static public void Initialize(out LTCData ltcData)
{
ltcData.magnitude = 1;
ltcData.fresnel = 1;
ltcData.X.x = 1;
ltcData.X.y = 0;
ltcData.X.z = 0;
ltcData.Y.x = 0;
ltcData.Y.y = 1;
ltcData.Y.z = 0;
ltcData.Z.x = 0;
ltcData.Z.y = 0;
ltcData.Z.z = 1;
ltcData.m11 = 1;
ltcData.m22 = 1;
ltcData.m13 = 0;
ltcData.error = 0;
ltcData.iterationsCount = 0;
ltcData.detM = 0;
MatrixUtilities.Initialize(out ltcData.M);
MatrixUtilities.Initialize(out ltcData.invM);
}
public void Fit(int roughnessIndex, int thetaIndex, NelderMead fitter, IBRDF brdf)
{
// Compute the roughness and cosTheta for this sample
float roughness, cosTheta;
GetRoughnessAndAngle(roughnessIndex, thetaIndex, tableResolution, parametrization, out roughness, out cosTheta);
// Compute the matching view vector
Vector3 tsView = new Vector3(Mathf.Sqrt(1 - cosTheta * cosTheta), 0, cosTheta);
// Compute BRDF's magnitude and average direction
LTCData currentLTCData;
LTCDataUtilities.Initialize(out currentLTCData);
LTCDataUtilities.ComputeAverageTerms(brdf, ref tsView, roughness, sampleCount, ref currentLTCData);
// Otherwise use average direction as Z vector
int previousLTCDataIndex = (thetaIndex - 1) * tableResolution + roughnessIndex;
LTCData previousLTC = ltcData[previousLTCDataIndex];
currentLTCData.m11 = previousLTC.m11;
currentLTCData.m22 = previousLTC.m22;
currentLTCData.m13 = previousLTC.m13;
LTCDataUtilities.Update(ref currentLTCData);
// Find best-fit LTC lobe (scale, alphax, alphay)
if (currentLTCData.magnitude > 1e-6)
{
double[] startFit = LTCDataUtilities.GetFittingParms(in currentLTCData);
double[] resultFit = new double[startFit.Length];
int localSampleCount = sampleCount;
currentLTCData.error = (float)fitter.FindFit(resultFit, startFit, (double)k_FitExploreDelta, (double)k_Tolerance, k_MaxIterations, (double[] parameters) =>
{
LTCDataUtilities.SetFittingParms(ref currentLTCData, parameters, false);
return(ComputeError(currentLTCData, brdf, localSampleCount, ref tsView, roughness));
});
currentLTCData.iterationsCount = fitter.m_lastIterationsCount;
// Update LTC with final best fitting values
LTCDataUtilities.SetFittingParms(ref currentLTCData, resultFit, false);
}
// Store new valid result
int currentLTCDataIndex = thetaIndex * tableResolution + roughnessIndex;
ltcData[currentLTCDataIndex] = currentLTCData;
}
// Compute the error between the BRDF and the LTC using Multiple Importance Sampling
static float ComputeError(LTCData ltcData, IBRDF brdf, int sampleCount, ref Vector3 _tsView, float _alpha)
{
Vector3 tsLight = Vector3.zero;
double pdf_BRDF, eval_BRDF;
double pdf_LTC, eval_LTC;
float sumError = 0.0f;
for (int j = 0; j < sampleCount; ++j)
{
for (int i = 0; i < sampleCount; ++i)
{
float U1 = (i + 0.5f) / sampleCount;
float U2 = (j + 0.5f) / sampleCount;
// importance sample LTC
{
// sample
LTCDataUtilities.GetSamplingDirection(ltcData, U1, U2, ref tsLight);
eval_BRDF = brdf.Eval(ref _tsView, ref tsLight, _alpha, out pdf_BRDF);
eval_LTC = (float)LTCDataUtilities.Eval(ltcData, ref tsLight);
pdf_LTC = eval_LTC / ltcData.magnitude;
// error with MIS weight
float error = Mathf.Abs((float)(eval_BRDF - eval_LTC));
