to1[2] = to[2]; to1[3] = to[3]; } // calculate coefficients if ( (1.0 - cosom) > 0.1f ) { // standard case (slerp) omega = Q_acos(cosom); sinom = sin(omega); scale0 = sin((1.0 - t) * omega) / sinom; scale1 = sin(t * omega) / sinom; } else { // "from" and "to" quaternions are very close // ... so we can do a linear interpolation scale0 = 1.0 - t; scale1 = t; } // calculate final values res[0] = scale0 * from[0] + scale1 * to1[0]; res[1] = scale0 * from[1] + scale1 * to1[1]; res[2] = scale0 * from[2] + scale1 * to1[2]; res[3] = scale0 * from[3] + scale1 * to1[3]; */ } /* ================ AnglesToQuaternion Converts euler angles to a quaternion ================ */ void AnglesToQuaternion( const vec3_t angles, vec4_t quat){ float t[3][3]; // OPTIMIZE: See if this can be simplified AnglesToOrientation( angles, t ); OrientationToQuaternion( t, quat ); // based on Quaternion function from 'Rotating Objects Using Quaternions' by Nick Bobick /* float cr, cp, cy, sr, sp, sy, spcy, spsy; float tr, s; int i, j, k; vec3_t t[3]; // calculate trig identities cr = cos(angles[ROLL] * M_PI / 180.0f); cp = cos(angles[PITCH] * M_PI / 180.0f); cy = cos(angles[YAW] * M_PI / 180.0f); sr = sin(angles[ROLL] * M_PI / 180.0f); sp = sin(angles[PITCH] * M_PI / 180.0f); sy = sin(angles[YAW] * M_PI / 180.0f); spcy = sp * cy; spsy = sp * sy; t[0][0] = (-sr*spcy + cr*sy); t[1][0] = (-sr*spsy - cr*cy); t[2][0] = -sr*cp; t[0][1] = cp*cy; t[1][1] = cp*sy; t[2][1] = -sp; t[0][2] = (cr*spcy + sr*sy); t[1][2] = (cr*spsy - sr*cy); t[2][2] = cr*cp; */ /* tr = t[0][0] + t[1][1] + t[2][2]; // check the diagonal if (tr > 0.0) { s = sqrt (tr + 1.0); quat[3] = s / 2.0; s = 0.5 / s; quat[0] = (t[1][2] - t[2][1]) * s; quat[1] = (t[2][0] - t[0][2]) * s; quat[2] = (t[0][1] - t[1][0]) * s; } else { // diagonal is negative i = 0; if (t[1][1] > t[0][0]) i = 1; if (t[2][2] > t[i][i]) i = 2; j = (i+1) % 3; k = (j+1) % 3; s = sqrt ((t[i][i] - (t[j][j] + t[k][k])) + 1.0); quat[i] = s * 0.5; if (s != 0.0) s = 0.5 / s; quat[3] = (t[j][k] - t[k][j]) * s; quat[j] = (t[i][j] + t[j][i]) * s; quat[k] = (t[i][k] + t[k][i]) * s; } */ /* // Quaternion function code from skwid vec4_t qy = { 0, sin(angles[YAW] * M_PI / 180.0f), 0, cos(angles[YAW] * M_PI / 180.0f) }; vec4_t qp = { sin(angles[PITCH] * M_PI / 180.0f), 0, 0, cos(angles[PITCH] * M_PI / 180.0f) }; vec4_t qr = { 0, 0, sin(angles[ROLL] * M_PI / 180.0f), cos(angles[ROLL] * M_PI / 180.0f) }; Com_Printf("qy %f %f %f %f\n", qy[0], qy[1], qy[2], qy[3]); Com_Printf("qp %f %f %f %f\n", qp[0], qp[1], qp[2], qp[3]); Com_Printf("qr %f %f %f %f\n", qr[0], qr[1], qr[2], qr[3]); QuaternionMultiply( qy, qp, quat ); Com_Printf("quat %f %f %f %f\n", quat[0], quat[1], quat[2], quat[3]); QuaternionMultiply( quat, qr, quat ); */ } /* ================ QuaternionToAngles Converts a quaternion to angles ================ */ void QuaternionToAngles( const vec4_t quat, vec3_t angles ){ float t[3][3]; // OPTIMIZE: See if this can be simplified, some parts of t dont need to be calculated QuaternionToOrientation( quat, t ); OrientationToAngles( t, angles ); /* float wx, wy, wz, xx, yy, yz, xy, xz, zz; float x2, y2, z2; vec3_t f, r, u; float cp, as; // calculate coefficients x2 = quat[0] + quat[0]; y2 = quat[1] + quat[1]; z2 = quat[2] + quat[2]; xx = quat[0] * x2; xy = quat[0] * y2; xz = quat[0] * z2; yy = quat[1] * y2; yz = quat[1] * z2; zz = quat[2] * z2; wx = quat[3] * x2; wy = quat[3] * y2; wz = quat[3] * z2; right[0] = 1.0 - (yy + zz); right[1] = xy - wz; right[2] = xz + wy; forward[0] = xy + wz; forward[1] = 1.0 - (xx + zz); forward[2] = yz - wx; up[0] = xz - wy; up[1] = yz + wx; up[2] = 1.0 - (xx + yy); */ /* // Quaternion function code based on skwids float wx, wy, wz, xx, yy, yz, xy, xz, zz; float x2, y2, z2; vec3_t f, r, u; float cp, as; float s = 2 / QuaternionNormal( quat ); xx = quat[0] * quat[0]; xy = quat[0] * quat[1]; xz = quat[0] * quat[2]; yy = quat[1] * quat[1]; yz = quat[1] * quat[2]; zz = quat[2] * quat[2]; wx = quat[3] * quat[0]; wy = quat[3] * quat[1]; wz = quat[3] * quat[2]; // r[0] = 1 - s * (yy + zz); r[1] = s * (xy - wz); r[2] = s * (xz + wy); f[0] = s * (xy + wz); f[1] = 1 - s * (xx + zz); f[2] = s * (yz - wx); // u[0] = s * (xz - wy); u[1] = s * (yz + wx); u[2] = 1 - s * (xx + yy); angles[PITCH] = Q_asin(-f[2]) * 180.0f / M_PI; if (u[2] < 0.0f) angles[PITCH] = 180 - angles[PITCH]; cp = cos(angles[PITCH] / 180.0f * M_PI); if (cp){ // fix small floating point errors that would cause it to // have asin() of a number > 1.00 as = f[1] / cp > 1.00f ? 1.00f : f[1] / cp; as = as < -1.00f ? -1.00f : as; angles[YAW] = Q_asin(as) * 180.0f / M_PI; if (f[0] < 0.0f) angles[YAW] = 180 - angles[YAW]; if (u[2] < 0.0f) angles[YAW] = 180 - angles[YAW]; as = -r[2] / cp > 1.00f ? 1.00f : -r[2] / cp; as = as < -1.00f ? -1.00f : as; angles[ROLL] = Q_asin(as) * 180 / M_PI; } else { angles[YAW]=0; angles[ROLL]=0; } // we still want yaw to be facing the front of the car so spin yaw // 180 and adjust pitch and roll to keep car in the same position if (fabs(angles[PITCH]) > 90){ angles[YAW] += 180; angles[PITCH] = 180 - angles[PITCH]; angles[ROLL] += 180; } */ } /* ================ OrientationToQuaternion Converts orientation matrix to a quaternion ================ */ void OrientationToQuaternion( float t[3][3], vec4_t quat ){ // from racer int i; float qw2, qx2, qy2, qz2, tmp; // Quaternion components squared qw2 = 0.25 * (t[0][0] + t[1][1] + t[2][2] + 1.0); qx2 = qw2 - 0.5 * (t[1][1] + t[2][2]); qy2 = qw2 - 0.5 * (t[2][2] + t[0][0]); qz2 = qw2 - 0.5 * (t[0][0] + t[1][1]); // Decide maximum magnitude component i = ( qw2 > qx2 ) ? ( ( qw2 > qy2 ) ? (( qw2 > qz2 ) ? 