#include "RenderPCH.h" #pragma warning(push) #pragma warning(disable:4244) // conversion from 'double' to 'float', possible loss of data #pragma warning(disable:4305) // truncation from 'double' to 'float' void utlMtx2Euler(int ord, float m[3][3], float rot[3]); static void utlMtx2Quat(float m[3][3], float quat[4]); // ========== utlDecompMatrix ========== // // SYNOPSIS // Decompose a matrix to it's components, translate, // rotate ( a quaternion) and scale. // static void utlDecompMatrix( const float *mat, DECOMP_MAT *dmat, char *rotOrder) { int i, j, order; static float Sxy, Sxz, rot[3], quat[4], det, m[3][3]; dmat->translate[0] = mat[3*4+0]; dmat->translate[1] = mat[3*4+1]; dmat->translate[2] = mat[3*4+2]; m[0][0] = mat[0*4+0]; m[0][1] = mat[0*4+1]; m[0][2] = mat[0*4+2]; dmat->scale[0] = sqrt_tpl( m[0][0]*m[0][0] + m[0][1]*m[0][1] + m[0][2]*m[0][2]); /* Normalize second row */ m[0][0] /= dmat->scale[0]; m[0][1] /= dmat->scale[0]; m[0][2] /= dmat->scale[0]; /* Determine xy shear */ Sxy = mat[0*4+0] * mat[1*4+0] + mat[0*4+1] * mat[1*4+1] + mat[0*4+2] * mat[1*4+2]; m[1][0] = mat[1*4+0] - Sxy * mat[0*4+0]; m[1][1] = mat[1*4+1] - Sxy * mat[0*4+1]; m[1][2] = mat[1*4+2] - Sxy * mat[0*4+2]; dmat->scale[1] = sqrt_tpl( m[1][0]*m[1][0] + m[1][1]*m[1][1] + m[1][2]*m[1][2]); /* Normalize second row */ m[1][0] /= dmat->scale[1]; m[1][1] /= dmat->scale[1]; m[1][2] /= dmat->scale[1]; /* Determine xz shear */ Sxz = mat[0*4+0] * mat[2*4+0] + mat[0*4+1] * mat[2*4+1] + mat[0*4+2] * mat[2*4+2]; m[2][0] = mat[2*4+0] - Sxz * mat[0*4+0]; m[2][1] = mat[2*4+1] - Sxz * mat[0*4+1]; m[2][2] = mat[2*4+2] - Sxz * mat[0*4+2]; dmat->scale[2] = sqrt_tpl( m[2][0]*m[2][0] + m[2][1]*m[2][1] + m[2][2]*m[2][2]); /* Normalize third row */ m[2][0] /= dmat->scale[2]; m[2][1] /= dmat->scale[2]; m[2][2] /= dmat->scale[2]; det = (m[0][0]*m[1][1]*m[2][2]) + (m[0][1]*m[1][2]*m[2][0]) + (m[0][2]*m[1][0]*m[2][1]) - (m[0][2]*m[1][1]*m[2][0]) - (m[0][0]*m[1][2]*m[2][1]) - (m[0][1]*m[1][0]*m[2][2]); /* If the determinant of the rotation matrix is negative, */ /* negate the matrix and scale factors. */ if ( det < 0.0) { for ( i = 0; i < 3; i++) { for ( j = 0; j < 3; j++) m[i][j] *= -1.0; dmat->scale[i] *= -1.0; } } // Copy the 3x3 rotation matrix into the decomposition // structure. // memcpy( dmat->rotMatrix, m, sizeof( float)*9); /*rot[1] = asin( -m[0][2]); if ( fabsf( cos( rot[1])) > 0.0001) { rot[0] = asin( m[1][2]/cos( rot[1])); rot[2] = asin( m[0][1]/cos( rot[1])); } else { rot[0] = acos( m[1][1]); rot[2] = 0.0; }*/ switch( rotOrder[2]) { case XROT: if ( rotOrder[1] == YROT) order = UTL_ROT_XYZ; else order = UTL_ROT_XZY; break; case YROT: if ( rotOrder[1] == XROT) order = UTL_ROT_YXZ; else order = UTL_ROT_YZX; break; case ZROT: if ( rotOrder[1] == XROT) order = UTL_ROT_ZXY; else order = UTL_ROT_ZYX; break; default: order = UTL_ROT_XYZ; break; } utlMtx2Euler( order, m, rot); dmat->rotation[0] = rot[0]; dmat->rotation[1] = rot[1]; dmat->rotation[2] = rot[2]; utlMtx2Quat(m,quat); dmat->quaternion[0] = quat[0]; dmat->quaternion[1] = quat[1]; dmat->quaternion[2] = quat[2]; dmat->quaternion[3] = quat[3]; } /* * ========== CapQuat2Euler ========== * * SYNOPSIS * Convert a quaternion to Euler angles. * * PARAMETERS * int The order of rotations * float mat[3][3] rotation matrix * float rot[3] xyz-rotation values * * DESCRIPTION * This routine converts a mateix to Euler angles. * There are a few caveats: * The rotation order for the returned angles is always zyx. * The derivation of this algorithm is taken from Ken Shoemake's * paper: * SIGGRAPH 1985, Vol. 19, # 3, pp. 253-254 * * RETURN VALUE * None. */ #ifdef WIN32 #define M_PI_2 3.14159/2.0 #endif void utlMtx2Euler(int ord, float m[3][3], float rot[3]) { /* * Ken Shoemake's recommended algorithm is to convert the * quaternion to a matrix and the matrix to Euler angles. * We do this, of course, without generating unused matrix * elements. */ float zr, sxr, cxr, yr, syr, cyr, xr, szr, czr; static float epsilon = 1.0e-5f; switch ( ord) { case UTL_ROT_ZYX: syr = -m[0][2]; cyr = sqrt_tpl(1 - syr * syr); if (cyr < epsilon) { /* Insufficient accuracy, assume that yr = PI/2 && zr = 0 */ xr = cry_atan2f(-m[2][1], m[1][1]); yr = (syr > 0) ? M_PI_2 : -M_PI_2; /* +/- 90 deg */ zr = 0.0; } else { xr = cry_atan2f(m[1][2], m[2][2]); yr = cry_atan2f(syr, cyr); zr = cry_atan2f(m[0][1], m[0][0]); } break; case UTL_ROT_YZX: szr = m[0][1]; czr = sqrt_tpl(1 - szr * szr); if (czr < epsilon) { /* Insufficient accuracy, assume that zr = +/- PI/2 && yr = 0 */ xr = cry_atan2f(m[1][2], m[2][2]); yr = 0.0; zr = (szr > 0) ? M_PI_2 : -M_PI_2; } else { xr = cry_atan2f(-m[2][1], m[1][1]); yr = cry_atan2f(-m[0][2], m[0][0]); zr = cry_atan2f(szr, czr); } break; case UTL_ROT_ZXY: sxr = m[1][2]; cxr = sqrt_tpl(1 - sxr * sxr); if (cxr < epsilon) { /* Insufficient accuracy, assume that xr = PI/2 && zr = 0 */ xr = (sxr > 0) ? M_PI_2 : -M_PI_2; yr = cry_atan2f(m[2][0], m[0][0]); zr = 0.0; } else { xr = cry_atan2f( sxr, cxr); yr = cry_atan2f(-m[0][2], m[2][2]); zr = cry_atan2f(-m[1][0], m[1][1]); } break; case UTL_ROT_XZY: szr = -m[1][0]; czr = sqrt_tpl(1 - szr * szr); if (czr < epsilon) { /* Insufficient accuracy, assume that zr = PI / 2 && xr = 0 */ xr = 0.0; yr = cry_atan2f(-m[0][2], m[2][2]); zr = (szr > 0) ? M_PI_2 : -M_PI_2; } else { xr = cry_atan2f(m[0][2], m[1][1]); yr = cry_atan2f(m[2][0], m[0][0]); zr = cry_atan2f(szr, czr); } break; case UTL_ROT_YXZ: sxr = -m[2][1]; cxr = sqrt_tpl(1 - sxr * sxr); if (cxr < epsilon) { /* Insufficient accuracy, assume that xr = PI/2 && yr = 0 */ xr = (sxr > 0) ? M_PI_2 : -M_PI_2; yr = 0.0; zr = cry_atan2f(-m[1][0], m[0][0]); } else { xr = cry_atan2f(sxr, cxr); yr = cry_atan2f(m[2][0], m[2][2]); zr = cry_atan2f(m[0][1], m[1][1]); } break; case UTL_ROT_XYZ: syr = m[2][0]; cyr = sqrt_tpl(1 - syr * syr); if (cyr < epsilon) { /* Insufficient accuracy, assume that yr = PI / 2 && xr = 0 */ xr = 0.0; yr = (syr > 0) ? M_PI_2 : -M_PI_2; zr = cry_atan2f(m[0][1], m[1][1]); } else { xr = cry_atan2f(-m[2][1], m[2][2]); yr = cry_atan2f( syr, cyr); zr = cry_atan2f(-m[1][1], m[0][0]); } break; } rot[0] = xr; rot[1] = yr; rot[2] = zr; } /* * ========= utlMtx2Quat ==================== * * SYNOPSIS * Returns the w,x,y,z coordinates of the quaternion * given the rotation matrix. */ static void utlMtx2Quat(float m[3][3], float quat[4]) { // m stores the 3x3 rotation matrix. // Convert it to quaternion. float trace = m[0][0] + m[1][1] + m[2][2]; float s; if (trace > 0.0) { s = sqrt_tpl(trace + 1.0); quat[0] = s*0.5; s = 0.5/s; quat[1] = (m[1][2] - m[2][1])*s; quat[2] = (m[2][0] - m[0][2])*s; quat[3] = (m[0][1] - m[1][0])*s; } else { int i = 0; // i represents index of quaternion, so 0=scalar, 1=xaxis, etc. int nxt[3] = {1,2,0}; // next index for each component. if (m[1][1] > m[0][0]) i = 1; if (m[2][2] > m[i][i]) i = 2; int j = nxt[i]; int k = nxt[j]; s = sqrt_tpl( (m[i][i] - (m[j][j] + m[k][k])) + 1.0); float q[4]; q[i+1] = s*0.5; s=0.5/s; q[0] = (m[j][k] - m[k][j])*s; q[j+1] = (m[i][j]+m[j][i])*s; q[k+1] = (m[i][k]+m[k][i])*s; quat[0] = q[0]; quat[1] = q[1]; quat[2] = q[2]; quat[3] = q[3]; } } /* * ========== DtMatrixGetTranslation ========== * * SYNOPSIS * Return the x,y,z translation components of the * given matrix. The priority order is assumed to be ---. */ int DtMatrixGetTranslation( float *matrix, float *xTrans, float *yTrans, float *zTrans) { DECOMP_MAT dmat; if (matrix) { utlDecompMatrix( matrix, &dmat, "xyz" ); *xTrans = dmat.translate[0]; *yTrans = dmat.translate[1]; *zTrans = dmat.translate[2]; } else { *xTrans = *yTrans = *zTrans = 0.0; } return(1); } /* DtMatrixGetTranslation */ /* * ========== DtMatrixGetQuaternion ========== * * SYNOPSIS * Return the quaternion (scalar, xAxis, yAxis, zAxis) * defining the orientation represented in the given matrix. */ int DtMatrixGetQuaternion(float *matrix, float *scalar, float *xAxis, float *yAxis, float *zAxis) { DECOMP_MAT dmat; if (matrix) { utlDecompMatrix( matrix, &dmat, "xyz" ); *scalar = dmat.quaternion[0]; *xAxis = dmat.quaternion[1]; *yAxis = dmat.quaternion[2]; *zAxis = dmat.quaternion[3]; } else { *scalar = 1.0; *xAxis = *yAxis = *zAxis = 0.0; } return(1); } /* DtMatrixGetQuaternion */ /* * ========== DtMatrixGetRotation ========== * * SYNOPSIS * Return the x,y,z rotation components of the * given matrix. The priority order is assumed to be ---. */ int DtMatrixGetRotation(float *matrix, float *xRotation, float *yRotation, float *zRotation) { DECOMP_MAT dmat; if (matrix) { utlDecompMatrix( matrix, &dmat, "xyz" ); *xRotation = dmat.rotation[0]; *yRotation = dmat.rotation[1]; *zRotation = dmat.rotation[2]; } else { *xRotation = *yRotation = *zRotation = 0.0; } return(1); } /* DtMatrixGetRotation */ /* * ========== DtMatrixGetScale ========== * * SYNOPSIS * Return the x,y,z scale components of the given * matrix. The priority order is assumed to be ---. */ int DtMatrixGetScale(float *matrix, float *xScale, float *yScale, float *zScale) { DECOMP_MAT dmat; if (matrix) { utlDecompMatrix( matrix, &dmat, "xyz" ); *xScale = dmat.scale[0]; *yScale = dmat.scale[1]; *zScale = dmat.scale[2]; } else { *xScale = *yScale = *zScale = 1.0; } return(1); } /* DtMatrixGetScale */ /* * ========== DtMatrixGetTransforms ========== * * SYNOPSIS * Return the x,y,z translation, scale quaternion and * Euler angles in "xyz" order of the given * matrix. */ int DtMatrixGetTransforms(float *matrix, float *translate, float *scale, float *quaternion, float *rotation) { DECOMP_MAT dmat; if (matrix) { utlDecompMatrix( matrix, &dmat, "xyz" ); if (translate) { translate[0] = dmat.translate[0]; translate[1] = dmat.translate[1]; translate[2] = dmat.translate[2]; } if (scale) { scale[0] = dmat.scale[0]; scale[1] = dmat.scale[1]; scale[2] = dmat.scale[2]; } if (quaternion) { quaternion[0] = dmat.quaternion[0]; quaternion[1] = dmat.quaternion[1]; quaternion[2] = dmat.quaternion[2]; quaternion[3] = dmat.quaternion[3]; } if (rotation) { rotation[0] = dmat.rotation[0]; rotation[1] = dmat.rotation[1]; rotation[2] = dmat.rotation[2]; } return(1); } return(0); } //============================================================================== float gSinTable[1024] = { 0.000000,0.001534,0.003068,0.004602,0.006136,0.007670,0.009204,0.010738, 0.012272,0.013805,0.015339,0.016873,0.018407,0.019940,0.021474,0.023008, 0.024541,0.026075,0.027608,0.029142,0.030675,0.032208,0.033741,0.035274, 0.036807,0.038340,0.039873,0.041406,0.042938,0.044471,0.046003,0.047535, 0.049068,0.050600,0.052132,0.053664,0.055195,0.056727,0.058258,0.059790, 0.061321,0.062852,0.064383,0.065913,0.067444,0.068974,0.070505,0.072035, 0.073565,0.075094,0.076624,0.078153,0.079682,0.081211,0.082740,0.084269, 0.085797,0.087326,0.088854,0.090381,0.091909,0.093436,0.094963,0.096490, 0.098017,0.099544,0.101070,0.102596,0.104122,0.105647,0.107172,0.108697, 0.110222,0.111747,0.113271,0.114795,0.116319,0.117842,0.119365,0.120888, 0.122411,0.123933,0.125455,0.126977,0.128498,0.130019,0.131540,0.133061, 0.134581,0.136101,0.137620,0.139139,0.140658,0.142177,0.143695,0.145213, 0.146730,0.148248,0.149765,0.151281,0.152797,0.154313,0.155828,0.157343, 0.158858,0.160372,0.161886,0.163400,0.164913,0.166426,0.167938,0.169450, 0.170962,0.172473,0.173984,0.175494,0.177004,0.178514,0.180023,0.181532, 0.183040,0.184548,0.186055,0.187562,0.189069,0.190575,0.192080,0.193586, 0.195090,0.196595,0.198098,0.199602,0.201105,0.202607,0.204109,0.205610, 0.207111,0.208612,0.210112,0.211611,0.213110,0.214609,0.216107,0.217604, 0.219101,0.220598,0.222094,0.223589,0.225084,0.226578,0.228072,0.229565, 0.231058,0.232550,0.234042,0.235533,0.237024,0.238514,0.240003,0.241492, 0.242980,0.244468,0.245955,0.247442,0.248928,0.250413,0.251898,0.253382, 0.254866,0.256349,0.257831,0.259313,0.260794,0.262275,0.263755,0.265234, 0.266713,0.268191,0.269668,0.271145,0.272621,0.274097,0.275572,0.277046, 0.278520,0.279993,0.281465,0.282937,0.284408,0.285878,0.287347,0.288816, 0.290285,0.291752,0.293219,0.294685,0.296151,0.297616,0.299080,0.300543, 0.302006,0.303468,0.304929,0.306390,0.307850,0.309309,0.310767,0.312225, 0.313682,0.315138,0.316593,0.318048,0.319502,0.320955,0.322408,0.323859, 0.325310,0.326760,0.328210,0.329658,0.331106,0.332553,0.334000,0.335445, 0.336890,0.338334,0.339777,0.341219,0.342661,0.344101,0.345541,0.346980, 0.348419,0.349856,0.351293,0.352729,0.354164,0.355598,0.357031,0.358463, 0.359895,0.361326,0.362756,0.364185,0.365613,0.367040,0.368467,0.369892, 0.371317,0.372741,0.374164,0.375586,0.377007,0.378428,0.379847,0.381266, 0.382683,0.384100,0.385516,0.386931,0.388345,0.389758,0.391170,0.392582, 