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//-----------------------------------------------------------------------------------
// DirectXSH.cpp -- C++ Spherical Harmonics Math Library
//
// Copyright (c) Microsoft Corporation.
// Licensed under the MIT License.
//
// http://go.microsoft.com/fwlink/p/?LinkId=262885
//-------------------------------------------------------------------------------------
#ifdef _MSC_VER
#pragma warning( disable : 4619 4456 5264)
// C4619 #pragma warning warnings
// C4456 declaration hides previous local declaration
// C5264 'const' variable is not used
#endif
#ifdef __clang__
#pragma clang diagnostic ignored "-Wold-style-cast"
#pragma clang diagnostic ignored "-Wshadow"
#pragma clang diagnostic ignored "-Wunused-const-variable"
#pragma clang diagnostic ignored "-Wunused-function"
#pragma clang diagnostic ignored "-Wunknown-warning-option"
#pragma clang diagnostic ignored "-Wunsafe-buffer-usage"
#endif
#include "DirectXSH.h"
#include <cassert>
using namespace DirectX;
namespace
{
#ifdef _PREFAST_
#pragma prefast(disable:246, "generated code by maple (nested const variable definitions)")
#endif
const float fExtraNormFac[XM_SH_MAXORDER] = { 2.0f*sqrtf(XM_PI), 2.0f / 3.0f*sqrtf(3.0f*XM_PI), 2.0f / 5.0f*sqrtf(5.0f*XM_PI), 2.0f / 7.0f*sqrtf(7.0f*XM_PI), 2.0f / 3.0f*sqrtf(XM_PI), 2.0f / 11.0f*sqrtf(11.0f*XM_PI) };
// computes the integral of a constant function over a solid angular
// extent. No error checking - only used internaly. This function
// only returns the Yl0 coefficients, since the rest are zero for
// circularly symmetric functions.
const float ComputeCapInt_t1 = sqrtf(0.3141593E1f);
const float ComputeCapInt_t5 = sqrtf(3.0f);
const float ComputeCapInt_t11 = sqrtf(5.0f);
const float ComputeCapInt_t18 = sqrtf(7.0f);
const float ComputeCapInt_t32 = sqrtf(11.0f);
inline void ComputeCapInt(const size_t order, float angle, float *pR)
{
const float t2 = cosf(angle);
const float t3 = ComputeCapInt_t1*t2;
const float t7 = sinf(angle);
const float t8 = t7*t7;
pR[0] = -t3 + ComputeCapInt_t1;
pR[1] = ComputeCapInt_t5*ComputeCapInt_t1*t8 / 2.0f;
if (order > 2)
{
const float t13 = t2*t2;
pR[2] = -ComputeCapInt_t11*ComputeCapInt_t1*t2*(t13 - 1.0f) / 2.0f;
if (order > 3)
{
const float t19 = ComputeCapInt_t18*ComputeCapInt_t1;
const float t20 = t13*t13;
pR[3] = -5.0f / 8.0f*t19*t20 + 3.0f / 4.0f*t19*t13 - t19 / 8.0f;
if (order > 4)
{
pR[4] = -3.0f / 8.0f*t3*(7.0f*t20 - 10.0f*t13 + 3.0f);
if (order > 5)
{
const float t33 = ComputeCapInt_t32*ComputeCapInt_t1;
pR[5] = -21.0f / 16.0f*t33*t20*t13 + 35.0f / 16.0f*t33*t20 - 15.0f / 16.0f*t33*t13 + t33 / 16.0f;
}
}
}
}
}
// input pF only consists of Yl0 values, normalizes coefficients for directional
// lights.
inline float CosWtInt(const size_t order)
{
const float fCW0 = 0.25f;
const float fCW1 = 0.5f;
const float fCW2 = 5.0f / 16.0f;
//const float fCW3 = 0.0f;
const float fCW4 = -3.0f / 32.0f;
//const float fCW5 = 0.0f;
// order has to be at least linear...
float fRet = fCW0 + fCW1;
if (order > 2) fRet += fCW2;
if (order > 4) fRet += fCW4;
// odd degrees >= 3 evaluate to zero integrated against cosine...
return fRet;
}
const float SHEvalHemisphereLight_fSqrtPi = sqrtf(XM_PI);
const float SHEvalHemisphereLight_fSqrtPi3 = sqrtf(XM_PI / 3.0f);
using REAL = float;
#define CONSTANT(x) (x ## f)
// routine generated programmatically for evaluating SH basis for degree 1
// inputs (x,y,z) are a point on the sphere (i.e., must be unit length)
// output is vector b with SH basis evaluated at (x,y,z).
//
inline void sh_eval_basis_1(REAL x, REAL y, REAL z, REAL b[4])
{
/* m=0 */
// l=0
const REAL p_0_0 = CONSTANT(0.282094791773878140);
b[0] = p_0_0; // l=0,m=0
// l=1
const REAL p_1_0 = CONSTANT(0.488602511902919920)*z;
b[2] = p_1_0; // l=1,m=0
/* m=1 */
const REAL s1 = y;
const REAL c1 = x;
// l=1
const REAL p_1_1 = CONSTANT(-0.488602511902919920);
b[1] = p_1_1*s1; // l=1,m=-1
b[3] = p_1_1*c1; // l=1,m=+1
}
// routine generated programmatically for evaluating SH basis for degree 2
// inputs (x,y,z) are a point on the sphere (i.e., must be unit length)
// output is vector b with SH basis evaluated at (x,y,z).