0 : 3) : (( qy2 > qz2 ) ? 2 : 3)) : ( ( qx2 > qy2 ) ? (( qx2 > qz2 ) ? 1 : 3) : (( qy2 > qz2 ) ? 2 : 3)); // Compute signed quat components using numerically stable method switch( i ) { case 0: quat[3] = sqrt(qw2); tmp = 0.25f / quat[3]; quat[0] = (t[1][2] - t[2][1]) * tmp; quat[1] = (t[2][0] - t[0][2]) * tmp; quat[2] = (t[0][1] - t[1][0]) * tmp; break; case 1: quat[0] = sqrt(qx2); tmp = 0.25f / quat[0]; quat[3] = (t[1][2] - t[2][1]) * tmp; quat[1] = (t[1][0] + t[0][1]) * tmp; quat[2] = (t[0][2] + t[2][0]) * tmp; break; case 2: quat[1] = sqrt(qy2); tmp = 0.25f / quat[1]; quat[3] = (t[2][0] - t[0][2]) * tmp; quat[0] = (t[1][0] + t[0][1]) * tmp; quat[2] = (t[2][1] + t[1][2]) * tmp; break; case 3: quat[2] = sqrt(qz2); tmp = 0.25f / quat[2]; quat[3] = (t[0][1] - t[1][0]) * tmp; quat[0] = (t[2][0] + t[0][2]) * tmp; quat[1] = (t[2][1] + t[1][2]) * tmp; break; } // Always keep all components positive // (note that scalar*quat is equivalent to quat, so q==-q) if ( i && quat[3] < 0.0f ) { quat[3] = -quat[3]; quat[0] = -quat[0]; quat[1] = -quat[1]; quat[2] = -quat[2]; } // Normalize it to be safe QuaternionFastNormalize( quat ); // tmp = 1.0f / sqrt( quat[3]*quat[3] + quat[0]*quat[0] + quat[1]*quat[1] + quat[2]*quat[2] ); // quat[3] *= tmp; // quat[0] *= tmp; // quat[1] *= tmp; // quat[2] *= tmp; // Quaternion function from 'Rotating Objects Using Quaternions' by Nick Bobick /* float tr, s; int i, j, k; int nxt[3] = {1, 2, 0}; tr = t[0][0] + t[1][1] + t[2][2]; // check the diagonal if (tr > 0.0) { s = sqrt (tr + 1.0); quat[3] = s / 2.0; s = 0.5 / s; quat[0] = (t[1][2] - t[2][1]) * s; quat[1] = (t[2][0] - t[0][2]) * s; quat[2] = (t[0][1] - t[1][0]) * s; } else { // diagonal is negative i = 0; if (t[1][1] > t[0][0]) i = 1; if (t[2][2] > t[i][i]) i = 2; j = nxt[i]; k = nxt[j]; s = sqrt ((t[i][i] - (t[j][j] + t[k][k])) + 1.0); quat[i] = s * 0.5; if (s != 0.0) s = 0.5 / s; quat[3] = (t[j][k] - t[k][j]) * s; quat[j] = (t[i][j] + t[j][i]) * s; quat[k] = (t[i][k] + t[k][i]) * s; } */ /* // thanks to skwid for the equations quat[3] = 0.5f * sqrt( t[0][0] + t[1][1] + t[2][2] + 1.0f ); quat[0] = (t[1][2] - t[2][1]) / (4 * quat[3]); quat[1] = (t[2][0] - t[0][2]) / (4 * quat[3]); quat[2] = (t[0][1] - t[1][0]) / (4 * quat[3]); */ } /* ================ QuaternionToOrientation Converts normalized quaternion to a orientation matrix ================ */ void QuaternionToOrientation( const vec4_t quat, float t[3][3] ){ float xy, wz, xz, wy, yz, wx, x2, y2, z2; // based on code from racer x2 = quat[0] * quat[0]; y2 = quat[1] * quat[1]; z2 = quat[2] * quat[2]; xy = quat[0] * quat[1]; wz = quat[3] * quat[2]; xz = quat[0] * quat[2]; wy = quat[3] * quat[1]; yz = quat[1] * quat[2]; wx = quat[3] * quat[0]; t[0][0] = 1.0f - 2.0f * (y2 + z2); t[1][0] = 2.0f * (xy - wz); t[2][0] = 2.0f * (xz + wy); t[0][1] = 2.0f * (xy + wz); t[1][1] = 1.0f - 2.0f * (z2 + x2); t[2][1] = 2.0f * (yz - wx); t[0][2] = 2.0f * (xz - wy); t[1][2] = 2.0f * (yz + wx); t[2][2] = 1.0f - 2.0f * (x2 + y2); /* Quaternion function from 'Rotating Objects Using Quaternions' by Nick Bobick float x2, y2, z2; // calculate coefficients x2 = quat[0] + quat[0]; y2 = quat[1] + quat[1]; z2 = quat[2] + quat[2]; xx = quat[0] * x2; xy = quat[0] * y2; xz = quat[0] * z2; yy = quat[1] * y2; yz = quat[1] * z2; zz = quat[2] * z2; wx = quat[3] * x2; wy = quat[3] * y2; wz = quat[3] * z2; t[0][0] = 1.0 - (yy + zz); t[1][0] = xy - wz; t[2][0] = xz + wy; t[0][1] = xy + wz; t[1][1] = 1.0 - (xx + zz); t[2][1] = yz - wx; t[0][2] = xz - wy; t[1][2] = yz + wx; t[2][2] = 1.0 - (xx + yy); */ /* // Quaternion function code based on skwids float s = 2 / QuaternionNormal( quat ); xx = quat[0] * quat[0]; xy = quat[0] * quat[1]; xz = quat[0] * quat[2]; yy = quat[1] * quat[1]; yz = quat[1] * quat[2]; zz = quat[2] * quat[2]; wx = quat[3] * quat[0]; wy = quat[3] * quat[1]; wz = quat[3] * quat[2]; t[0][0] = 1 - s * (yy + zz); t[1][0] = s * (xy - wz); t[2][0] = s * (xz + wy); t[0][1] = s * (xy + wz); t[1][1] = 1 - s * (xx + zz); t[2][1] = s * (yz - wx); t[0][2] = s * (xz - wy); t[1][2] = s * (yz + wx); t[2][2] = 1 - s * (xx + yy); */ } /* ================ QuaternionL2ToOrientation Converts non-normalize quaternion to a orientation matrix 'l2' is the squared length of the quaternion, used to get 't' orthogonal ================ */ void QuaternionL2ToOrientation( const vec4_t quat, const float l2, float t[3][3] ){ float xy, wz, xz, wy, yz, wx, x2, y2, z2, s; // based on code from racer x2 = quat[0] * quat[0]; y2 = quat[1] * quat[1]; z2 = quat[2] * quat[2]; xy = quat[0] * quat[1]; wz = quat[3] * quat[2]; xz = quat[0] * quat[2]; wy = quat[3] * quat[1]; yz = quat[1] * quat[2]; wx = quat[3] * quat[0]; s = 2.0f / l2; t[0][0] = 1.0f - s * (y2 + z2); t[1][0] = s * (xy - wz); t[2][0] = s * (xz + wy); t[0][1] = s * (xy + wz); t[1][1] = 1.0f - s * (z2 + x2); t[2][1] = s * (yz - wx); t[0][2] = s * (xz - wy); t[1][2] = s * (yz + wx); t[2][2] = 1.0f - s * (x2 + y2); } /* ================ QuaternionToVectors Converts a quaternion to angle vectors ================ */ void QuaternionToVectors( const vec4_t quat, vec3_t forward, vec3_t right, vec3_t up ) { float t[3][3]; QuaternionToOrientation( quat, t ); OrientationToVectors( t, forward, right, up ); /* float wx, wy, wz, xx, yy, yz, xy, xz, zz, x2, y2, z2; // calculate coefficients