0.393992,0.395401,0.396810,0.398218,0.399624,0.401030,0.402435,0.403838, 0.405241,0.406643,0.408044,0.409444,0.410843,0.412241,0.413638,0.415034, 0.416430,0.417824,0.419217,0.420609,0.422000,0.423390,0.424780,0.426168, 0.427555,0.428941,0.430326,0.431711,0.433094,0.434476,0.435857,0.437237, 0.438616,0.439994,0.441371,0.442747,0.444122,0.445496,0.446869,0.448241, 0.449611,0.450981,0.452350,0.453717,0.455084,0.456449,0.457813,0.459177, 0.460539,0.461900,0.463260,0.464619,0.465976,0.467333,0.468689,0.470043, 0.471397,0.472749,0.474100,0.475450,0.476799,0.478147,0.479494,0.480839, 0.482184,0.483527,0.484869,0.486210,0.487550,0.488889,0.490226,0.491563, 0.492898,0.494232,0.495565,0.496897,0.498228,0.499557,0.500885,0.502212, 0.503538,0.504863,0.506187,0.507509,0.508830,0.510150,0.511469,0.512786, 0.514103,0.515418,0.516732,0.518045,0.519356,0.520666,0.521975,0.523283, 0.524590,0.525895,0.527199,0.528502,0.529804,0.531104,0.532403,0.533701, 0.534998,0.536293,0.537587,0.538880,0.540171,0.541462,0.542751,0.544039, 0.545325,0.546610,0.547894,0.549177,0.550458,0.551738,0.553017,0.554294, 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0.983105,0.983385,0.983662,0.983937,0.984210,0.984480,0.984749,0.985014, 0.985278,0.985539,0.985798,0.986054,0.986308,0.986560,0.986809,0.987057, 0.987301,0.987544,0.987784,0.988022,0.988258,0.988491,0.988722,0.988950, 0.989177,0.989400,0.989622,0.989841,0.990058,0.990273,0.990485,0.990695, 0.990903,0.991108,0.991311,0.991511,0.991710,0.991906,0.992099,0.992291, 0.992480,0.992666,0.992850,0.993032,0.993212,0.993389,0.993564,0.993737, 0.993907,0.994075,0.994240,0.994404,0.994565,0.994723,0.994879,0.995033, 0.995185,0.995334,0.995481,0.995625,0.995767,0.995907,0.996045,0.996180, 0.996313,0.996443,0.996571,0.996697,0.996820,0.996941,0.997060,0.997176, 0.997290,0.997402,0.997511,0.997618,0.997723,0.997825,0.997925,0.998023, 0.998118,0.998211,0.998302,0.998390,0.998476,0.998559,0.998640,0.998719, 0.998795,0.998870,0.998941,0.999011,0.999078,0.999142,0.999205,0.999265, 0.999322,0.999378,0.999431,0.999481,0.999529,0.999575,0.999619,0.999660, 0.999699,0.999735,0.999769,0.999801,0.999831,0.999858,0.999882,0.999905, 0.999925,0.999942,0.999958,0.999971,0.999981,0.999989,0.999995,0.999999 }; typedef union FastSqrtUnion { float f; unsigned int i; } FastSqrtUnion; unsigned int gFastSqrtTable[0x10000]; // declare table of square roots void build_sqrt_table() { unsigned int i; FastSqrtUnion s; for (i = 0; i <= 0x7FFF; i++) { // Build a float with the bit pattern i as mantissa // and an exponent of 0, stored as 127 s.i = (i << 8) | (0x7F << 23); s.f = (float)sqrt_tpl(s.f); // Take the square root then strip the first 7 bits of // the mantissa into the table gFastSqrtTable[i + 0x8000] = (s.i & 0x7FFFFF); // Repeat the process, this time with an exponent of 1, // stored as 128 s.i = (i << 8) | (0x80 << 23); s.f = (float)sqrt_tpl(s.f); gFastSqrtTable[i] = (s.i & 0x7FFFFF); } } #include /* * Initialize tables, etc for fast math functions. */ void init_math(void) { static bool initialized = false; if (!initialized) { build_sqrt_table(); initialized = true; } } #pragma warning(pop)