/// <summary>
/// Allow a hyperbolic transformation using an absolute offset.
/// offset is specified in the respective geometry.
/// </summary>
public void Hyperbolic2(Geometry g, Complex fixedPlus, Complex point, double offset)
{
// To the origin.
Mobius m = new Mobius();
m.Isometry(g, 0, fixedPlus * -1);
double eRadius = m.Apply(point).Magnitude;
double scale = 1;
switch (g)
{
case Geometry.Spherical:
double sRadius = Spherical2D.e2sNorm(eRadius);
sRadius += offset;
scale = Spherical2D.s2eNorm(sRadius) / eRadius;
break;
case Geometry.Euclidean:
scale = (eRadius + offset) / eRadius;
break;
case Geometry.Hyperbolic:
double hRadius = DonHatch.e2hNorm(eRadius);
hRadius += offset;
scale = DonHatch.h2eNorm(hRadius) / eRadius;
break;
}
Hyperbolic(g, fixedPlus, scale);
}
/// <summary>
/// Move from a point p1 -> p2 along a geodesic.
/// Also somewhat from Don.
/// factor can be used to only go some fraction of the distance from p1 to p2.
/// </summary>
public void Geodesic(Geometry g, Complex p1, Complex p2, double factor = 1.0)
{
Mobius t = new Mobius();
t.Isometry(g, 0, p1 * -1);
Complex p2t = t.Apply(p2);
// Only implemented for hyperbolic so far.
if (factor != 1.0 && g == Geometry.Hyperbolic)
{
double newMag = DonHatch.h2eNorm(DonHatch.e2hNorm(p2t.Magnitude) * factor);
Vector3D temp = Vector3D.FromComplex(p2t);
temp.Normalize();
temp *= newMag;
p2t = temp.ToComplex();
}
Mobius m1 = new Mobius(), m2 = new Mobius();
m1.Isometry(g, 0, p1 * -1);
m2.Isometry(g, 0, p2t);
Mobius m3 = m1.Inverse();
this = m3 * m2 * m1;
}
