| public static S3toR3 ( Vector3D p ) : Vector3D | ||
| p | Vector3D | |
| return | Vector3D | |
public static void Hypercube()
{
List <Vector3D> vertices = new List <Vector3D>();
vertices.Add(new Vector3D(1, 1, 1, 1));
vertices.Add(new Vector3D(1, 1, 1, -1));
vertices.Add(new Vector3D(1, 1, -1, 1));
vertices.Add(new Vector3D(1, 1, -1, -1));
vertices.Add(new Vector3D(1, -1, 1, 1));
vertices.Add(new Vector3D(1, -1, 1, -1));
vertices.Add(new Vector3D(1, -1, -1, 1));
vertices.Add(new Vector3D(1, -1, -1, -1));
vertices.Add(new Vector3D(-1, 1, 1, 1));
vertices.Add(new Vector3D(-1, 1, 1, -1));
vertices.Add(new Vector3D(-1, 1, -1, 1));
vertices.Add(new Vector3D(-1, 1, -1, -1));
vertices.Add(new Vector3D(-1, -1, 1, 1));
vertices.Add(new Vector3D(-1, -1, 1, -1));
vertices.Add(new Vector3D(-1, -1, -1, 1));
vertices.Add(new Vector3D(-1, -1, -1, -1));
HashSet <H3.Cell.Edge> edges = new HashSet <H3.Cell.Edge>(new H3.Cell.EdgeEqualityComparer());
foreach (Vector3D v1 in vertices)
{
foreach (Vector3D v2 in vertices)
{
if (v1.Dist(v2) == 2)
{
edges.Add(new H3.Cell.Edge(v1, v2));
}
}
}
// Radial project to S3, then stereographic to R3.
foreach (H3.Cell.Edge edge in edges)
{
edge.Start.Normalize();
edge.Start = Sterographic.S3toR3(edge.Start);
edge.End.Normalize();
edge.End = Sterographic.S3toR3(edge.End);
}
PovRay.WriteEdges(new PovRay.Parameters()
{
AngularThickness = .05
}, Geometry.Spherical, edges.ToArray(), "433.pov", append: false);
}
/// <summary>
/// Inputs and Outputs are in R3 (stereographically projected).
/// </summary>
public static Vector3D[] GeodesicPoints(Vector3D v1, Vector3D v2)
{
Vector3D start = Sterographic.R3toS3(v1);
Vector3D end = Sterographic.R3toS3(v2);
AvoidNorthPole(ref start, end);
AvoidNorthPole(ref end, start);
int div = 42;
//int div = 56; // 343
//int div = 50; // 333
Segment seg = Segment.Line(start, end);
Vector3D[] result = seg.Subdivide(div);
for (int i = 0; i < result.Length; i++)
{
result[i].Normalize();
result[i] = Sterographic.S3toR3(result[i]);
}
return(result);
}