//
inline void sh_eval_basis_2(REAL x, REAL y, REAL z, REAL b[9])
{
const REAL z2 = z*z;
/* m=0 */
// l=0
const REAL p_0_0 = CONSTANT(0.282094791773878140);
b[0] = p_0_0; // l=0,m=0
// l=1
const REAL p_1_0 = CONSTANT(0.488602511902919920)*z;
b[2] = p_1_0; // l=1,m=0
// l=2
const REAL p_2_0 = CONSTANT(0.946174695757560080)*z2 + CONSTANT(-0.315391565252520050);
b[6] = p_2_0; // l=2,m=0
/* m=1 */
const REAL s1 = y;
const REAL c1 = x;
// l=1
const REAL p_1_1 = CONSTANT(-0.488602511902919920);
b[1] = p_1_1*s1; // l=1,m=-1
b[3] = p_1_1*c1; // l=1,m=+1
// l=2
const REAL p_2_1 = CONSTANT(-1.092548430592079200)*z;
b[5] = p_2_1*s1; // l=2,m=-1
b[7] = p_2_1*c1; // l=2,m=+1
/* m=2 */
const REAL s2 = x*s1 + y*c1;
const REAL c2 = x*c1 - y*s1;
// l=2
const REAL p_2_2 = CONSTANT(0.546274215296039590);
b[4] = p_2_2*s2; // l=2,m=-2
b[8] = p_2_2*c2; // l=2,m=+2
}
// routine generated programmatically for evaluating SH basis for degree 3
// inputs (x,y,z) are a point on the sphere (i.e., must be unit length)
// output is vector b with SH basis evaluated at (x,y,z).
//
void sh_eval_basis_3(REAL x, REAL y, REAL z, REAL b[16])
{
const REAL z2 = z*z;
/* m=0 */
// l=0
const REAL p_0_0 = CONSTANT(0.282094791773878140);
b[0] = p_0_0; // l=0,m=0
// l=1
const REAL p_1_0 = CONSTANT(0.488602511902919920)*z;
b[2] = p_1_0; // l=1,m=0
// l=2
const REAL p_2_0 = CONSTANT(0.946174695757560080)*z2 + CONSTANT(-0.315391565252520050);
b[6] = p_2_0; // l=2,m=0
// l=3
const REAL p_3_0 = z*(CONSTANT(1.865881662950577000)*z2 + CONSTANT(-1.119528997770346200));
b[12] = p_3_0; // l=3,m=0
/* m=1 */
const REAL s1 = y;
const REAL c1 = x;
// l=1
const REAL p_1_1 = CONSTANT(-0.488602511902919920);
b[1] = p_1_1*s1; // l=1,m=-1
b[3] = p_1_1*c1; // l=1,m=+1
// l=2
const REAL p_2_1 = CONSTANT(-1.092548430592079200)*z;
b[5] = p_2_1*s1; // l=2,m=-1
b[7] = p_2_1*c1; // l=2,m=+1
// l=3
const REAL p_3_1 = CONSTANT(-2.285228997322328800)*z2 + CONSTANT(0.457045799464465770);
b[11] = p_3_1*s1; // l=3,m=-1
b[13] = p_3_1*c1; // l=3,m=+1
/* m=2 */
const REAL s2 = x*s1 + y*c1;
const REAL c2 = x*c1 - y*s1;
// l=2
const REAL p_2_2 = CONSTANT(0.546274215296039590);
b[4] = p_2_2*s2; // l=2,m=-2
b[8] = p_2_2*c2; // l=2,m=+2
// l=3
const REAL p_3_2 = CONSTANT(1.445305721320277100)*z;
b[10] = p_3_2*s2; // l=3,m=-2
b[14] = p_3_2*c2; // l=3,m=+2
/* m=3 */
const REAL s3 = x*s2 + y*c2;
const REAL c3 = x*c2 - y*s2;
// l=3
const REAL p_3_3 = CONSTANT(-0.590043589926643520);
b[9] = p_3_3*s3; // l=3,m=-3
b[15] = p_3_3*c3; // l=3,m=+3
}
// routine generated programmatically for evaluating SH basis for degree 4
// inputs (x,y,z) are a point on the sphere (i.e., must be unit length)
// output is vector b with SH basis evaluated at (x,y,z).
//
void sh_eval_basis_4(REAL x, REAL y, REAL z, REAL b[25])
{
const REAL z2 = z*z;
/* m=0 */
// l=0
const REAL p_0_0 = CONSTANT(0.282094791773878140);
b[0] = p_0_0; // l=0,m=0
// l=1
const REAL p_1_0 = CONSTANT(0.488602511902919920)*z;
b[2] = p_1_0; // l=1,m=0
// l=2
const REAL p_2_0 = CONSTANT(0.946174695757560080)*z2 + CONSTANT(-0.315391565252520050);
b[6] = p_2_0; // l=2,m=0
// l=3
const REAL p_3_0 = z*(CONSTANT(1.865881662950577000)*z2 + CONSTANT(-1.119528997770346200));
b[12] = p_3_0; // l=3,m=0
// l=4
const REAL p_4_0 = CONSTANT(1.984313483298443000)*z*p_3_0 + CONSTANT(-1.006230589874905300)*p_2_0;
b[20] = p_4_0; // l=4,m=0
/* m=1 */
const REAL s1 = y;
const REAL c1 = x;
// l=1
const REAL p_1_1 = CONSTANT(-0.488602511902919920);
