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//-------------------------------------------------------------------------------------
// DirectXSH.cpp -- C++ Spherical Harmonics Math Library
//
// THIS CODE AND INFORMATION IS PROVIDED "AS IS" WITHOUT WARRANTY OF
// ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING BUT NOT LIMITED TO
// THE IMPLIED WARRANTIES OF MERCHANTABILITY AND/OR FITNESS FOR A
// PARTICULAR PURPOSE.
//
// Copyright (c) Microsoft Corporation. All rights reserved.
//
// http://go.microsoft.com/fwlink/p/?LinkId=262885
//-------------------------------------------------------------------------------------
#include "DirectXSH.h"
#include <assert.h>
using namespace DirectX;
#pragma warning( disable : 4619 4456 )
namespace
{
#pragma prefast(disable:246, "generated code by maple (nested const variable definitions)")
static 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.
static const float ComputeCapInt_t1 = sqrtf(0.3141593E1f);
static const float ComputeCapInt_t5 = sqrtf(3.0f);
static const float ComputeCapInt_t11 = sqrtf(5.0f);
static const float ComputeCapInt_t18 = sqrtf(7.0f);
static const float ComputeCapInt_t32 = sqrtf(11.0f);
static 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.
static 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;
}
static const float SHEvalHemisphereLight_fSqrtPi = sqrtf(XM_PI);
static const float SHEvalHemisphereLight_fSqrtPi3 = sqrtf(XM_PI/3.0f);
typedef float REAL;
#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 static 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 static 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).
//
static 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).
//
static 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).
//
static 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
}
static const REAL M_PIjs = (REAL) (4.0*atan(1.0));
static const REAL maxang = (REAL) (M_PIjs/2);
static const int NSH0 = 1;
static const int NSH1 = 4;
static const int NSH2 = 9;
static const int NSH3 = 16;
static const int NSH4 = 25;
static const int NSH5 = 36;
static const int NSH6 = 49;
static const int NSH7 = 64;
static const int NSH8 = 81;
static const int NSH9 = 100;
static const int NL0 = 1;
static const int NL1 = 3;
static const int NL2 = 5;
static const int NL3 = 7;
static const int NL4 = 9;
static const int NL5 = 11;
static const int NL6 = 13;
static const int NL7 = 15;
static const int NL8 = 17;
static const int NL9 = 19;
static 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;
}
static 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;
}
static inline void rot_1(REAL ct,REAL st,REAL ctm[1],REAL stm[1])
{
ctm[0] = ct;
stm[0] = st;
}
static 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;
}
static 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;
}
static 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];
}
static 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];
}
static 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]);
}
static 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]);
}
static 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]);
}
static 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]);
}
static 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)
static REAL fx_1_001 = (REAL) ( sqrt(1.0)/1.0); // 1
static REAL fx_1_002 = (REAL) (-sqrt(1.0)/1.0); // -1.00000030843
static 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];
};
static 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];
}
static REAL fx_2_001 = (REAL) ( sqrt(4.0)/2.0); // 1
static REAL fx_2_002 = (REAL) (-sqrt(4.0)/2.0); // -1
static REAL fx_2_003 = (REAL) (-sqrt(1.0)/2.0); // -0.500000257021
static REAL fx_2_004 = (REAL) (-sqrt(3.0)/2.0); // -0.866025848959
static REAL fx_2_005 = (REAL) ( sqrt(1.0)/2.0); // 0.5
static 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];
};
static 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];
}
static REAL fx_3_001 = (REAL) (-sqrt(10.0)/4.0); // -0.790569415042
static REAL fx_3_002 = (REAL) ( sqrt(6.0)/4.0); // 0.612372435696
static REAL fx_3_003 = (REAL) (-sqrt(16.0)/4.0); // -1
static REAL fx_3_004 = (REAL) (-sqrt(6.0)/4.0); // -0.612372435695
static REAL fx_3_005 = (REAL) (-sqrt(1.0)/4.0); // -0.25
static REAL fx_3_006 = (REAL) (-sqrt(15.0)/4.0); // -0.968245836551
static REAL fx_3_007 = (REAL) ( sqrt(1.0)/4.0); // 0.25
static REAL fx_3_008 = (REAL) ( sqrt(10.0)/4.0); // 0.790569983984
