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@ -4,6 +4,7 @@
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#define NV_MATH_SPHERICALHARMONIC_H
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#include "nvmath.h"
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#include "Vector.h"
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#include <string.h> // memcpy
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@ -31,33 +32,33 @@ namespace nv
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public:
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/// Construct a spherical harmonic of the given order.
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Sh(int o) : m_order(o)
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Sh(int o) : order(o)
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{
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m_elemArray = new float[basisNum()];
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coef = new float[basisNum()];
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}
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/// Copy constructor.
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Sh(const Sh & sh) : m_order(sh.order())
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Sh(const Sh & sh) : order(sh.order)
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{
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m_elemArray = new float[basisNum()];
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memcpy(m_elemArray, sh.m_elemArray, sizeof(float) * basisNum());
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coef = new float[basisNum()];
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memcpy(coef, sh.coef, sizeof(float) * basisNum());
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}
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/// Destructor.
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~Sh()
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{
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delete [] m_elemArray;
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m_elemArray = NULL;
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delete [] coef;
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coef = NULL;
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}
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/// Get number of bands.
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static int bandNum(int m_order) {
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return m_order + 1;
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static int bandNum(int order) {
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return order + 1;
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}
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/// Get number of sh basis.
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static int basisNum(int m_order) {
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return (m_order + 1) * (m_order + 1);
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static int basisNum(int order) {
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return (order + 1) * (order + 1);
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}
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/// Get the index for the given coefficients.
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@ -65,46 +66,40 @@ namespace nv
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return l * l + l + m;
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}
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/// Get sh order.
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int order() const
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{
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return m_order;
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}
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/// Get sh order.
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int bandNum() const
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{
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return bandNum(m_order);
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return bandNum(order);
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}
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/// Get sh order.
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int basisNum() const
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{
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return basisNum(m_order);
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return basisNum(order);
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}
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/// Get sh coefficient indexed by l,m.
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float elem( int l, int m ) const
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{
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return m_elemArray[index(l, m)];
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return coef[index(l, m)];
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}
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/// Get sh coefficient indexed by l,m.
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float & elem( int l, int m )
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{
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return m_elemArray[index(l, m)];
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return coef[index(l, m)];
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}
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/// Get sh coefficient indexed by i.
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float elemAt( int i ) const {
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return m_elemArray[i];
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return coef[i];
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}
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/// Get sh coefficient indexed by i.
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float & elemAt( int i )
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{
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return m_elemArray[i];
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return coef[i];
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}
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@ -112,47 +107,47 @@ namespace nv
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void reset()
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{
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for( int i = 0; i < basisNum(); i++ ) {
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m_elemArray[i] = 0.0f;
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coef[i] = 0.0f;
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}
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}
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/// Copy spherical harmonic.
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void operator= ( const Sh & sh )
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{
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nvDebugCheck(order() <= sh.order());
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nvDebugCheck(order <= sh.order);
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for(int i = 0; i < basisNum(); i++) {
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m_elemArray[i] = sh.m_elemArray[i];
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coef[i] = sh.coef[i];
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}
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}
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/// Add spherical harmonics.
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void operator+= ( const Sh & sh )
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{
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nvDebugCheck(order() == sh.order());
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nvDebugCheck(order == sh.order);
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for(int i = 0; i < basisNum(); i++) {
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m_elemArray[i] += sh.m_elemArray[i];
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coef[i] += sh.coef[i];
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}
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}
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/// Substract spherical harmonics.
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void operator-= ( const Sh & sh )
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{
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nvDebugCheck(order() == sh.order());
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nvDebugCheck(order == sh.order);
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for(int i = 0; i < basisNum(); i++) {
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m_elemArray[i] -= sh.m_elemArray[i];
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coef[i] -= sh.coef[i];
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}
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}
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// Not exactly convolution, nor product.
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void operator*= ( const Sh & sh )
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{
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nvDebugCheck(order() == sh.order());
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nvDebugCheck(order == sh.order);
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for(int i = 0; i < basisNum(); i++) {
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m_elemArray[i] *= sh.m_elemArray[i];
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coef[i] *= sh.coef[i];
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}
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}
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@ -160,17 +155,17 @@ namespace nv
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void operator*= ( float f )
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{
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for(int i = 0; i < basisNum(); i++) {
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m_elemArray[i] *= f;
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coef[i] *= f;
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}
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}
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/// Add scaled spherical harmonics.
