public static void CalcEScale()
{
// Euclidean scale is arbitrary, but put it in the middle of the projections of 433 and 435.
double r3 = Spherical2D.s2eNorm(Honeycomb.CircumRadius(4, 3, 3));
double r5 = DonHatch.h2eNorm(Honeycomb.CircumRadius(4, 3, 5));
m_eScale = (r3 + r5) / (2 * Math.Sqrt(3));
}
public static Vector3D EdgeMidpointSpherical(int p, int q, int r)
{
// Get a {q,p} tiling on the z=0 plane.
Segment[] baseTileSegments = BaseTileSegments(q, p);
Vector3D direction = H3Models.UHSToBall(baseTileSegments.First().Midpoint);
direction.Normalize();
double midRadius = Spherical2D.s2eNorm(Honeycomb.MidRadius(p, q, r));
return(direction * midRadius);
}
public static Vector3D FaceCenterSpherical(int p, int q, int r)
{
// Get a {q,p} tiling on the z=0 plane.
Segment[] baseTileSegments = BaseTileSegments(q, p);
// This will be unit length.
Vector3D pFaceDirection = H3Models.UHSToBall(baseTileSegments.First().P1);
// In-radius is in conformal model
double inRadius = Spherical2D.s2eNorm(Honeycomb.InRadius(p, q, r));
return(pFaceDirection * inRadius);
}
/// <summary>
/// Mirrors for Spherical geometry, in the ball model.
/// </summary>
public static Sphere[] MirrorsSpherical(int p, int q, int r)
{
// Get a {q,p} tiling on the z=0 plane.
Segment[] baseTileSegments = BaseTileSegments(q, p);
// This will be unit length.
Vector3D pFaceDirection = H3Models.UHSToBall(baseTileSegments.First().P1);
// In-radius is in conformal model
double inRadius = Spherical2D.s2eNorm(Honeycomb.InRadius(p, q, r));
double centerOfSphereNE = (1 - inRadius) / (1 + inRadius);
Vector3D center;
double radius;
H3Models.Ball.DupinCyclideSphere(-pFaceDirection * centerOfSphereNE, 1.0 /*geodesic circle*/, Geometry.Spherical, out center, out radius);
Sphere cellBoundary = new Sphere()
{
Center = center, Radius = radius, Invert = true
};
Sphere[] interior = InteriorMirrors(p, q);
interior = interior.Select(s => H3Models.UHSToBall(s)).ToArray();
Sphere[] surfaces = new Sphere[] { cellBoundary, interior[0], interior[1], interior[2] };
// Apply rotations.
bool applyRotations = false;
if (applyRotations)
{
double rotation = Math.PI / 2;
foreach (Sphere s in surfaces)
{
RotateSphere(s, rotation);
}
}
return(surfaces);
}
/// <summary>
/// Our approach will be:
/// (1) Generate a portion of one cell.
/// (2) Reflect all facets in the central facet, to get things filled-in inside the central facet. (Trim small edges here?)
/// (3) Copy this region around the plane, and go back to step (2) if density is not high enough.
/// (4) Map to Ball, trimming edges that become too small.
/// NOTE: All verts are on the boundary, so we can reflect around
// in circles on the plane at infinity, rather than spheres.
/// </summary>
public static void GenerateExotic(EHoneycomb honeycomb, H3.Settings settings)
{
settings.AngularThickness = 0.17;
Tiling tiling;
Tile baseTile;
GetAssociatedTiling(honeycomb, out tiling, out baseTile);
List <H3.Cell.Edge> edges = new List <H3.Cell.Edge>();
foreach (Segment seg in baseTile.Boundary.Segments)
{
edges.Add(new H3.Cell.Edge(seg.P1, seg.P2));
}
settings.Position = Polytope.Projection.FaceCentered;
double scale = 1;
Vector3D offset = new Vector3D();
if (settings.Position == Polytope.Projection.FaceCentered)
{
scale = FaceCenteredScale(baseTile.VertexCircle);
offset = new Vector3D();
}
else if (settings.Position == Polytope.Projection.EdgeCentered)
{
scale = EdgeCenteredScale(baseTile);
offset = baseTile.Boundary.Segments[0].Midpoint;
}
int iterations = m_params.Iterations;
for (int i = 0; i < iterations; i++)
{
edges = DoOneStep(edges, tiling, baseTile.VertexCircle);
}
edges = CopyAndProject(edges, tiling, scale, offset);
if (m_params.RemoveDangling)
{
Dictionary <H3.Cell.Edge, int> edgeDict = edges.ToDictionary(e => e, e => 1);
H3.RemoveDanglingEdgesRecursive(edgeDict);
edges = edgeDict.Keys.ToList();
}
string outputFileName = H3.m_baseDir + Honeycomb.String(honeycomb, false);
System.IO.File.Delete(outputFileName);
if (m_params.Output == H3.Output.STL)
{
outputFileName += ".stl";
// Now mesh the edges.
