const int SAMPLES_COUNT = 50; // Number of samples used to compute the average terms
// compute the average direction of the BRDF
public void ComputeAverageTerms(IBRDF _BRDF, ref float3 _tsView, float _alpha)
{
magnitude = 0.0;
fresnel = 0.0;
Z = float3.Zero;
error = 0.0;
double weight, pdf, eval;
float3 tsLight = float3.Zero;
float3 H = float3.Zero;
for (int j = 0; j < SAMPLES_COUNT; ++j)
{
for (int i = 0; i < SAMPLES_COUNT; ++i)
{
float U1 = (i + 0.5f) / SAMPLES_COUNT;
float U2 = (j + 0.5f) / SAMPLES_COUNT;
// sample
_BRDF.GetSamplingDirection(ref _tsView, _alpha, U1, U2, ref tsLight);
// eval
eval = _BRDF.Eval(ref _tsView, ref tsLight, _alpha, out pdf);
if (pdf == 0.0f)
{
continue;
}
H = (_tsView + tsLight).Normalized;
// accumulate
weight = eval / pdf;
if (double.IsNaN(weight))
{
throw new Exception("NaN!");
}
magnitude += weight;
fresnel += weight * Math.Pow(1 - Math.Max(0.0f, _tsView.Dot(H)), 5.0);
Z += (float)weight * tsLight;
}
}
magnitude /= SAMPLES_COUNT * SAMPLES_COUNT;
fresnel /= SAMPLES_COUNT * SAMPLES_COUNT;
// Finish building the average TBN orthogonal basis
Z.y = 0.0f; // clear y component, which should be zero with isotropic BRDFs
float length = Z.Length;
if (length > 0.0f)
{
Z /= length;
}
else
{
Z = float3.UnitZ;
}
X.Set(Z.z, 0, -Z.x);
Y = float3.UnitY;
}
// 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));
}