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void addScaled( const Sh & sh, float f )
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{
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nvDebugCheck(order() == sh.order());
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nvDebugCheck(order == sh.order);
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for(int i = 0; i < basisNum(); i++) {
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m_elemArray[i] += sh.m_elemArray[i] * f;
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coef[i] += sh.coef[i] * f;
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}
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}
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@ -188,7 +183,7 @@ namespace nv
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/// Evaluate
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void eval(const Vector3 & dir)
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{
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for(int l = 0; l <= m_order; l++) {
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for(int l = 0; l <= order; l++) {
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for(int m = -l; m <= l; m++) {
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elem(l, m) = shBasis(l, m, dir);
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}
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@ -199,17 +194,15 @@ namespace nv
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/// Evaluate the spherical harmonic function.
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float sample(const Vector3 & dir) const
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{
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Sh sh(order());
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Sh sh(order);
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sh.eval(dir);
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return dot(sh, *this);
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}
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protected:
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const int m_order;
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float * m_elemArray;
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const int order;
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float * coef;
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};
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@ -217,10 +210,10 @@ namespace nv
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/// Compute dot product of the spherical harmonics.
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inline float dot(const Sh & a, const Sh & b)
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{
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nvDebugCheck(a.order() == b.order());
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nvDebugCheck(a.order == b.order);
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float sum = 0;
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for( int i = 0; i < Sh::basisNum(a.order()); i++ ) {
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for( int i = 0; i < Sh::basisNum(a.order); i++ ) {
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sum += a.elemAt(i) * b.elemAt(i);
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}
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@ -239,9 +232,34 @@ namespace nv
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/// Copy constructor.
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Sh2(const Sh2 & sh) : Sh(sh) {}
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// Fast evaluation from: PPS' Efficient Spherical Harmonic Evaluation http://jcgt.org/published/0002/02/06/
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void eval(const Vector3 & dir) {
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float fZ2 = dir.z * dir.z;
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coef[0] = 0.2820947917738781f;
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coef[2] = 0.4886025119029199f * dir.z;
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coef[6] = 0.9461746957575601f * fZ2 + -0.3153915652525201f;
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float fC0 = dir.x;
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float fS0 = dir.y;
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float fTmpA = -0.48860251190292f;
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coef[3] = fTmpA * fC0;
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coef[1] = fTmpA * fS0;
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float fTmpB = -1.092548430592079f * dir.z;
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coef[7] = fTmpB * fC0;
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coef[5] = fTmpB * fS0;
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float fC1 = dir.x * fC0 - dir.y * fS0;
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float fS1 = dir.x * fS0 + dir.y * fC0;
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float fTmpC = 0.5462742152960395f;
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coef[8] = fTmpC * fC1;
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coef[4] = fTmpC * fS1;
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}
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/// Spherical harmonic resulting from projecting the clamped cosine transfer function to the SH basis.
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void cosineTransfer()
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{
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void cosineTransfer() {
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const float c1 = 0.282095f; // K(0, 0)
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const float c2 = 0.488603f; // K(1, 0)
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const float c3 = 1.092548f; // sqrt(15.0f / PI) / 2.0f = K(2, -2)
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@ -256,17 +274,17 @@ namespace nv
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const float const4 = c4 * normalization * (1.0f / 4.0f);
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const float const5 = c5 * normalization * (1.0f / 4.0f);
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m_elemArray[0] = const1;
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coef[0] = const1;
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m_elemArray[1] = -const2;
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m_elemArray[2] = const2;
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m_elemArray[3] = -const2;
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coef[1] = -const2;
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coef[2] = const2;
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coef[3] = -const2;
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m_elemArray[4] = const3;
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m_elemArray[5] = -const3;
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m_elemArray[6] = const4;
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m_elemArray[7] = -const3;
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m_elemArray[8] = const5;
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coef[4] = const3;
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coef[5] = -const3;
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coef[6] = const4;
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coef[7] = -const3;
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coef[8] = const5;
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}
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};
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@ -352,8 +370,8 @@ namespace nv
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/// Rotate the given coefficients.
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/*void transform( const Sh & restrict source, Sh * restrict dest ) const {
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nvCheck( &source != dest ); // Make sure there's no aliasing.
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nvCheck( dest->m_order <= m_order );
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nvCheck( m_order <= source.m_order );
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nvCheck( dest->order <= order );
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nvCheck( order <= source.order );
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if (m_identity) {
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*dest = source;
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@ -361,7 +379,7 @@ namespace nv
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}
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// Loop through each band.
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for (int l = 0; l <= dest->m_order; l++) {
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for (int l = 0; l <= dest->order; l++) {
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for (int mo = -l; mo <= l; mo++) {
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