x2 = quat[0] + quat[0]; y2 = quat[1] + quat[1]; z2 = quat[2] + quat[2]; xx = quat[0] * x2; xy = quat[0] * y2; xz = quat[0] * z2; yy = quat[1] * y2; yz = quat[1] * z2; zz = quat[2] * z2; wx = quat[3] * x2; wy = quat[3] * y2; wz = quat[3] * z2; right[0] = 1.0 - (yy + zz); right[1] = xy - wz; right[2] = xz + wy; forward[0] = xy + wz; forward[1] = 1.0 - (xx + zz); forward[2] = yz - wx; up[0] = xz - wy; up[1] = yz + wx; up[2] = 1.0 - (xx + yy); VectorNormalize(right); VectorNormalize(forward); VectorNormalize(up); */ } // END void AngleVectors( const vec3_t angles, vec3_t forward, vec3_t right, vec3_t up) { float angle; static float sr, sp, sy, cr, cp, cy; // static to help MS compiler fp bugs // STONELANCE // angle = angles[YAW] * (M_PI*2 / 360); angle = angles[YAW] * M_PI_180; // END sy = sin(angle); cy = cos(angle); // STONELANCE // angle = angles[PITCH] * (M_PI*2 / 360); angle = angles[PITCH] * M_PI_180; // END sp = sin(angle); cp = cos(angle); // STONELANCE // angle = angles[ROLL] * (M_PI*2 / 360); angle = angles[ROLL] * M_PI_180; // END sr = sin(angle); cr = cos(angle); if (forward) { forward[0] = cp*cy; forward[1] = cp*sy; forward[2] = -sp; } if (right) { right[0] = (-1*sr*sp*cy+-1*cr*-sy); right[1] = (-1*sr*sp*sy+-1*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; } } /* ** assumes "src" is normalized */ void PerpendicularVector( vec3_t dst, const vec3_t src ) { int pos; int i; float minelem = 1.0F; vec3_t tempvec; /* ** find the smallest magnitude axially aligned vector */ for ( pos = 0, i = 0; i < 3; i++ ) { if ( fabs( src[i] ) < minelem ) { pos = i; minelem = fabs( src[i] ); } } tempvec[0] = tempvec[1] = tempvec[2] = 0.0F; tempvec[pos] = 1.0F; /* ** project the point onto the plane defined by src */ ProjectPointOnPlane( dst, tempvec, src ); /* ** normalize the result */ VectorNormalize( dst ); } /* ================ Q_isnan Don't pass doubles to this ================ */ int Q_isnan( float x ) { floatint_t fi; fi.f = x; fi.ui &= 0x7FFFFFFF; fi.ui = 0x7F800000 - fi.ui; return (int)( (unsigned int)fi.ui >> 31 ); } //------------------------------------------------------------------------ #ifndef Q3_VM /* ===================== Q_acos the msvc acos doesn't always return a value between 0 and PI: int i; i = 1065353246; acos(*(float*) &i) == -1.#IND0 ===================== */ float Q_acos(float c) { float angle; angle = acos(c); if (angle > M_PI) { return M_PI; } if (angle < 0.0f) { return 0.0f; } return angle; } /* ===================== Q_asin the msvc asin probably has same type of behavior as acos ===================== */ float Q_asin(float c) { float angle; angle = asin(c); if (angle > M_PI_2) { return M_PI_2; } if (angle < -M_PI_2) { return -M_PI_2; } return angle; } #endif