public static void Experiment()
{
TilingConfig config = new TilingConfig(4, 3);
Tiling tiling = new Tiling();
tiling.Generate(config);
HashSet <H3.Cell.Edge> completed = new HashSet <H3.Cell.Edge>(new H3.Cell.EdgeEqualityComparer());
string fileName = "hopf.pov";
using (StreamWriter sw = File.CreateText(fileName))
{
Tile[] tiles = tiling.Tiles.ToArray();
//foreach( Tile t in tiling.Tiles )
foreach (Tile t in new Tile[] { tiles[0] })
{
foreach (Segment seg in t.Boundary.Segments)
{
H3.Cell.Edge e = new H3.Cell.Edge(seg.P1, seg.P2);
if (completed.Contains(e))
{
continue;
}
HopfLink(sw,
Sterographic.PlaneToSphereSafe(e.Start),
Sterographic.PlaneToSphereSafe(e.End), anti: false);
completed.Add(e);
}
}
}
}
private static Vector3D Halfway(Vector3D v1, Vector3D v2)
{
Vector3D v1_ = Sterographic.PlaneToSphereSafe(v1);
Vector3D v2_ = Sterographic.PlaneToSphereSafe(v2);
Vector3D result = (v1_ + v2_) / 2;
result.Normalize();
return(Sterographic.SphereToPlane(result));
}
public static Vector3D[] CalcViaProjections(Vector3D p1, Vector3D p2, Vector3D p3, int divisions, Geometry g)
{
if (g == Geometry.Euclidean)
{
throw new System.NotImplementedException();
}
Vector3D h1 = new Vector3D(), h2 = new Vector3D(), h3 = new Vector3D();
if (g == Geometry.Hyperbolic)
{
h1 = Sterographic.PlaneToHyperboloid(p1);
h2 = Sterographic.PlaneToHyperboloid(p2);
h3 = Sterographic.PlaneToHyperboloid(p3);
}
else if (g == Geometry.Spherical)
{
h1 = Sterographic.PlaneToSphereSafe(p1);
h2 = Sterographic.PlaneToSphereSafe(p2);
h3 = Sterographic.PlaneToSphereSafe(p3);
}
List <Vector3D> temp = new List <Vector3D>();
Segment seg1 = Segment.Line(h1, h2);
Segment seg2 = Segment.Line(h3, h2);
Vector3D[] s1 = seg1.Subdivide(divisions);
Vector3D[] s2 = seg2.Subdivide(divisions);
for (int i = 0; i < divisions; i++)
{
Segment seg = Segment.Line(s1[i], s2[i]);
temp.AddRange(seg.Subdivide(divisions - i));
}
temp.Add(h2);
List <Vector3D> result = new List <Vector3D>();
foreach (Vector3D v in temp)
{
Vector3D copy = v;
if (g == Geometry.Hyperbolic)
{
Sterographic.NormalizeToHyperboloid(ref copy);
result.Add(Sterographic.HyperboloidToPlane(copy));
}
else if (g == Geometry.Spherical)
{
copy.Normalize();
result.Add(Sterographic.SphereToPlane(copy));
}
}
return(result.ToArray());
}
// https://plus.google.com/u/0/117663015413546257905/posts/BnCEkdNiTZ2
public static void TwinDodecs()
{
Tiling tiling = new Tiling();
TilingConfig config = new TilingConfig(5, 3);
tiling.GenerateInternal(config, Polytope.Projection.VertexCentered); // Vertex-centered makes infinities tricky
Dodec dodec = new Dodec();
foreach (Tile tile in tiling.Tiles)
{
foreach (Segment seg in tile.Boundary.Segments)
{
Vector3D p1 = seg.P1, p2 = seg.P2;
if (Infinity.IsInfinite(p1))
{
p1 = Infinity.InfinityVector;
}
if (Infinity.IsInfinite(p2))
{
p2 = Infinity.InfinityVector;
}
dodec.Verts.Add(p1);
dodec.Verts.Add(p2);
dodec.Midpoints.Add(Halfway(p1, p2));
}
}
// Now recursively add more vertices.
HashSet <Vector3D> allVerts = new HashSet <Vector3D>();
foreach (Vector3D v in dodec.Verts)
{
allVerts.Add(v);
}
RecurseTwins(allVerts, dodec, 0);
using (StreamWriter sw = File.CreateText("dual_dodecs_points_sphere.pov"))
{
foreach (Vector3D vert in allVerts)
{
Vector3D onSphere = Sterographic.PlaneToSphereSafe(vert);
sw.WriteLine(PovRay.Sphere(new Sphere()
{
Center = onSphere, Radius = 0.01
}));
//if( !Infinity.IsInfinite( vert ) )
// sw.WriteLine( PovRay.Sphere( new Sphere() { Center = vert, Radius = 0.01 } ) );
}
}
}
public static Vector3D Centroid(Geometry g, Vector3D[] conformalVerts)
{
if (g == Geometry.Euclidean)
{
Vector3D result = new Vector3D();
foreach (Vector3D v in conformalVerts)
{
result += v;
}
return(result / conformalVerts.Length);
}
Vector3D[] verts = conformalVerts.Select(v =>
{
switch (g)
{
case Geometry.Spherical:
return(Sterographic.PlaneToSphereSafe(v));
case Geometry.Hyperbolic:
return(Sterographic.PlaneToHyperboloid(v));
}
throw new System.ArgumentException();
}).ToArray();
// https://math.stackexchange.com/a/2173370/300001
Vector3D sum = new Vector3D();
for (int i = 0; i < verts.Length; i++)
{
sum += verts[i];
}
Vector3D centroid = sum / Math.Sqrt(DotInGeometry(g, sum, sum));
NormalizeInGeometry(g, ref centroid);
switch (g)
{
case Geometry.Spherical:
return(Sterographic.SphereToPlane(centroid));
case Geometry.Hyperbolic:
return(Sterographic.HyperboloidToPlane(centroid));
}
throw new System.ArgumentException();
}