// Rotates a dodec about a vertex or edge to get a dual dodec.
private static Dodec GetDual(Dodec dodec, Vector3D rotationPoint)
{
//double rot = System.Math.PI / 2; // Edge-centered
double rot = 4 * (-Math.Atan((2 + Math.Sqrt(5) - 2 * Math.Sqrt(3 + Math.Sqrt(5))) / Math.Sqrt(3))); // Vertex-centered
Mobius m = new Mobius();
if (Infinity.IsInfinite(rotationPoint))
{
m.Elliptic(Geometry.Spherical, new Vector3D(), -rot);
}
else
{
m.Elliptic(Geometry.Spherical, rotationPoint, rot);
}
Dodec dual = new Dodec();
foreach (Vector3D v in dodec.Verts)
{
Vector3D rotated = m.ApplyInfiniteSafe(v);
dual.Verts.Add(rotated);
}
foreach (Vector3D v in dodec.Midpoints)
{
Vector3D rotated = m.ApplyInfiniteSafe(v);
dual.Midpoints.Add(rotated);
}
return(dual);
}