error = error * error * error; // Use L3 norm to favor large values over smaller ones
if (error != 0.0f)
{
error /= (float)pdf_LTC + (float)pdf_BRDF;
}
if (double.IsNaN(error))
{
// SHOULD NEVER HAPPEN
}
sumError += error;
}
// importance sample BRDF
{
// sample
brdf.GetSamplingDirection(ref _tsView, _alpha, U1, U2, ref tsLight);
// error with MIS weight
eval_BRDF = brdf.Eval(ref _tsView, ref tsLight, _alpha, out pdf_BRDF);
eval_LTC = LTCDataUtilities.Eval(ltcData, ref tsLight);
pdf_LTC = eval_LTC / ltcData.magnitude;
float error = Mathf.Abs((float)(eval_BRDF - eval_LTC));
error = error * error * error; // Use L3 norm to favor large values over smaller ones
if (error != 0.0f)
{
error /= (float)pdf_LTC + (float)pdf_BRDF;
}
if (double.IsNaN(error))
{
// SHOULD NEVER HAPPEN
}
sumError += error;
}
}
}
return(sumError / ((float)sampleCount * sampleCount));
}
static public void FitInitial(BRDFGenerator brdfGenerator, NelderMead fitter, NativeArray <LTCData> ltcData, int roughnessIndex, int thetaIndex)
{
// Compute the roughness and cosTheta for this sample
float roughness, cosTheta;
GetRoughnessAndAngle(roughnessIndex, thetaIndex, brdfGenerator.tableResolution, brdfGenerator.parametrization, out roughness, out cosTheta);
// Compute the matching view vector
Vector3 tsView = new Vector3(Mathf.Sqrt(1 - cosTheta * cosTheta), 0, cosTheta);
// Compute BRDF's magnitude and average direction
LTCData currentLTCData;
LTCDataUtilities.Initialize(out currentLTCData);
LTCDataUtilities.ComputeAverageTerms(brdfGenerator.brdf, ref tsView, roughness, brdfGenerator.sampleCount, ref currentLTCData);
// if theta == 0 the lobe is rotationally symmetric and aligned with Z = (0 0 1)
currentLTCData.X.x = 1;
currentLTCData.X.y = 0;
currentLTCData.X.z = 0;
currentLTCData.Y.x = 0;
currentLTCData.Y.y = 1;
currentLTCData.Y.z = 0;
currentLTCData.Z.x = 0;
currentLTCData.Z.y = 0;
currentLTCData.Z.z = 1;
if (roughnessIndex == (brdfGenerator.tableResolution - 1))
{
// roughness = 1 or no available result
currentLTCData.m11 = 1.0f;
currentLTCData.m22 = 1.0f;
}
else
{
// init with roughness of previous fit
LTCData previousLTC = ltcData[roughnessIndex + 1];
currentLTCData.m11 = previousLTC.m11;
currentLTCData.m22 = previousLTC.m22;
}
currentLTCData.m13 = 0;
LTCDataUtilities.Update(ref currentLTCData);
// Find best-fit LTC lobe (scale, alphax, alphay)
if (currentLTCData.magnitude > 1e-6)
{
double[] startFit = LTCDataUtilities.GetFittingParms(in currentLTCData);
double[] resultFit = new double[startFit.Length];
currentLTCData.error = (float)fitter.FindFit(resultFit, startFit, k_FitExploreDelta, k_Tolerance, k_MaxIterations, (double[] parameters) =>
{
LTCDataUtilities.SetFittingParms(ref currentLTCData, parameters, true);
return(ComputeError(currentLTCData, brdfGenerator.brdf, brdfGenerator.sampleCount, ref tsView, roughness));
});
currentLTCData.iterationsCount = fitter.m_lastIterationsCount;
// Update LTC with final best fitting values
LTCDataUtilities.SetFittingParms(ref currentLTCData, resultFit, true);
}
// Store new valid result
ltcData[roughnessIndex] = currentLTCData;
}