static 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];
};
static 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];
}
static REAL fx_4_001 = (REAL) (-sqrt(56.0)/8.0); // -0.935414346694
static REAL fx_4_002 = (REAL) ( sqrt(8.0)/8.0); // 0.353553390593
static REAL fx_4_003 = (REAL) (-sqrt(36.0)/8.0); // -0.75
static REAL fx_4_004 = (REAL) ( sqrt(28.0)/8.0); // 0.661437827766
static REAL fx_4_005 = (REAL) (-sqrt(8.0)/8.0); // -0.353553390593
static REAL fx_4_006 = (REAL) ( sqrt(36.0)/8.0); // 0.749999999999
static REAL fx_4_007 = (REAL) ( sqrt(9.0)/8.0); // 0.37500034698
static REAL fx_4_008 = (REAL) ( sqrt(20.0)/8.0); // 0.559017511622
static REAL fx_4_009 = (REAL) ( sqrt(35.0)/8.0); // 0.739510657141
static REAL fx_4_010 = (REAL) ( sqrt(16.0)/8.0); // 0.5
static REAL fx_4_011 = (REAL) (-sqrt(28.0)/8.0); // -0.661437827766
static REAL fx_4_012 = (REAL) ( sqrt(1.0)/8.0); // 0.125
static REAL fx_4_013 = (REAL) ( sqrt(56.0)/8.0); // 0.935414346692
static 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];
};
static 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];
}
static REAL fx_5_001 = (REAL) ( sqrt(126.0)/16.0); // 0.70156076002
static REAL fx_5_002 = (REAL) (-sqrt(120.0)/16.0); // -0.684653196882
static REAL fx_5_003 = (REAL) ( sqrt(10.0)/16.0); // 0.197642353761
static REAL fx_5_004 = (REAL) (-sqrt(64.0)/16.0); // -0.5
static REAL fx_5_005 = (REAL) ( sqrt(192.0)/16.0); // 0.866025403784
static REAL fx_5_006 = (REAL) ( sqrt(70.0)/16.0); // 0.522912516584
static REAL fx_5_007 = (REAL) ( sqrt(24.0)/16.0); // 0.306186217848
static REAL fx_5_008 = (REAL) (-sqrt(162.0)/16.0); // -0.795495128835
static REAL fx_5_009 = (REAL) ( sqrt(64.0)/16.0); // 0.5
static REAL fx_5_010 = (REAL) ( sqrt(60.0)/16.0); // 0.484122918274
static REAL fx_5_011 = (REAL) ( sqrt(112.0)/16.0); // 0.661437827763
static REAL fx_5_012 = (REAL) ( sqrt(84.0)/16.0); // 0.572821961867
static REAL fx_5_013 = (REAL) ( sqrt(4.0)/16.0); // 0.125
static REAL fx_5_014 = (REAL) ( sqrt(42.0)/16.0); // 0.405046293649
static REAL fx_5_015 = (REAL) ( sqrt(210.0)/16.0); // 0.905711046633
static REAL fx_5_016 = (REAL) ( sqrt(169.0)/16.0); // 0.8125
static REAL fx_5_017 = (REAL) (-sqrt(45.0)/16.0); // -0.419262745781
static REAL fx_5_018 = (REAL) ( sqrt(1.0)/16.0); // 0.0625
static REAL fx_5_019 = (REAL) (-sqrt(126.0)/16.0); // -0.701561553415
static REAL fx_5_020 = (REAL) ( sqrt(120.0)/16.0); // 0.684653196881
static REAL fx_5_021 = (REAL) (-sqrt(10.0)/16.0); // -0.197642353761
static REAL fx_5_022 = (REAL) (-sqrt(70.0)/16.0); // -0.522913107945
static REAL fx_5_023 = (REAL) (-sqrt(60.0)/16.0); // -0.48412346577
static 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];
};
static 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];
}
static 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;
}
static 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]);
}
static 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);
}
static 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);
}
static 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);
}
static 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).
*/
static 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)
}
}
static 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);
}
static 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);
}
static 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);
}
static 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);
}
static 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);
}
static 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);
}
static 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)
static 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
namespace DirectX
{
//-------------------------------------------------------------------------------------
// Evaluates the Spherical Harmonic basis functions
//
// http://msdn.microsoft.com/en-us/library/windows/desktop/bb205448.aspx
//-------------------------------------------------------------------------------------
float* XM_CALLCONV XMSHEvalDirection( _Out_writes_(order*order) float *result,
_In_ size_t order,
_In_ FXMVECTOR dir )
{
if ( !result )
return nullptr;
XMFLOAT4A dv;
XMStoreFloat4A( &dv, dir );
const float fX = dv.x;
const float fY = dv.y;
const float fZ = dv.z;
switch( order )
{
case 2:
sh_eval_basis_1(fX,fY,fZ,result);
break;
case 3:
sh_eval_basis_2(fX,fY,fZ,result);
break;