b[1] = p_1_1*s1; // l=1,m=-1
b[3] = p_1_1*c1; // l=1,m=+1
// l=2
const REAL p_2_1 = CONSTANT(-1.092548430592079200)*z;
b[5] = p_2_1*s1; // l=2,m=-1
b[7] = p_2_1*c1; // l=2,m=+1
// l=3
const REAL p_3_1 = CONSTANT(-2.285228997322328800)*z2 + CONSTANT(0.457045799464465770);
b[11] = p_3_1*s1; // l=3,m=-1
b[13] = p_3_1*c1; // l=3,m=+1
// l=4
const REAL p_4_1 = z*(CONSTANT(-4.683325804901024000)*z2 + CONSTANT(2.007139630671867200));
b[19] = p_4_1*s1; // l=4,m=-1
b[21] = p_4_1*c1; // l=4,m=+1
/* m=2 */
const REAL s2 = x*s1 + y*c1;
const REAL c2 = x*c1 - y*s1;
// l=2
const REAL p_2_2 = CONSTANT(0.546274215296039590);
b[4] = p_2_2*s2; // l=2,m=-2
b[8] = p_2_2*c2; // l=2,m=+2
// l=3
const REAL p_3_2 = CONSTANT(1.445305721320277100)*z;
b[10] = p_3_2*s2; // l=3,m=-2
b[14] = p_3_2*c2; // l=3,m=+2
// l=4
const REAL p_4_2 = CONSTANT(3.311611435151459800)*z2 + CONSTANT(-0.473087347878779980);
b[18] = p_4_2*s2; // l=4,m=-2
b[22] = p_4_2*c2; // l=4,m=+2
/* m=3 */
const REAL s3 = x*s2 + y*c2;
const REAL c3 = x*c2 - y*s2;
// l=3
const REAL p_3_3 = CONSTANT(-0.590043589926643520);
b[9] = p_3_3*s3; // l=3,m=-3
b[15] = p_3_3*c3; // l=3,m=+3
// l=4
const REAL p_4_3 = CONSTANT(-1.770130769779930200)*z;
b[17] = p_4_3*s3; // l=4,m=-3
b[23] = p_4_3*c3; // l=4,m=+3
/* m=4 */
const REAL s4 = x*s3 + y*c3;
const REAL c4 = x*c3 - y*s3;
// l=4
const REAL p_4_4 = CONSTANT(0.625835735449176030);
b[16] = p_4_4*s4; // l=4,m=-4
b[24] = p_4_4*c4; // l=4,m=+4
}
// routine generated programmatically for evaluating SH basis for degree 5
// inputs (x,y,z) are a point on the sphere (i.e., must be unit length)
// output is vector b with SH basis evaluated at (x,y,z).
//
void sh_eval_basis_5(REAL x, REAL y, REAL z, REAL b[36])
{
const REAL z2 = z*z;
/* m=0 */
// l=0
const REAL p_0_0 = CONSTANT(0.282094791773878140);
b[0] = p_0_0; // l=0,m=0
// l=1
const REAL p_1_0 = CONSTANT(0.488602511902919920)*z;
b[2] = p_1_0; // l=1,m=0
// l=2
const REAL p_2_0 = CONSTANT(0.946174695757560080)*z2 + CONSTANT(-0.315391565252520050);
b[6] = p_2_0; // l=2,m=0
// l=3
const REAL p_3_0 = z*(CONSTANT(1.865881662950577000)*z2 + CONSTANT(-1.119528997770346200));
b[12] = p_3_0; // l=3,m=0
// l=4
const REAL p_4_0 = CONSTANT(1.984313483298443000)*z*p_3_0 + CONSTANT(-1.006230589874905300)*p_2_0;
b[20] = p_4_0; // l=4,m=0
// l=5
const REAL p_5_0 = CONSTANT(1.989974874213239700)*z*p_4_0 + CONSTANT(-1.002853072844814000)*p_3_0;
b[30] = p_5_0; // l=5,m=0
/* m=1 */
const REAL s1 = y;
const REAL c1 = x;
// l=1
const REAL p_1_1 = CONSTANT(-0.488602511902919920);
b[1] = p_1_1*s1; // l=1,m=-1
b[3] = p_1_1*c1; // l=1,m=+1
// l=2
const REAL p_2_1 = CONSTANT(-1.092548430592079200)*z;
b[5] = p_2_1*s1; // l=2,m=-1
b[7] = p_2_1*c1; // l=2,m=+1
// l=3
const REAL p_3_1 = CONSTANT(-2.285228997322328800)*z2 + CONSTANT(0.457045799464465770);
b[11] = p_3_1*s1; // l=3,m=-1
b[13] = p_3_1*c1; // l=3,m=+1
// l=4
const REAL p_4_1 = z*(CONSTANT(-4.683325804901024000)*z2 + CONSTANT(2.007139630671867200));
b[19] = p_4_1*s1; // l=4,m=-1
b[21] = p_4_1*c1; // l=4,m=+1
// l=5
const REAL p_5_1 = CONSTANT(2.031009601158990200)*z*p_4_1 + CONSTANT(-0.991031208965114650)*p_3_1;
b[29] = p_5_1*s1; // l=5,m=-1
b[31] = p_5_1*c1; // l=5,m=+1
/* m=2 */
const REAL s2 = x*s1 + y*c1;
const REAL c2 = x*c1 - y*s1;
// l=2
const REAL p_2_2 = CONSTANT(0.546274215296039590);
b[4] = p_2_2*s2; // l=2,m=-2
b[8] = p_2_2*c2; // l=2,m=+2
// l=3
const REAL p_3_2 = CONSTANT(1.445305721320277100)*z;
b[10] = p_3_2*s2; // l=3,m=-2
