public static Matrix Rotation(Tuple u, Tuple v)
{
double cosPhi = u.DotProduct(v);
var uv = u * v;
var uvMagnitude = u.Magnitude * v.Magnitude;
double sinPhi = uv.Magnitude / uvMagnitude;
Tuple n = uv / sinPhi;
// https://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula
var m1 = new Matrix(4,
cosPhi, 0, 0, 0,
0, cosPhi, 0, 0,
0, 0, cosPhi, 0,
0, 0, 0, 1
);
var m2 = new Matrix(4,
n.X * n.X, n.X * n.Y, n.X * n.Z, 0,
n.X * n.Y, n.Y * n.Y, n.Y * n.Z, 0,
n.X * n.Z, n.Z * n.Y, n.Z * n.Z, 0,
0, 0, 0, 0
);
var m3 = new Matrix(4,
0, -n.Z, n.Y, 0,
n.Z, 0, -n.X, 0,
-n.Y, n.X, 0, 0,
0, 0, 0, 0);
var m = m1 + (1 - cosPhi) * m2 + sinPhi * m3;
return(m);
}
// https://www.scratchapixel.com/lessons/3d-basic-rendering/minimal-ray-tracer-rendering-simple-shapes/ray-plane-and-ray-disk-intersection
public static bool IntersectPlane(ref Tuple normal, ref Tuple p0, ref Tuple l0, ref Tuple l, ref double t)
{
// assuming vectors are all normalized
double denom = normal.DotProduct(l);
if (Math.Abs(denom) > Epsilon)
{
var p0l0 = p0 - l0;
t = p0l0.DotProduct(normal) / denom;
return(t >= 0);
}
return(false);
}