public static bool IsExotic(EHoneycomb honeycomb)
{
return
(honeycomb == EHoneycomb.H444 ||
honeycomb == EHoneycomb.H636 ||
honeycomb == EHoneycomb.H363);
}
public static double EdgeLength(EHoneycomb honeycomb)
{
int p, q, r;
PQR(honeycomb, out p, out q, out r);
return(EdgeLength(p, q, r));
}
public static double CircumRadius(EHoneycomb honeycomb)
{
int p, q, r;
PQR(honeycomb, out p, out q, out r);
return(CircumRadius(p, q, r));
}
private static void GetAssociatedTiling(EHoneycomb honeycomb, out Tiling tiling, out Tile baseTile)
{
int p, q;
GetPQ(honeycomb, out p, out q);
TilingConfig tilingConfig = new TilingConfig(p, q, maxTiles: m_params.MaxTiles);
tiling = new Tiling();
tiling.Generate(tilingConfig);
baseTile = Tiling.CreateBaseTile(tilingConfig);
}
public static void PQR(EHoneycomb honeycomb, out int p, out int q, out int r)
{
switch (honeycomb)
{
case EHoneycomb.H435:
p = 4; q = 3; r = 5; return;
case EHoneycomb.H534:
p = 5; q = 3; r = 4; return;
case EHoneycomb.H535:
p = 5; q = 3; r = 5; return;
case EHoneycomb.H353:
p = 3; q = 5; r = 3; return;
case EHoneycomb.H336:
p = 3; q = 3; r = 6; return;
case EHoneycomb.H436:
p = 4; q = 3; r = 6; return;
case EHoneycomb.H536:
p = 5; q = 3; r = 6; return;
case EHoneycomb.H344:
p = 3; q = 4; r = 4; return;
case EHoneycomb.H444:
p = 4; q = 4; r = 4; return;
case EHoneycomb.H363:
p = 3; q = 6; r = 3; return;
case EHoneycomb.H636:
p = 6; q = 3; r = 6; return;
case EHoneycomb.H337:
p = 3; q = 3; r = 7; return;
case EHoneycomb.H33I:
p = 3; q = 3; r = -1; return;
}
throw new System.ArgumentException();
}
public static string String(EHoneycomb honeycomb, bool dual)
{
switch (honeycomb)
{
case EHoneycomb.H435:
return(dual ? "{5,3,4}" : "{4,3,5}");
case EHoneycomb.H534:
return(dual ? "{4,3,5}" : "{5,3,4}");
case EHoneycomb.H535:
return("{5,3,5}");
case EHoneycomb.H353:
return("{3,5,3}");
case EHoneycomb.H336:
return(dual ? "{6,3,3}" : "{3,3,6}");
case EHoneycomb.H436:
return(dual ? "{6,3,4}" : "{4,3,6}");
case EHoneycomb.H536:
return(dual ? "{6,3,5}" : "{5,3,6}");
case EHoneycomb.H344:
return(dual ? "{4,4,3}" : "{3,4,4}");
case EHoneycomb.H444:
return("{4,4,4}");
case EHoneycomb.H636:
return("{6,3,6}");
case EHoneycomb.H363:
return("{3,6,3}");
case EHoneycomb.H337:
return(dual ? "{7,3,3}" : "{3,3,7}");
case EHoneycomb.H33I:
return(dual ? "{inf,3,3}" : "{3,3,inf}");
}
throw new System.ArgumentException("Unknown honeycomb type");
}
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 double EdgeLength( EHoneycomb honeycomb )
{
int p, q, r;
PQR( honeycomb, out p, out q, out r );
return EdgeLength( p, q, r );
}
public static double CircumRadius( EHoneycomb honeycomb )
{
int p, q, r;
PQR( honeycomb, out p, out q, out r );
return CircumRadius( p, q, r );
}
public static string String( EHoneycomb honeycomb, bool dual )
{
switch( honeycomb )
{
case EHoneycomb.H435:
return dual ? "{5,3,4}" : "{4,3,5}";
case EHoneycomb.H534:
return dual ? "{4,3,5}" : "{5,3,4}";
case EHoneycomb.H535:
return "{5,3,5}";
case EHoneycomb.H353:
return "{3,5,3}";
case EHoneycomb.H336:
return dual ? "{6,3,3}" : "{3,3,6}";
case EHoneycomb.H436:
return dual ? "{6,3,4}" : "{4,3,6}";
case EHoneycomb.H536:
return dual ? "{6,3,5}" : "{5,3,6}";
case EHoneycomb.H344:
return dual ? "{4,4,3}" : "{3,4,4}";
case EHoneycomb.H444:
return "{4,4,4}";
case EHoneycomb.H636:
return "{6,3,6}";
case EHoneycomb.H363:
return "{3,6,3}";
case EHoneycomb.H337:
return dual ? "{7,3,3}" : "{3,3,7}";
case EHoneycomb.H33I:
return dual ? "{inf,3,3}" : "{3,3,inf}";
}
throw new System.ArgumentException( "Unknown honeycomb type" );
}
public static void PQR( EHoneycomb honeycomb, out int p, out int q, out int r )
{
switch( honeycomb )
{
case EHoneycomb.H435:
p = 4; q = 3; r = 5; return;
case EHoneycomb.H534:
p = 5; q = 3; r = 4; return;
case EHoneycomb.H535:
p = 5; q = 3; r = 5; return;
case EHoneycomb.H353:
p = 3; q = 5; r = 3; return;
case EHoneycomb.H336:
p = 3; q = 3; r = 6; return;
case EHoneycomb.H436:
p = 4; q = 3; r = 6; return;
case EHoneycomb.H536:
p = 5; q = 3; r = 6; return;
case EHoneycomb.H344:
p = 3; q = 4; r = 4; return;
case EHoneycomb.H444:
p = 4; q = 4; r = 4; return;
case EHoneycomb.H363:
p = 3; q = 6; r = 3; return;
case EHoneycomb.H636:
p = 6; q = 3; r = 6; return;
case EHoneycomb.H337:
p = 3; q = 3; r = 7; return;
case EHoneycomb.H33I:
p = 3; q = 3; r = -1; return;
}
throw new System.ArgumentException();
}
private static void GetAssociatedTiling( EHoneycomb honeycomb, out Tiling tiling, out Tile baseTile )
{
int p, q;
GetPQ( honeycomb, out p, out q );
TilingConfig tilingConfig = new TilingConfig( p, q, maxTiles: m_params.MaxTiles );
tiling = new Tiling();
tiling.Generate( tilingConfig );
baseTile = Tiling.CreateBaseTile( tilingConfig );
}
/// <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 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");
}
/// <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);
}
}
public static bool IsExotic( EHoneycomb honeycomb )
{
return
honeycomb == EHoneycomb.H444 ||
honeycomb == EHoneycomb.H636 ||
honeycomb == EHoneycomb.H363;
}
