protected void GetSHCoefficients(WMath.Vector _Direction, ref double[] _Coefficients)
{
float x = -_Direction.z;
float y = _Direction.y;
float z = _Direction.x;
// Build the SH coefficients from analytical formulae given in http://www-graphics.stanford.edu/papers/envmap/
_Coefficients[0] = 0.282095; // Y00
_Coefficients[1] = 0.488603 * z; // Y1-1
_Coefficients[2] = 0.488603 * y; // Y10
_Coefficients[3] = 0.488603 * x; // Y1+1
_Coefficients[4] = 1.092548 * x * z; // Y2-2
_Coefficients[5] = 1.092548 * y * z; // Y2-1
_Coefficients[6] = 0.315392 * (3 * y * y - 1); // Y20
_Coefficients[7] = 1.092548 * x * y; // Y2+1
_Coefficients[8] = 0.546274 * (x * x - z * z); // Y2+2
}
/// <summary>
/// Initializes the collection of samples
/// </summary>
/// <param name="_Order">The order of the SH</param>
/// <param name="_ThetaSamplesCount">The amount of samples on Theta (total samples count will be 2*N*N)</param>
/// <param name="_Up">The vector to use as the Up direction (use [0,1,0] if not sure)</param>
public void Initialize(int _Order, int _ThetaSamplesCount, WMath.Vector _Up)
{
m_Order = _Order;
m_ThetaSamplesCount = _ThetaSamplesCount;
m_SamplesCount = 2 * m_ThetaSamplesCount * m_ThetaSamplesCount;
m_Random = new Random(m_RandomSeed);
// Compute the rotation matrix
Matrix3x3 Rotation = new Matrix3x3();
Vector Ortho = new Vector(0, 1, 0) ^ _Up;
float fNorm = Ortho.SquareMagnitude();
if (fNorm < 1e-6f)
{
Rotation.MakeIdentity();
}
else
{
Ortho /= (float)Math.Sqrt(fNorm);
Rotation.SetRow0(Ortho);
Rotation.SetRow1(_Up);
Rotation.SetRow2(Ortho ^ _Up);
}
// Initialize the SH samples
m_SHSamples = new SHSample[m_SamplesCount];
// Build the samples using stratified sampling
int SampleIndex = 0;
for (int ThetaIndex = 0; ThetaIndex < m_ThetaSamplesCount; ThetaIndex++)
{
for (int PhiIndex = 0; PhiIndex < 2 * m_ThetaSamplesCount; PhiIndex++)
{
double fTheta = 2.0 * System.Math.Acos(System.Math.Sqrt(1.0 - (ThetaIndex + m_Random.NextDouble()) / m_ThetaSamplesCount));
double fPhi = System.Math.PI * (PhiIndex + m_Random.NextDouble()) / m_ThetaSamplesCount;
// Compute direction, rotate it then cast it back to sphercial coordinates
Vector Direction = SphericalHarmonics.SHFunctions.SphericalToCartesian(fTheta, fPhi);
Direction *= Rotation;
SphericalHarmonics.SHFunctions.CartesianToSpherical(Direction, out fTheta, out fPhi);
// Fill up the new sample
m_SHSamples[SampleIndex] = new SHSample((float)fPhi, (float)fTheta);
m_SHSamples[SampleIndex].m_SHFactors = new double[m_Order * m_Order];
// Build the SH Factors
SHFunctions.InitializeSHCoefficients(m_Order, fTheta, fPhi, m_SHSamples[SampleIndex].m_SHFactors);
SampleIndex++;
}
}
}