| public static R3toS3 ( Vector3D p ) : Vector3D | ||
| p | Vector3D | |
| Результат | Vector3D | |
public static void EdgesToStl(H3.Cell.Edge[] edges)
{
Shapeways mesh = new Shapeways();
int divisions = 25;
foreach (H3.Cell.Edge edge in edges)
{
Segment seg = Segment.Line(
Sterographic.R3toS3(edge.Start),
Sterographic.R3toS3(edge.End));
Vector3D[] points = seg.Subdivide(divisions);
ProjectAndAddS3Points(mesh, points);
}
for (int i = 0; i < mesh.Mesh.Triangles.Count; i++)
{
mesh.Mesh.Triangles[i] = new Mesh.Triangle(
SphericalModels.StereoToEqualVolume(mesh.Mesh.Triangles[i].a),
SphericalModels.StereoToEqualVolume(mesh.Mesh.Triangles[i].b),
SphericalModels.StereoToEqualVolume(mesh.Mesh.Triangles[i].c));
}
STL.SaveMeshToSTL(mesh.Mesh, @"output.stl");
}
// Maps unit disk to Boy's surface.
public static Vector3D MapToBoys(Vector3D v)
{
// https://en.wikipedia.org/wiki/Boy%27s_surface#Parametrization_of_Boy.27s_surface
Complex w = v.ToComplex();
Complex t0 = (Complex.Pow(w, 6) + Complex.Pow(w, 3) * Math.Sqrt(5) - 1);
Complex t1 = w * (1 - Complex.Pow(w, 4)) / t0;
Complex t2 = w * (1 + Complex.Pow(w, 4)) / t0;
Complex t3 = (1 + Complex.Pow(w, 6)) / t0;
double g1 = -3 / 2 * t1.Imaginary;
double g2 = -3 / 2 * t2.Real;
double g3 = t3.Imaginary - 0.5;
double denom = g1 * g1 + g2 * g2 + g3 * g3;
v = new Vector3D(g1, g2, g3);
v /= denom;
// The above is actually a map to R^3, but we want a surface in S^3
return(Sterographic.R3toS3(v));
}
/// <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);
}