bool FindDirections(double u, double v, out Vector3d dir1, out Vector3d dir2, out Vector3d refA1, out Vector3d refA2)
{
RefSurface.Evaluate(u, v, 1, out var _, out var refDerivatives);
refA1 = refDerivatives[0];
refA2 = refDerivatives[1];
ActSurface.Evaluate(u, v, 1, out var _, out var actDerivatives);
var actA1 = actDerivatives[0];
var actA2 = actDerivatives[1];
var e = default(Vector3d);
e[0] = actA1 * refA1 - refA1.SquareLength;
e[1] = actA2 * refA2 - refA2.SquareLength;
e[2] = 0.5 * (actA1 * refA2 + actA2 * refA1) - refA1 * refA2;
e.Transform(TransformToLocalCartesian(refA1, refA2));
e.Transform(Material);
var tmp = Math.Sqrt(Math.Pow(e[0] - e[1], 2) + 4 * Math.Pow(e[2], 2));
var n1 = 0.5 * (e[0] + e[1] + tmp);
var n2 = 0.5 * (e[0] + e[1] - tmp);
if (n1 * n2 < 0)
{
dir1 = Vector3d.Unset;
dir2 = Vector3d.Unset;
return(false);
}
var normal = Vector3d.CrossProduct(refA1, refA2);
if (Math.Abs(e[2]) < 1e-8)
{
dir1 = refA1 / refA1.Length;
}
else
{
var alpha = Math.Atan2(2 * e[2], e[0] - e[1]) / 2;
dir1 = refA1 / refA1.Length;
dir1.Rotate(alpha, normal);
}
dir2 = dir1;
var angle = Math.Atan(Math.Sqrt(n2 / n1));
dir1.Rotate(angle, normal);
dir2.Rotate(-angle, normal);
return(true);
}
bool FindDirections(double u, double v, out Vector3d dir1, out Vector3d dir2, out Vector3d refA1, out Vector3d refA2)
{
RefSurface.Evaluate(u, v, 1, out var _, out var refDerivatives);
refA1 = refDerivatives[0];
refA2 = refDerivatives[1];
ActSurface.Evaluate(u, v, 1, out var _, out var actDerivatives);
var actA1 = actDerivatives[0];
var actA2 = actDerivatives[1];
var e = default(Vector3d);
e[0] = actA1 * refA1 - refA1.SquareLength;
e[1] = actA2 * refA2 - refA2.SquareLength;
e[2] = 0.5 * (actA1 * refA2 + actA2 * refA1) - refA1 * refA2;
e.Transform(TransformToLocalCartesian(refA1, refA2));
e.Transform(Material);
var normal = Vector3d.CrossProduct(refA1, refA2);
if (Math.Abs(e[2]) < 1e-8)
{
dir1 = refA1 / refA1.Length;
}
else
{
var alpha = Math.Atan2(2 * e[2], e[0] - e[1]) / 2;
dir1 = refA1 / refA1.Length;
dir1.Rotate(alpha, normal);
}
dir2 = dir1;
dir2.Rotate(Math.PI / 2, normal);
return(true);
}