public static UnitVector DirectionInHemisphere(this IRandomSequence randomSequence, UnitVector normal)
{
var r1 = randomSequence.Double(0.0, 1.0);
var r2 = randomSequence.Double(0.0, 1.0);
var(vb1, vb2) = normal.Perpendiculars();
var theta = Math.Asin(Math.Sqrt(r1));
var phi = Math.PI * Math.PI * r2;
var sinTheta = Math.Sin(theta);
var cosTheta = Math.Cos(theta);
var sinPhi = Math.Sin(phi);
var cosPhi = Math.Cos(phi);
var v1 = vb1 * (sinTheta * sinPhi);
var v2 = normal * cosTheta;
var v3 = vb2 * (cosPhi * sinTheta);
return((v1 + v2 + v3).Normalize());
}
public static (UnitVector, UnitVector) NormalizedPerpendiculars(this UnitVector v)
{
(var p1, var p2) = v.Perpendiculars();
return(p1.Normalize(), p2.Normalize());
}