b[14] = p_3_2*c2; // l=3,m=+2
// l=4
const REAL p_4_2 = CONSTANT(3.311611435151459800)*z2 + CONSTANT(-0.473087347878779980);
b[18] = p_4_2*s2; // l=4,m=-2
b[22] = p_4_2*c2; // l=4,m=+2
// l=5
const REAL p_5_2 = z*(CONSTANT(7.190305177459987500)*z2 + CONSTANT(-2.396768392486662100));
b[28] = p_5_2*s2; // l=5,m=-2
b[32] = p_5_2*c2; // l=5,m=+2
/* m=3 */
const REAL s3 = x*s2 + y*c2;
const REAL c3 = x*c2 - y*s2;
// l=3
const REAL p_3_3 = CONSTANT(-0.590043589926643520);
b[9] = p_3_3*s3; // l=3,m=-3
b[15] = p_3_3*c3; // l=3,m=+3
// l=4
const REAL p_4_3 = CONSTANT(-1.770130769779930200)*z;
b[17] = p_4_3*s3; // l=4,m=-3
b[23] = p_4_3*c3; // l=4,m=+3
// l=5
const REAL p_5_3 = CONSTANT(-4.403144694917253700)*z2 + CONSTANT(0.489238299435250430);
b[27] = p_5_3*s3; // l=5,m=-3
b[33] = p_5_3*c3; // l=5,m=+3
/* m=4 */
const REAL s4 = x*s3 + y*c3;
const REAL c4 = x*c3 - y*s3;
// l=4
const REAL p_4_4 = CONSTANT(0.625835735449176030);
b[16] = p_4_4*s4; // l=4,m=-4
b[24] = p_4_4*c4; // l=4,m=+4
// l=5
const REAL p_5_4 = CONSTANT(2.075662314881041100)*z;
b[26] = p_5_4*s4; // l=5,m=-4
b[34] = p_5_4*c4; // l=5,m=+4
/* m=5 */
const REAL s5 = x*s4 + y*c4;
const REAL c5 = x*c4 - y*s4;
// l=5
const REAL p_5_5 = CONSTANT(-0.656382056840170150);
b[25] = p_5_5*s5; // l=5,m=-5
b[35] = p_5_5*c5; // l=5,m=+5
}
const REAL M_PIjs = (REAL)(4.0*atan(1.0));
const REAL maxang = (REAL)(M_PIjs / 2);
const int NSH0 = 1;
const int NSH1 = 4;
const int NSH2 = 9;
const int NSH3 = 16;
const int NSH4 = 25;
const int NSH5 = 36;
const int NSH6 = 49;
const int NSH7 = 64;
const int NSH8 = 81;
const int NSH9 = 100;
const int NL0 = 1;
const int NL1 = 3;
const int NL2 = 5;
const int NL3 = 7;
const int NL4 = 9;
const int NL5 = 11;
const int NL6 = 13;
const int NL7 = 15;
const int NL8 = 17;
const int NL9 = 19;
inline void rot(REAL ct, REAL st, REAL x, REAL y, REAL &xout, REAL &yout)
{
xout = x*ct - y*st;
yout = y*ct + x*st;
}
inline void rot_inv(REAL ct, REAL st, REAL x, REAL y, REAL &xout, REAL &yout)
{
xout = x*ct + y*st;
yout = y*ct - x*st;
}
inline void rot_1(REAL ct, REAL st, REAL ctm[1], REAL stm[1])
{
ctm[0] = ct;
stm[0] = st;
}
inline void rot_2(REAL ct, REAL st, REAL ctm[2], REAL stm[2])
{
REAL ct2 = CONSTANT(2.0)*ct;
ctm[0] = ct;
stm[0] = st;
ctm[1] = ct2*ct - CONSTANT(1.0);
stm[1] = ct2*st;
}
inline void rot_3(REAL ct, REAL st, REAL ctm[3], REAL stm[3])
{
REAL ct2 = CONSTANT(2.0)*ct;
ctm[0] = ct;
stm[0] = st;
ctm[1] = ct2*ct - CONSTANT(1.0);
stm[1] = ct2*st;
ctm[2] = ct2*ctm[1] - ct;
stm[2] = ct2*stm[1] - st;
}
inline void rot_4(REAL ct, REAL st, REAL ctm[4], REAL stm[4])
{
REAL ct2 = CONSTANT(2.0)*ct;
ctm[0] = ct;
stm[0] = st;
ctm[1] = ct2*ct - CONSTANT(1.0);
stm[1] = ct2*st;
ctm[2] = ct2*ctm[1] - ct;
stm[2] = ct2*stm[1] - st;
ctm[3] = ct2*ctm[2] - ctm[1];
stm[3] = ct2*stm[2] - stm[1];
}
inline void rot_5(REAL ct, REAL st, REAL ctm[5], REAL stm[5])
{
REAL ct2 = CONSTANT(2.0)*ct;
ctm[0] = ct;
stm[0] = st;
ctm[1] = ct2*ct - CONSTANT(1.0);
stm[1] = ct2*st;
ctm[2] = ct2*ctm[1] - ct;
stm[2] = ct2*stm[1] - st;
ctm[3] = ct2*ctm[2] - ctm[1];
stm[3] = ct2*stm[2] - stm[1];
ctm[4] = ct2*ctm[3] - ctm[2];
stm[4] = ct2*stm[3] - stm[2];
}
inline void sh_rotz_1(REAL ctm[1], REAL stm[1], REAL y[NL1], REAL yr[NL1])
{
yr[1] = y[1];
rot_inv(ctm[0], stm[0], y[0], y[2], yr[0], yr[2]);
}
inline void sh_rotz_2(REAL ctm[2], REAL stm[2], REAL y[NL2], REAL yr[NL2])
{
yr[2] = y[2];
rot_inv(ctm[0], stm[0], y[1], y[3], yr[1], yr[3]);
rot_inv(ctm[1], stm[1], y[0], y[4], yr[0], yr[4]);
