private static List <Vector3D[]> BasePointsTiling()
{
TilingConfig config = new TilingConfig(3, 7, maxTiles: 100);
Tiling tiling = new Tiling();
tiling.Generate(config);
HashSet <H3.Cell.Edge> finished = new HashSet <H3.Cell.Edge>(new H3.Cell.EdgeEqualityComparer());
int numPerSeg = 25;
List <Vector3D[]> basePoints = new List <Vector3D[]>();
foreach (Tile t in tiling.Tiles)
{
foreach (Segment s in t.Boundary.Segments)
{
H3.Cell.Edge e = new H3.Cell.Edge(s.P1, s.P2);
if (finished.Contains(e))
{
continue;
}
finished.Add(e);
Vector3D[] points = s.Subdivide(numPerSeg).Select(p =>
{
p = new Vector3D(p.X, 0, p.Y);
return(H3Models.BallToUHS(p));
}).ToArray();
basePoints.Add(points);
}
}
return(basePoints);
}
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);
}
}
}
}
public static void Cell633()
{
TilingConfig config = new TilingConfig(6, 3, maxTiles: 20000);
Tiling tiling = new Tiling();
tiling.GenerateInternal(config, Polytope.Projection.VertexCentered);
double edgeLength = Honeycomb.EdgeLength(6, 3, 3);
double z = 0.25;
double offset = H3Models.UHS.ToEHorizontal(edgeLength, z);
double scale = offset / tiling.Tiles.First().Boundary.Segments.First().Length;
foreach (Tile tile in tiling.Tiles)
{
tile.Transform(Mobius.Scale(scale));
}
Vector3D dummy;
double radius;
H3Models.UHS.Geodesic(new Vector3D(0, 0, z), new Vector3D(scale, 0, z), out dummy, out radius);
Vector3D midradius = H3Models.UHSToBall(new Vector3D(0, 0, radius));
double temp = midradius.Z;
double temp2 = (1 - temp) / 2;
double temp3 = temp + temp2;
double temp4 = temp3;
Vector3D circumradius = H3Models.UHSToBall(new Vector3D(0, 0, z));
temp = circumradius.Z;
temp2 = (1 - temp) / 2;
temp3 = temp + temp2;
temp4 = temp3;
// Checking
/*
* Vector3D test = new Vector3D( offset, 0, z );
* test = H3Models.UHSToBall( test );
* double edgeLength2 = DonHatch.e2hNorm( test.Abs() );
* edgeLength2 += 0;
*/
HashSet <H3.Cell.Edge> edges = new HashSet <H3.Cell.Edge>();
foreach (Tile tile in tiling.Tiles)
{
foreach (Segment seg in tile.Boundary.Segments)
{
H3.Cell.Edge edge = new H3.Cell.Edge(
H3Models.UHSToBall(seg.P1 + new Vector3D(0, 0, z)),
H3Models.UHSToBall(seg.P2 + new Vector3D(0, 0, z)));
edges.Add(edge);
}
}
PovRay.WriteH3Edges(new PovRay.Parameters(), edges.ToArray(), "edges.pov");
}
// 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 } ) );
}
}
}
/// <summary>
/// Get a distribution of points on a sphere.
/// The points are the vertices of a geodesic dome.
/// </summary>
private static Vector3D[] SpherePoints()
{
List <Vector3D> spherePoints = new List <Vector3D>();
TilingConfig config = new TilingConfig(3, 5);
Tiling tiling = new Tiling();
tiling.GenerateInternal(config);
Tile baseTile = tiling.Tiles.First();
Vector3D[] templateTextureCoords = TextureHelper.TextureCoords(baseTile.Boundary, Geometry.Spherical, doGeodesicDome: true);
foreach (Tile tile in tiling.Tiles)
{
Isometry isom = new Isometry();
isom.CalculateFromTwoPolygons(baseTile, tile, Geometry.Spherical);
Vector3D[] textureCoords = Isometry.TransformVertices(templateTextureCoords, isom.Inverse());
spherePoints.AddRange(textureCoords);
}
return(spherePoints.Select(p => H3Models.UHSToBall(p)).Distinct().ToArray());
}
public static void Polarity()
{
TilingConfig config = new TilingConfig(3, 7, 50);
Tiling tiling = new Tiling();
tiling.GenerateInternal(config);
List <Vector3D> points = new List <Vector3D>();
List <H3.Cell.Edge> edges = new List <H3.Cell.Edge>();
foreach (Polygon p in tiling.Tiles.Select(t => t.Boundary))
{
foreach (Segment s in p.Segments)
{
foreach (Vector3D v in s.Subdivide(25))
{
Vector3D klein = HyperbolicModels.PoincareToKlein(v);
H3.Cell.Edge e = Dual(klein);
points.Add(klein);
edges.Add(e);
}
}
}
using (StreamWriter sw = File.CreateText("polarity.pov"))
{
double rad = 0.01;
foreach (Vector3D vert in points)
{
sw.WriteLine(PovRay.Sphere(new Sphere()
{
Center = vert, Radius = rad
}));
}
foreach (H3.Cell.Edge edge in edges)
{
sw.WriteLine(PovRay.Cylinder(edge.Start, edge.End, rad / 2));
}
}
}
private static void HyperidealSquares()
{
Mobius rot = new Mobius();
rot.Isometry(Geometry.Spherical, Math.PI / 4, new Vector3D());
List <Segment> segs = new List <Segment>();
int[] qs = new int[] { 5, -1 };
foreach (int q in qs)
{
TilingConfig config = new TilingConfig(4, q, 1);
Tile t = Tiling.CreateBaseTile(config);
List <Segment> polySegs = t.Boundary.Segments;
polySegs = polySegs.Select(s => { s.Transform(rot); return(s); }).ToList();
segs.AddRange(polySegs);
}
Vector3D v1 = new Vector3D(1, 0);
v1.RotateXY(Math.PI / 6);
Vector3D v2 = v1;
v2.Y *= -1;
Vector3D cen;
double rad;
H3Models.Ball.OrthogonalCircle(v1, v2, out cen, out rad);
Segment seg = Segment.Arc(v1, v2, cen, false);
rot.Isometry(Geometry.Spherical, Math.PI / 2, new Vector3D());
for (int i = 0; i < 4; i++)
{
seg.Transform(rot);
segs.Add(seg.Clone());
}
SVG.WriteSegments("output1.svg", segs);
System.Func <Segment, Segment> PoincareToKlein = s =>
{
return(Segment.Line(
HyperbolicModels.PoincareToKlein(s.P1),
HyperbolicModels.PoincareToKlein(s.P2)));
};
segs = segs.Select(s => PoincareToKlein(s)).ToList();
Vector3D v0 = new Vector3D(v1.X, v1.X);
Vector3D v3 = v0;
v3.Y *= -1;
Segment seg1 = Segment.Line(v0, v1), seg2 = Segment.Line(v2, v3);
Segment seg3 = Segment.Line(new Vector3D(1, 1), new Vector3D(1, -1));
for (int i = 0; i < 4; i++)
{
seg1.Transform(rot);
seg2.Transform(rot);
seg3.Transform(rot);
segs.Add(seg1.Clone());
segs.Add(seg2.Clone());
segs.Add(seg3.Clone());
}
SVG.WriteSegments("output2.svg", segs);
}
