| public static PlaneToSphere ( Vector3D planePoint ) : Vector3D | ||
| planePoint | Vector3D | |
| return | Vector3D | |
private static void HopfFibration(Tiling tiling)
{
int segDivisions = 10;
Shapeways mesh = new Shapeways();
HashSet <Vector3D> done = new HashSet <Vector3D>();
foreach (Tile tile in tiling.Tiles)
{
foreach (Segment seg in tile.Boundary.Segments)
{
if (done.Contains(seg.Midpoint))
{
continue;
}
// Subdivide the segment, and project points to S2.
Vector3D[] points = seg.Subdivide(segDivisions).Select(v => Spherical2D.PlaneToSphere(v)).ToArray();
foreach (Vector3D point in points)
{
Vector3D[] circlePoints = OneHopfCircle(point);
ProjectAndAddS3Points(mesh, circlePoints, shrink: false);
}
done.Add(seg.Midpoint);
}
}
STL.SaveMeshToSTL(mesh.Mesh, @"D:\p4\R3\sample\out1.stl");
}
private static void HopfFibration(Tiling tiling)
{
int segDivisions = 10;
int circleDivisions = 125;
Shapeways mesh = new Shapeways();
HashSet <Vector3D> done = new HashSet <Vector3D>();
foreach (Tile tile in tiling.Tiles)
{
foreach (Segment seg in tile.Boundary.Segments)
{
if (done.Contains(seg.Midpoint))
{
continue;
}
// Subdivide the segment, and project points to S2.
Vector3D[] points = seg.Subdivide(segDivisions).Select(v => Spherical2D.PlaneToSphere(v)).ToArray();
foreach (Vector3D point in points)
{
// Get the hopf circle and add to mesh.
// http://en.wikipedia.org/wiki/Hopf_fibration#Explicit_formulae
double a = point.X;
double b = point.Y;
double c = point.Z;
double factor = 1 / (Math.Sqrt(1 + c));
if (Tolerance.Equal(c, -1))
{
continue;
}
List <Vector3D> circlePoints = new List <Vector3D>();
double angleInc = 2 * Math.PI / circleDivisions;
double angle = 0;
for (int i = 0; i <= circleDivisions; i++)
{
double sinTheta = Math.Sin(angle);
double cosTheta = Math.Cos(angle);
circlePoints.Add(new Vector3D(
(1 + c) * cosTheta,
a * sinTheta - b * cosTheta,
a * cosTheta + b * sinTheta,
(1 + c) * sinTheta));
angle += angleInc;
}
bool shrink = false;
ProjectAndAddS3Points(mesh, circlePoints.ToArray(), shrink);
}
done.Add(seg.Midpoint);
}
}
STL.SaveMeshToSTL(mesh.Mesh, @"D:\p4\R3\sample\out1.stl");
}
/// <summary>
/// Outputs edges to an stl file.
/// </summary>
public void Output()
{
System.Func <Vector3D, Vector3D> p2s = v => Spherical2D.PlaneToSphere(v);
System.Func <Vector3D, Vector3D> transform = v => H3Models.Ball.ApplyMobius(Mobius.Scale(3), v);
double min = double.MaxValue;
Cell cell = m_cells.First();
foreach (Vector3D v1 in cell.Tiles[0].Boundary.Vertices)
{
foreach (Vector3D v2 in cell.Tiles[1].Boundary.Vertices)
{
min = Math.Min(min, p2s(v1).Dist(p2s(v2)));
}
}
// XXX - code below so ugly to read!
Dictionary <TileVertex, TileVertex> vMap = new Dictionary <TileVertex, TileVertex>();
for (int tile_i = 0; tile_i < cell.Tiles.Length; tile_i++)
{
for (int tile_j = tile_i + 1; tile_j < cell.Tiles.Length; tile_j++)
{
for (int vertex_i = 0; vertex_i < cell.Tiles[tile_i].Boundary.Vertices.Length; vertex_i++)
{
for (int vertex_j = 0; vertex_j < cell.Tiles[tile_j].Boundary.Vertices.Length; vertex_j++)
{
Vector3D v1 = cell.Tiles[tile_i].Boundary.Vertices[vertex_i];
Vector3D v2 = cell.Tiles[tile_j].Boundary.Vertices[vertex_j];
if (Tolerance.Equal(p2s(v1).Dist(p2s(v2)), min))
{
vMap[new TileVertex(tile_i, vertex_i)] = new TileVertex(tile_j, vertex_j);
}
}
}
}
}
HashSet <H3.Cell.Edge> edges = new HashSet <H3.Cell.Edge>(new H3.Cell.EdgeEqualityComparer());
foreach (Cell c in m_cells)
{
foreach (KeyValuePair <TileVertex, TileVertex> kvp in vMap)
{
Vector3D v1 = transform(p2s(c.Tiles[kvp.Key.Item1].Boundary.Vertices[kvp.Key.Item2]));
Vector3D v2 = transform(p2s(c.Tiles[kvp.Value.Item1].Boundary.Vertices[kvp.Value.Item2]));
edges.Add(new H3.Cell.Edge(v1, v2));
}
}
//H3.m_settings.ThinEdges = true;
H3.SaveToFile("ultrainf", edges.ToArray(), finite: false);
}