}
inline void sh_rotz_3(REAL ctm[3], REAL stm[3], REAL y[NL3], REAL yr[NL3])
{
yr[3] = y[3];
rot_inv(ctm[0], stm[0], y[2], y[4], yr[2], yr[4]);
rot_inv(ctm[1], stm[1], y[1], y[5], yr[1], yr[5]);
rot_inv(ctm[2], stm[2], y[0], y[6], yr[0], yr[6]);
}
inline void sh_rotz_4(REAL ctm[4], REAL stm[4], REAL y[NL4], REAL yr[NL4])
{
yr[4] = y[4];
rot_inv(ctm[0], stm[0], y[3], y[5], yr[3], yr[5]);
rot_inv(ctm[1], stm[1], y[2], y[6], yr[2], yr[6]);
rot_inv(ctm[2], stm[2], y[1], y[7], yr[1], yr[7]);
rot_inv(ctm[3], stm[3], y[0], y[8], yr[0], yr[8]);
}
inline void sh_rotz_5(REAL ctm[5], REAL stm[5], REAL y[NL5], REAL yr[NL5])
{
yr[5] = y[5];
rot_inv(ctm[0], stm[0], y[4], y[6], yr[4], yr[6]);
rot_inv(ctm[1], stm[1], y[3], y[7], yr[3], yr[7]);
rot_inv(ctm[2], stm[2], y[2], y[8], yr[2], yr[8]);
rot_inv(ctm[3], stm[3], y[1], y[9], yr[1], yr[9]);
rot_inv(ctm[4], stm[4], y[0], y[10], yr[0], yr[10]);
}
// rotation code generated programmatically by rotatex (2000x4000 samples, eps=1e-008)
const REAL fx_1_001 = (REAL)(sqrt(1.0) / 1.0); // 1
const REAL fx_1_002 = (REAL)(-sqrt(1.0) / 1.0); // -1.00000030843
inline void sh_rotx90_1(REAL y[], REAL yr[])
{
yr[0] = fx_1_001*y[1];
yr[1] = fx_1_002*y[0];
yr[2] = fx_1_001*y[2];
};
inline void sh_rotx90_inv_1(REAL y[], REAL yr[])
{
yr[0] = fx_1_002*y[1];
yr[1] = fx_1_001*y[0];
yr[2] = fx_1_001*y[2];
}
const REAL fx_2_001 = (REAL)(sqrt(4.0) / 2.0); // 1
const REAL fx_2_002 = (REAL)(-sqrt(4.0) / 2.0); // -1
const REAL fx_2_003 = (REAL)(-sqrt(1.0) / 2.0); // -0.500000257021
const REAL fx_2_004 = (REAL)(-sqrt(3.0) / 2.0); // -0.866025848959
const REAL fx_2_005 = (REAL)(sqrt(1.0) / 2.0); // 0.5
inline void sh_rotx90_2(REAL y[], REAL yr[])
{
yr[0] = fx_2_001*y[3];
yr[1] = fx_2_002*y[1];
yr[2] = fx_2_003*y[2] + fx_2_004*y[4];
yr[3] = fx_2_002*y[0];
yr[4] = fx_2_004*y[2] + fx_2_005*y[4];
};
inline void sh_rotx90_inv_2(REAL y[], REAL yr[])
{
yr[0] = fx_2_002*y[3];
yr[1] = fx_2_002*y[1];
yr[2] = fx_2_003*y[2] + fx_2_004*y[4];
yr[3] = fx_2_001*y[0];
yr[4] = fx_2_004*y[2] + fx_2_005*y[4];
}
const REAL fx_3_001 = (REAL)(-sqrt(10.0) / 4.0); // -0.790569415042
const REAL fx_3_002 = (REAL)(sqrt(6.0) / 4.0); // 0.612372435696
const REAL fx_3_003 = (REAL)(-sqrt(16.0) / 4.0); // -1
const REAL fx_3_004 = (REAL)(-sqrt(6.0) / 4.0); // -0.612372435695
const REAL fx_3_005 = (REAL)(-sqrt(1.0) / 4.0); // -0.25
const REAL fx_3_006 = (REAL)(-sqrt(15.0) / 4.0); // -0.968245836551
const REAL fx_3_007 = (REAL)(sqrt(1.0) / 4.0); // 0.25
const REAL fx_3_008 = (REAL)(sqrt(10.0) / 4.0); // 0.790569983984
inline void sh_rotx90_3(REAL y[], REAL yr[])
{
yr[0] = fx_3_001*y[3] + fx_3_002*y[5];
yr[1] = fx_3_003*y[1];
yr[2] = fx_3_004*y[3] + fx_3_001*y[5];
yr[3] = fx_3_008*y[0] + fx_3_002*y[2];
yr[4] = fx_3_005*y[4] + fx_3_006*y[6];
yr[5] = fx_3_004*y[0] - fx_3_001*y[2];
yr[6] = fx_3_006*y[4] + fx_3_007*y[6];
};
inline void sh_rotx90_inv_3(REAL y[], REAL yr[])
{
yr[0] = fx_3_008*y[3] + fx_3_004*y[5];
yr[1] = fx_3_003*y[1];
yr[2] = fx_3_002*y[3] - fx_3_001*y[5];
yr[3] = fx_3_001*y[0] + fx_3_004*y[2];
yr[4] = fx_3_005*y[4] + fx_3_006*y[6];
yr[5] = fx_3_002*y[0] + fx_3_001*y[2];
yr[6] = fx_3_006*y[4] + fx_3_007*y[6];
}
const REAL fx_4_001 = (REAL)(-sqrt(56.0) / 8.0); // -0.935414346694
const REAL fx_4_002 = (REAL)(sqrt(8.0) / 8.0); // 0.353553390593
const REAL fx_4_003 = (REAL)(-sqrt(36.0) / 8.0); // -0.75
const REAL fx_4_004 = (REAL)(sqrt(28.0) / 8.0); // 0.661437827766
const REAL fx_4_005 = (REAL)(-sqrt(8.0) / 8.0); // -0.353553390593
