float ComputeOneDir(Vector3 outDir, Vector3 inDir)
{
// Compute the half vector
float eta = ShadingSpace.CosTheta(outDir) > 0 ? (insideIOR / outsideIOR) : (outsideIOR / insideIOR);
Vector3 wh = outDir + inDir * eta;
if (wh == Vector3.Zero)
{
return(0); // Prevent NaN if outDir and inDir exactly align
}
wh = Vector3.Normalize(wh);
if (Vector3.Dot(outDir, wh) * Vector3.Dot(inDir, wh) > 0)
{
return(0);
}
// Compute change of variables _dwh\_dinDir_ for microfacet transmission
float sqrtDenom = Vector3.Dot(outDir, wh) + eta * Vector3.Dot(inDir, wh);
if (sqrtDenom == 0)
{
return(0); // Prevent NaN in corner case
}
float dwh_dinDir = Math.Abs((eta * eta * Vector3.Dot(inDir, wh)) / (sqrtDenom * sqrtDenom));
float result = distribution.Pdf(outDir, wh) * dwh_dinDir;
Debug.Assert(float.IsFinite(result));
return(result);
}
/// <summary>
/// Warps the given primary sample to follow the pdf computed by <see cref="Pdf(Vector3, Vector3)"/>.
/// </summary>
/// <returns>The direction that corresponds to the given primary sample.</returns>
public Vector3 Sample(Vector3 outDir, Vector2 primary)
{
bool flip = ShadingSpace.CosTheta(outDir) < 0;
var wh = TrowbridgeReitzSample(flip ? -outDir : outDir, AlphaX, AlphaY, primary.X, primary.Y);
if (flip)
{
wh = -wh;
}
return(wh);
}
public Vector3?Sample(Vector3 outDir, bool isOnLightSubpath, Vector2 primarySample)
{
if (outDir.Z == 0)
{
return(null);
}
Vector3 wh = distribution.Sample(outDir, primarySample);
if (Vector3.Dot(outDir, wh) < 0)
{
return(null);
}
float eta = ShadingSpace.CosTheta(outDir) > 0 ? (outsideIOR / insideIOR) : (insideIOR / outsideIOR);
var inDir = ShadingSpace.Refract(outDir, wh, eta);
return(inDir);
}
public RgbColor Evaluate(Vector3 outDir, Vector3 inDir, bool isOnLightSubpath)
{
if (ShadingSpace.SameHemisphere(outDir, inDir))
{
return(RgbColor.Black); // transmission only
}
float cosThetaO = ShadingSpace.CosTheta(outDir);
float cosThetaI = ShadingSpace.CosTheta(inDir);
if (cosThetaI == 0 || cosThetaO == 0)
{
return(RgbColor.Black);
}
// Compute the half vector
float eta = ShadingSpace.CosTheta(outDir) > 0 ? (insideIOR / outsideIOR) : (outsideIOR / insideIOR);
Vector3 wh = Vector3.Normalize(outDir + inDir * eta);
if (ShadingSpace.CosTheta(wh) < 0)
{
wh = -wh;
}
if (Vector3.Dot(outDir, wh) * Vector3.Dot(inDir, wh) > 0)
{
return(RgbColor.Black);
}
var F = new RgbColor(FresnelDielectric.Evaluate(Vector3.Dot(outDir, wh), outsideIOR, insideIOR));
float sqrtDenom = Vector3.Dot(outDir, wh) + eta * Vector3.Dot(inDir, wh);
float factor = isOnLightSubpath ? (1 / eta) : 1;
var numerator = distribution.NormalDistribution(wh) * distribution.MaskingShadowing(outDir, inDir);
numerator *= eta * eta * Math.Abs(Vector3.Dot(inDir, wh)) * Math.Abs(Vector3.Dot(outDir, wh));
numerator *= factor * factor;
var denom = (cosThetaI * cosThetaO * sqrtDenom * sqrtDenom);
Debug.Assert(float.IsFinite(denom));
return((RgbColor.White - F) * transmittance * Math.Abs(numerator / denom));
}
public RgbColor Evaluate(Vector3 outDir, Vector3 inDir, bool isOnLightSubpath)
{
if (!ShadingSpace.SameHemisphere(outDir, inDir))
{
return(RgbColor.Black);
}
float cosThetaO = ShadingSpace.AbsCosTheta(outDir);
float cosThetaI = ShadingSpace.AbsCosTheta(inDir);
Vector3 halfVector = inDir + outDir;
// Handle degenerate cases for microfacet reflection
if (cosThetaI == 0 || cosThetaO == 0)
{
return(RgbColor.Black);
}
if (halfVector.X == 0 && halfVector.Y == 0 && halfVector.Z == 0)
{
return(RgbColor.Black);
}
// For the Fresnel call, make sure that wh is in the same hemisphere
// as the surface normal, so that total internal reflection is handled correctly.
halfVector = Vector3.Normalize(halfVector);
if (ShadingSpace.CosTheta(halfVector) < 0)
{
halfVector = -halfVector;
}
var cosine = Vector3.Dot(inDir, halfVector);
var f = fresnel.Evaluate(cosine);
var nd = distribution.NormalDistribution(halfVector);
var ms = distribution.MaskingShadowing(outDir, inDir);
return(tint * nd * ms * f / (4 * cosThetaI * cosThetaO));
}
static Vector3 TrowbridgeReitzSample(Vector3 wi, float alpha_x,
float alpha_y, float U1, float U2)
{
// 1. stretch wi
Vector3 wiStretched = Vector3.Normalize(new Vector3(alpha_x * wi.X, alpha_y * wi.Y, wi.Z));
// 2. simulate P22_{wi}(x_slope, y_slope, 1, 1)
float slope_x, slope_y;
TrowbridgeReitzSample11(ShadingSpace.CosTheta(wiStretched), U1, U2, out slope_x, out slope_y);
// 3. rotate
float tmp = ShadingSpace.CosPhi(wiStretched) * slope_x - ShadingSpace.SinPhi(wiStretched) * slope_y;
slope_y = ShadingSpace.SinPhi(wiStretched) * slope_x + ShadingSpace.CosPhi(wiStretched) * slope_y;
slope_x = tmp;
// 4. unstretch
slope_x = alpha_x * slope_x;
slope_y = alpha_y * slope_y;
// 5. compute normal
return(Vector3.Normalize(new Vector3(-slope_x, -slope_y, 1)));
}