Shapeways mesh = new Shapeways();
foreach (H3.Cell.Edge edge in edges)
{
// Append to the file vs. writing out all at once because I was running out of memory otherwise.
mesh = new Shapeways();
int div;
H3Models.Ball.LODThin(edge.Start, edge.End, out div);
mesh.Div = div;
H3.Util.AddToMeshInternal(mesh, edge.Start, edge.End);
mesh.Mesh.Scale(settings.Scale);
STL.AppendMeshToSTL(mesh.Mesh, outputFileName);
}
}
else
{
outputFileName += ".pov";
PovRay.WriteH3Edges(new PovRay.Parameters()
{
AngularThickness = settings.AngularThickness,
Halfspace = settings.Halfspace,
ThinEdges = settings.ThinEdges,
},
edges.ToArray(), outputFileName);
}
}
private static void GetPQ(EHoneycomb honeycomb, out int p, out int q)
{
int r;
Honeycomb.PQR(honeycomb, out p, out q, out r);
}
public static Vector3D VertexSpherical(int p, int q, int r)
{
double circumRadius = Spherical2D.s2eNorm(Honeycomb.CircumRadius(p, q, r));
return(new Vector3D(0, 0, -circumRadius));
}
public static void Generate(EHoneycomb honeycomb, H3.Settings settings)
{
// XXX - Block the same as in H3. Share code better.
H3.Cell template = null;
{
int p, q, r;
Honeycomb.PQR(honeycomb, out p, out q, out r);
// Get data we need to generate the honeycomb.
Polytope.Projection projection = Polytope.Projection.FaceCentered;
double phi, chi, psi;
H3.HoneycombData(honeycomb, out phi, out chi, out psi);
H3.SetupCentering(honeycomb, settings, phi, chi, psi, ref projection);
Tiling tiling = new Tiling();
TilingConfig config = new TilingConfig(p, q);
tiling.GenerateInternal(config, projection);
H3.Cell first = new H3.Cell(p, H3.GenFacets(tiling));
first.ToSphere(); // Work in ball model.
first.ScaleToCircumSphere(1.0);
first.ApplyMobius(settings.Mobius);
template = first;
}
// Center
Vector3D center = template.Center;
// Face
H3.Cell.Facet facet = template.Facets[0];
Sphere s = H3Models.Ball.OrthogonalSphereInterior(facet.Verts[0], facet.Verts[1], facet.Verts[2]);
Vector3D face = s.Center;
face.Normalize();
face *= DistOriginToOrthogonalSphere(s.Radius);
// Edge
Circle3D c;
H3Models.Ball.OrthogonalCircleInterior(facet.Verts[0], facet.Verts[1], out c);
Vector3D edge = c.Center;
edge.Normalize();
edge *= DistOriginToOrthogonalSphere(c.Radius);
// Vertex
Vector3D vertex = facet.Verts[0];
Tet fundamental = new Tet(center, face, edge, vertex);
// Recurse.
int level = 1;
Dictionary <Tet, int> completedTets = new Dictionary <Tet, int>(new TetEqualityComparer());
completedTets.Add(fundamental, level);
List <Tet> tets = new List <Tet>();
tets.Add(fundamental);
ReflectRecursive(level, tets, completedTets, settings);
Shapeways mesh = new Shapeways();
foreach (KeyValuePair <Tet, int> kvp in completedTets)
{
if (Utils.Odd(kvp.Value))
{
continue;
}
Tet tet = kvp.Key;
// XXX - really want sphere surfaces here.
mesh.Mesh.Triangles.Add(new Mesh.Triangle(tet.Verts[0], tet.Verts[1], tet.Verts[2]));
mesh.Mesh.Triangles.Add(new Mesh.Triangle(tet.Verts[0], tet.Verts[3], tet.Verts[1]));
mesh.Mesh.Triangles.Add(new Mesh.Triangle(tet.Verts[0], tet.Verts[2], tet.Verts[3]));
mesh.Mesh.Triangles.Add(new Mesh.Triangle(tet.Verts[1], tet.Verts[3], tet.Verts[2]));
}
mesh.Mesh.Scale(settings.Scale);
STL.SaveMeshToSTL(mesh.Mesh, H3.m_baseDir + "fundamental" + ".stl");
}
public static double PiOverNSafe(int n)
{
return(Honeycomb.PiOverNSafe(n));
}
public static Geometry GetGeometry(int p, int q, int r)
{
return(Honeycomb.GetGeometry(p, q, r));
}