const REAL fx_4_006 = (REAL)(sqrt(36.0) / 8.0); // 0.749999999999
const REAL fx_4_007 = (REAL)(sqrt(9.0) / 8.0); // 0.37500034698
const REAL fx_4_008 = (REAL)(sqrt(20.0) / 8.0); // 0.559017511622
const REAL fx_4_009 = (REAL)(sqrt(35.0) / 8.0); // 0.739510657141
const REAL fx_4_010 = (REAL)(sqrt(16.0) / 8.0); // 0.5
const REAL fx_4_011 = (REAL)(-sqrt(28.0) / 8.0); // -0.661437827766
const REAL fx_4_012 = (REAL)(sqrt(1.0) / 8.0); // 0.125
const REAL fx_4_013 = (REAL)(sqrt(56.0) / 8.0); // 0.935414346692
inline void sh_rotx90_4(REAL y[], REAL yr[])
{
yr[0] = fx_4_001*y[5] + fx_4_002*y[7];
yr[1] = fx_4_003*y[1] + fx_4_004*y[3];
yr[2] = fx_4_005*y[5] + fx_4_001*y[7];
yr[3] = fx_4_004*y[1] + fx_4_006*y[3];
yr[4] = fx_4_007*y[4] + fx_4_008*y[6] + fx_4_009*y[8];
yr[5] = fx_4_013*y[0] + fx_4_002*y[2];
yr[6] = fx_4_008*y[4] + fx_4_010*y[6] + fx_4_011*y[8];
yr[7] = fx_4_005*y[0] - fx_4_001*y[2];
yr[8] = fx_4_009*y[4] + fx_4_011*y[6] + fx_4_012*y[8];
};
inline void sh_rotx90_inv_4(REAL y[], REAL yr[])
{
yr[0] = fx_4_013*y[5] + fx_4_005*y[7];
yr[1] = fx_4_003*y[1] + fx_4_004*y[3];
yr[2] = fx_4_002*y[5] - fx_4_001*y[7];
yr[3] = fx_4_004*y[1] + fx_4_006*y[3];
yr[4] = fx_4_007*y[4] + fx_4_008*y[6] + fx_4_009*y[8];
yr[5] = fx_4_001*y[0] + fx_4_005*y[2];
yr[6] = fx_4_008*y[4] + fx_4_010*y[6] + fx_4_011*y[8];
yr[7] = fx_4_002*y[0] + fx_4_001*y[2];
yr[8] = fx_4_009*y[4] + fx_4_011*y[6] + fx_4_012*y[8];
}
const REAL fx_5_001 = (REAL)(sqrt(126.0) / 16.0); // 0.70156076002
const REAL fx_5_002 = (REAL)(-sqrt(120.0) / 16.0); // -0.684653196882
const REAL fx_5_003 = (REAL)(sqrt(10.0) / 16.0); // 0.197642353761
const REAL fx_5_004 = (REAL)(-sqrt(64.0) / 16.0); // -0.5
const REAL fx_5_005 = (REAL)(sqrt(192.0) / 16.0); // 0.866025403784
const REAL fx_5_006 = (REAL)(sqrt(70.0) / 16.0); // 0.522912516584
const REAL fx_5_007 = (REAL)(sqrt(24.0) / 16.0); // 0.306186217848
const REAL fx_5_008 = (REAL)(-sqrt(162.0) / 16.0); // -0.795495128835
const REAL fx_5_009 = (REAL)(sqrt(64.0) / 16.0); // 0.5
const REAL fx_5_010 = (REAL)(sqrt(60.0) / 16.0); // 0.484122918274
const REAL fx_5_011 = (REAL)(sqrt(112.0) / 16.0); // 0.661437827763
const REAL fx_5_012 = (REAL)(sqrt(84.0) / 16.0); // 0.572821961867
const REAL fx_5_013 = (REAL)(sqrt(4.0) / 16.0); // 0.125
const REAL fx_5_014 = (REAL)(sqrt(42.0) / 16.0); // 0.405046293649
const REAL fx_5_015 = (REAL)(sqrt(210.0) / 16.0); // 0.905711046633
const REAL fx_5_016 = (REAL)(sqrt(169.0) / 16.0); // 0.8125
const REAL fx_5_017 = (REAL)(-sqrt(45.0) / 16.0); // -0.419262745781
const REAL fx_5_018 = (REAL)(sqrt(1.0) / 16.0); // 0.0625
const REAL fx_5_019 = (REAL)(-sqrt(126.0) / 16.0); // -0.701561553415
const REAL fx_5_020 = (REAL)(sqrt(120.0) / 16.0); // 0.684653196881
const REAL fx_5_021 = (REAL)(-sqrt(10.0) / 16.0); // -0.197642353761
const REAL fx_5_022 = (REAL)(-sqrt(70.0) / 16.0); // -0.522913107945
const REAL fx_5_023 = (REAL)(-sqrt(60.0) / 16.0); // -0.48412346577
inline void sh_rotx90_5(REAL y[], REAL yr[])
{
yr[0] = fx_5_001*y[5] + fx_5_002*y[7] + fx_5_003*y[9];
yr[1] = fx_5_004*y[1] + fx_5_005*y[3];
yr[2] = fx_5_006*y[5] + fx_5_007*y[7] + fx_5_008*y[9];
yr[3] = fx_5_005*y[1] + fx_5_009*y[3];
yr[4] = fx_5_010*y[5] + fx_5_011*y[7] + fx_5_012*y[9];
yr[5] = fx_5_019*y[0] + fx_5_022*y[2] + fx_5_023*y[4];
yr[6] = fx_5_013*y[6] + fx_5_014*y[8] + fx_5_015*y[10];
yr[7] = fx_5_020*y[0] - fx_5_007*y[2] - fx_5_011*y[4];
yr[8] = fx_5_014*y[6] + fx_5_016*y[8] + fx_5_017*y[10];
