public Normal3 Sample(Random random)
{
/// Compute Height
double theta = Math.Pow((random.NextDouble() - 0.5d) * Math.PI, Exponent);
double r = Math.Cos(theta);
double w = Math.Sin(theta);
/// Compute u and v
double angle = random.NextDouble() * 2 * Math.PI;
double u = r * Math.Cos(angle);
double v = r * Math.Sin(angle);
/// Transform to Orientation
Normal3 uDirection = Normal3.AnyPerpendicular(Orientation);
Normal3 vDirection = Normal3.Perpendicular(Orientation, uDirection);
return(new Normal3(uDirection * (float)u + vDirection * (float)v + Orientation * (float)w));
}
public Normal3 Sample(Random random)
{
/// Get Point uniformly on Disc
double angle = random.NextDouble() * 2 * Math.PI;
double r = random.NextDouble() + random.NextDouble();
r = r < 1 ? r : 2 - r;
double u = r * Math.Cos(angle);
double v = r * Math.Sin(angle);
/// Raise Disc point to Hemisphere
double w = Math.Sqrt(1 - u * u - v * v);
Normal3 uDirection = Normal3.AnyPerpendicular(Orientation);
Normal3 vDirection = Normal3.Perpendicular(Orientation, uDirection);
return(new Normal3(uDirection * (float)u + vDirection * (float)v + Orientation * (float)w));
}
Vector3 SampleVNDF(float r1, float r2)
{
// Rotate so UnitZ is up, and flip incoming to outgoing direction
Normal3 up = Normal3.UnitZ;
OpenTK.Mathematics.Quaternion rotation;
if (Orientation == -up)
{
rotation = new OpenTK.Mathematics.Quaternion(Normal3.AnyPerpendicular(up).Vector, 0f);
}
else
{
rotation = new OpenTK.Mathematics.Quaternion(Vector3.Cross(Orientation.Vector, up.Vector), Vector3.Dot(Orientation.Vector, up.Vector) + 1f).Normalized();
}
Vector3 Ve = rotation * -IncomingDirection.Vector;
// Section 3.2: transforming the view direction to the hemisphere configuration
Vector3 Vh = new Vector3(Roughness * Ve.X, Roughness * Ve.Y, Ve.Z).Normalized();
// Section 4.1: orthonormal basis (with special case if cross product is zero)
float lensq = Vh.X * Vh.X + Vh.Y * Vh.Y;
Vector3 T1 = lensq > 0 ? new Vector3(-Vh.Y, Vh.X, 0) / (float)Math.Sqrt(lensq) : new Vector3(1f, 0f, 0f);
Vector3 T2 = Vector3.Cross(Vh, T1);
// Section 4.2: parameterization of the projected area
float r = (float)Math.Sqrt(r1);
float phi = 2.0f * (float)Math.PI * r2;
float t1 = r * (float)Math.Cos(phi);
float t2 = r * (float)Math.Sin(phi);
float s = 0.5f * (1f + Vh.Z);
t2 = (1f - s) * (float)Math.Sqrt(1f - t1 * t1) + s * t2;
// Section 4.3: reprojection onto hemisphere
Vector3 Nh = t1 * T1 + t2 * T2 + (float)Math.Sqrt(Math.Max(0f, 1f - t1 * t1 - t2 * t2)) * Vh;
// Section 3.4: transforming the normal back to the ellipsoid configuration
Vector3 Ne = new(Roughness * Nh.X, Roughness *Nh.Y, (float)Math.Max(0.0, Nh.Z));
return(rotation.Inverted() * Ne);
}
