/// <summary>
/// Creates the vertices of an icosahedron with vertices at (0, 0, 1) and (0, 0, -1)
/// </summary>
private List <Vertex> MakeIcosahedronVertices()
{
var vertices = new List <Vertex>
{
new Vertex(new Point3D(0, 0, 1), new Vector3D(0, 0, 1), new Point(0, 0)),
new Vertex(new Point3D(0, 0, -1), new Vector3D(0, 0, -1), new Point(1, 1))
};
double thetaHi = Math.PI / 2 - Math.Atan(.5);
double thetaLo = Math.PI / 2 + Math.Atan(.5);
const double deltaPhi = 2 * Math.PI / 10;
bool alternator = true;
for (double iphi = 0; iphi < Math.PI * 2 + deltaPhi / 2; iphi += deltaPhi)
// The addition to the cutoff avoids roundoff issues
{
double theta = alternator ? thetaHi : thetaLo;
Vector3D position = Vector3DExtensions.SphericalCoordinates(1, iphi, theta);
double u = iphi / (2 * Math.PI);
double v = theta / (Math.PI);
vertices.Add(new Vertex(ConvertToPoint3D(position), position, new Point(u, v)));
// Switch the alternator
alternator = alternator ? false : true;
}
return(vertices);
}
/// <summary>
/// Finds the midpoint between two points on the unit sphere
/// </summary>
private Vertex CreateMidpoint(Vertex one, Vertex two)
{
Vector3D midpoint = Vector3DExtensions.Midpoint(ConvertToVector3D(one.Position), ConvertToVector3D(two.Position));
double u = midpoint.Azimuthal() / (2 * Math.PI);
double v = midpoint.Polar() / Math.PI;
midpoint.Normalize();
return(new Vertex(ConvertToPoint3D(midpoint), midpoint, new Point(u, v)));
}