yr[9] = fx_5_021*y[0] - fx_5_008*y[2] - fx_5_012*y[4];
yr[10] = fx_5_015*y[6] + fx_5_017*y[8] + fx_5_018*y[10];
};
inline void sh_rotx90_inv_5(REAL y[], REAL yr[])
{
yr[0] = fx_5_019*y[5] + fx_5_020*y[7] + fx_5_021*y[9];
yr[1] = fx_5_004*y[1] + fx_5_005*y[3];
yr[2] = fx_5_022*y[5] - fx_5_007*y[7] - fx_5_008*y[9];
yr[3] = fx_5_005*y[1] + fx_5_009*y[3];
yr[4] = fx_5_023*y[5] - fx_5_011*y[7] - fx_5_012*y[9];
yr[5] = fx_5_001*y[0] + fx_5_006*y[2] + fx_5_010*y[4];
yr[6] = fx_5_013*y[6] + fx_5_014*y[8] + fx_5_015*y[10];
yr[7] = fx_5_002*y[0] + fx_5_007*y[2] + fx_5_011*y[4];
yr[8] = fx_5_014*y[6] + fx_5_016*y[8] + fx_5_017*y[10];
yr[9] = fx_5_003*y[0] + fx_5_008*y[2] + fx_5_012*y[4];
yr[10] = fx_5_015*y[6] + fx_5_017*y[8] + fx_5_018*y[10];
}
inline void sh_rot_1(REAL m[3 * 3], REAL y[NL1], REAL yr[NL1])
{
REAL yr0 = m[4] * y[0] - m[5] * y[1] + m[3] * y[2];
REAL yr1 = m[8] * y[1] - m[7] * y[0] - m[6] * y[2];
REAL yr2 = m[1] * y[0] - m[2] * y[1] + m[0] * y[2];
yr[0] = yr0;
yr[1] = yr1;
yr[2] = yr2;
}
inline void sh_roty_1(REAL ctm[1], REAL stm[1], REAL y[NL1], REAL yr[NL1])
{
yr[0] = y[0];
rot_inv(ctm[0], stm[0], y[1], y[2], yr[1], yr[2]);
}
inline void sh_roty_2(REAL ctm[2], REAL stm[2], REAL y[NL2], REAL yr[NL2])
{
REAL ytmp[NL2];
sh_rotx90_2(y, yr);
sh_rotz_2(ctm, stm, yr, ytmp);
sh_rotx90_inv_2(ytmp, yr);
}
inline void sh_roty_3(REAL ctm[3], REAL stm[3], REAL y[NL3], REAL yr[NL3])
{
REAL ytmp[NL3];
sh_rotx90_3(y, yr);
sh_rotz_3(ctm, stm, yr, ytmp);
sh_rotx90_inv_3(ytmp, yr);
}
inline void sh_roty_4(REAL ctm[4], REAL stm[4], REAL y[NL4], REAL yr[NL4])
{
REAL ytmp[NL4];
sh_rotx90_4(y, yr);
sh_rotz_4(ctm, stm, yr, ytmp);
sh_rotx90_inv_4(ytmp, yr);
}
inline void sh_roty_5(REAL ctm[5], REAL stm[5], REAL y[NL5], REAL yr[NL5])
{
REAL ytmp[NL5];
sh_rotx90_5(y, yr);
sh_rotz_5(ctm, stm, yr, ytmp);
sh_rotx90_inv_5(ytmp, yr);
}
#define ROT_TOL CONSTANT(1e-4)
/*
Finds cosine,sine pairs for zyz rotation (i.e. rotation R_z2 R_y R_z1 v).
The rotation is one which maps mx to (1,0,0) and mz to (0,0,1).
*/
inline void zyz(REAL m[3 * 3], REAL &zc1, REAL &zs1, REAL &yc, REAL &ys, REAL &zc2, REAL &zs2)
{
REAL cz = m[8];
// rotate so that (cx,cy,0) aligns to (1,0,0)
REAL cxylen = (REAL)sqrtf(1.0f - cz*cz);
if (cxylen >= ROT_TOL)
{
// if above is a NaN, will do the correct thing
yc = cz;
ys = cxylen;
REAL len67inv = 1.0f / sqrtf(m[6] * m[6] + m[7] * m[7]);
zc1 = -m[6] * len67inv;
zs1 = m[7] * len67inv;
REAL len25inv = 1.0f / sqrtf(m[2] * m[2] + m[5] * m[5]);
zc2 = m[2] * len25inv;
zs2 = m[5] * len25inv;
}
else { // m[6],m[7],m[8] already aligned to (0,0,1)
zc1 = 1.0; zs1 = 0.0; // identity
yc = cz; ys = 0.0; // identity
zc2 = m[0] * cz; zs2 = -m[1]; // align x axis (mx[0],mx[1],0) to (1,0,0)
}
}
inline void sh_rotzyz_2(REAL zc1m[2], REAL zs1m[2], REAL ycm[2], REAL ysm[2], REAL zc2m[2], REAL zs2m[2], REAL y[NL2], REAL yr[NL2])
{
REAL ytmp[NL2];
sh_rotz_2(zc1m, zs1m, y, yr);
sh_roty_2(ycm, ysm, yr, ytmp);
sh_rotz_2(zc2m, zs2m, ytmp, yr);
}
inline void sh_rotzyz_3(REAL zc1m[3], REAL zs1m[3], REAL ycm[3], REAL ysm[3], REAL zc2m[3], REAL zs2m[3], REAL y[NL3], REAL yr[NL3])
{
REAL ytmp[NL3];
sh_rotz_3(zc1m, zs1m, y, yr);
sh_roty_3(ycm, ysm, yr, ytmp);
sh_rotz_3(zc2m, zs2m, ytmp, yr);
}
inline void sh_rotzyz_4(REAL zc1m[4], REAL zs1m[4], REAL ycm[4], REAL ysm[4], REAL zc2m[4], REAL zs2m[4], REAL y[NL4], REAL yr[NL4])
{
REAL ytmp[NL4];
sh_rotz_4(zc1m, zs1m, y, yr);
sh_roty_4(ycm, ysm, yr, ytmp);
sh_rotz_4(zc2m, zs2m, ytmp, yr);
}
inline void sh_rotzyz_5(REAL zc1m[5], REAL zs1m[5], REAL ycm[5], REAL ysm[5], REAL zc2m[5], REAL zs2m[5], REAL y[NL5], REAL yr[NL5])
{
REAL ytmp[NL5];
sh_rotz_5(zc1m, zs1m, y, yr);
sh_roty_5(ycm, ysm, yr, ytmp);
sh_rotz_5(zc2m, zs2m, ytmp, yr);
}
inline void sh3_rot(REAL m[3 * 3], REAL zc1, REAL zs1, REAL yc, REAL ys, REAL zc2, REAL zs2, REAL y[NSH3], REAL yr[NSH3])
{
REAL zc1m[3], zs1m[3];
rot_3(zc1, zs1, zc1m, zs1m);
REAL ycm[3], ysm[3];
rot_3(yc, ys, ycm, ysm);
REAL zc2m[3], zs2m[3];
rot_3(zc2, zs2, zc2m, zs2m);
yr[0] = y[0];
sh_rot_1(m, y + NSH0, yr + NSH0);
sh_rotzyz_2(zc1m, zs1m, ycm, ysm, zc2m, zs2m, y + NSH1, yr + NSH1);
sh_rotzyz_3(zc1m, zs1m, ycm, ysm, zc2m, zs2m, y + NSH2, yr + NSH2);
}
inline void sh4_rot(REAL m[3 * 3], REAL zc1, REAL zs1, REAL yc, REAL ys, REAL zc2, REAL zs2, REAL y[NSH4], REAL yr[NSH4])
{
REAL zc1m[4], zs1m[4];
rot_4(zc1, zs1, zc1m, zs1m);
REAL ycm[4], ysm[4];
rot_4(yc, ys, ycm, ysm);
REAL zc2m[4], zs2m[4];
rot_4(zc2, zs2, zc2m, zs2m);
yr[0] = y[0];
sh_rot_1(m, y + NSH0, yr + NSH0);
sh_rotzyz_2(zc1m, zs1m, ycm, ysm, zc2m, zs2m, y + NSH1, yr + NSH1);
sh_rotzyz_3(zc1m, zs1m, ycm, ysm, zc2m, zs2m, y + NSH2, yr + NSH2);
sh_rotzyz_4(zc1m, zs1m, ycm, ysm, zc2m, zs2m, y + NSH3, yr + NSH3);
}
inline void sh5_rot(REAL m[3 * 3], REAL zc1, REAL zs1, REAL yc, REAL ys, REAL zc2, REAL zs2, REAL y[NSH5], REAL yr[NSH5])
{
REAL zc1m[5], zs1m[5];
rot_5(zc1, zs1, zc1m, zs1m);
REAL ycm[5], ysm[5];
rot_5(yc, ys, ycm, ysm);
REAL zc2m[5], zs2m[5];
rot_5(zc2, zs2, zc2m, zs2m);
yr[0] = y[0];
sh_rot_1(m, y + NSH0, yr + NSH0);
sh_rotzyz_2(zc1m, zs1m, ycm, ysm, zc2m, zs2m, y + NSH1, yr + NSH1);
sh_rotzyz_3(zc1m, zs1m, ycm, ysm, zc2m, zs2m, y + NSH2, yr + NSH2);
sh_rotzyz_4(zc1m, zs1m, ycm, ysm, zc2m, zs2m, y + NSH3, yr + NSH3);
sh_rotzyz_5(zc1m, zs1m, ycm, ysm, zc2m, zs2m, y + NSH4, yr + NSH4);
}
inline void sh1_rot(REAL m[3 * 3], REAL y[NSH1], REAL yr[NSH1])
{
yr[0] = y[0];
sh_rot_1(m, y + NSH0, yr + NSH0);
}
inline void sh3_rot(REAL m[3 * 3], REAL y[NSH3], REAL yr[NSH3])
{
REAL zc1, zs1, yc, ys, zc2, zs2;
zyz(m, zc1, zs1, yc, ys, zc2, zs2);
sh3_rot(m, zc1, zs1, yc, ys, zc2, zs2, y, yr);
}
inline void sh4_rot(REAL m[3 * 3], REAL y[NSH4], REAL yr[NSH4])
{
REAL zc1, zs1, yc, ys, zc2, zs2;
zyz(m, zc1, zs1, yc, ys, zc2, zs2);
sh4_rot(m, zc1, zs1, yc, ys, zc2, zs2, y, yr);
}
inline void sh5_rot(REAL m[3 * 3], REAL y[NSH5], REAL yr[NSH5])
{
REAL zc1, zs1, yc, ys, zc2, zs2;
zyz(m, zc1, zs1, yc, ys, zc2, zs2);
sh5_rot(m, zc1, zs1, yc, ys, zc2, zs2, y, yr);
}
// simple matrix vector multiply for a square matrix (only used by ZRotation)
inline void SimpMatMul(size_t dim, const float *matrix, const float *input, float *result)
{
for (size_t iR = 0; iR < dim; ++iR)
{
result[iR + 0] = matrix[iR*dim + 0] * input[0];
for (size_t iC = 1; iC < dim; ++iC)
{
result[iR] += matrix[iR*dim + iC] * input[iC];
}
}
}
}; // anonymous namespace
//-------------------------------------------------------------------------------------
// Evaluates the Spherical Harmonic basis functions
//
// http://msdn.microsoft.com/en-us/library/windows/desktop/bb205448.aspx
//-------------------------------------------------------------------------------------
_Use_decl_annotations_
float* XM_CALLCONV DirectX::XMSHEvalDirection(
float *result,
size_t order,
FXMVECTOR dir) noexcept
{
if (!result)
return nullptr;
XMFLOAT4A dv;
XMStoreFloat4A(&dv, dir);
const float fX = dv.x;
const float fY = dv.y;
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