/// <summary>
/// Make an edge mesh of a regular tiling.
/// </summary>
public static Mesh MakeEdgeMesh( int p, int q )
{
Mesh mesh = new Mesh();
int maxTiles = 400;
Tiling tiling = new Tiling();
TilingConfig config = new TilingConfig( p, q, maxTiles: maxTiles );
config.Shrink = 0.6;
tiling.GenerateInternal( config );
TilingConfig boundaryConfig = new TilingConfig( 14, 7, maxTiles: 1 );
boundaryConfig.Shrink = 1.01;
Tile boundary = Tiling.CreateBaseTile( boundaryConfig );
AddSymmetryTriangles( mesh, tiling, boundary.Drawn );
//AddSymmetryTriangles( mesh, tiling, null );
return mesh;
HashSet<Vector3D> completed = new HashSet<Vector3D>();
int count = 0;
foreach( Tile tile in tiling.Tiles )
{
MeshEdges( mesh, tile, completed, null );
count++;
if( count >= maxTiles )
break;
}
return mesh;
}
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");
}
public Tile[] FundamentalCell()
{
Tile template = TemplateTile();
Tile.ShrinkTile(ref template, 0.9);
// Generate a cell tiling.
TilingConfig tilingConfig = new TilingConfig(Q, P);
Tiling poly = new Tiling();
poly.Generate(tilingConfig);
m_tiles = poly.Tiles.ToList();
//SetupTransformCircle( tile ); // Call this before transforming.
//SetupNeighborCircle( tile );
// Generate our cell.
List <Tile> cellTiles = new List <Tile>();
foreach (Tile t in poly.Tiles)
{
Tile temp = template.Clone();
temp.Transform(t.Isometry.Inverse());
cellTiles.Add(temp);
}
return(cellTiles.ToArray());
}
private static void GetAssociatedTiling(int p, int q, int maxTiles, out Tiling tiling)
{
TilingConfig tilingConfig = new TilingConfig(p, q, maxTiles: maxTiles);
tiling = new Tiling();
tiling.GenerateInternal(tilingConfig, p == 6 ? Polytope.Projection.VertexCentered : Polytope.Projection.FaceCentered);
}
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");
}
private static Segment[] BaseTileSegments(int p, int q)
{
Tiling tiling = new Tiling();
TilingConfig config = new TilingConfig(p, q, 1);
Tile baseTile = Tiling.CreateBaseTile(config);
//baseTile.Transform( Mobius.Scale( 2 ) ); // Only works in Euclidean case
return(baseTile.Boundary.Segments.ToArray());
}
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 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" );
}
/// <summary>
/// A static helper to generate two dual tilings.
/// </summary>
/// <remarks>{p,q} will have a vertex at the center.</remarks>
/// <remarks>{q,p} will have its center at the center.</remarks>
public static void MakeDualTilings(out Tiling tiling1, out Tiling tiling2, int p, int q)
{
tiling1 = new Tiling();
tiling2 = new Tiling();
int maxTiles = 2000;
TilingConfig config1 = new TilingConfig(p, q, maxTiles);
TilingConfig config2 = new TilingConfig(q, p, maxTiles);
tiling1.GenerateInternal(config1, Polytope.Projection.FaceCentered);
tiling2.GenerateInternal(config2, Polytope.Projection.VertexCentered);
/*
* Circle c = new Circle();
* c.Radius = .9;
* tiling1.Clip( c );
* tiling2.Clip( c );
*/
}
/// <summary>
/// Make an edge mesh of a regular tiling.
/// </summary>
public static Mesh MakeEdgeMesh(int p, int q)
{
Mesh mesh = new Mesh();
int maxTiles = 400;
Tiling tiling = new Tiling();
TilingConfig config = new TilingConfig(p, q, maxTiles: maxTiles);
config.Shrink = 0.6;
tiling.GenerateInternal(config);
TilingConfig boundaryConfig = new TilingConfig(14, 7, maxTiles: 1);
boundaryConfig.Shrink = 1.01;
Tile boundary = Tiling.CreateBaseTile(boundaryConfig);
AddSymmetryTriangles(mesh, tiling, boundary.Drawn);
//AddSymmetryTriangles( mesh, tiling, null );
return(mesh);
}
/// <summary>
/// Make an edge mesh of a regular tiling.
/// </summary>
public static Mesh MakeEdgeMesh(int p, int q)
{
Mesh mesh = new Mesh();
int maxTiles = 400;
Tiling tiling = new Tiling();
TilingConfig config = new TilingConfig(p, q, maxTiles: maxTiles);
config.Shrink = 0.6;
tiling.GenerateInternal(config);
TilingConfig boundaryConfig = new TilingConfig(14, 7, maxTiles: 1);
boundaryConfig.Shrink = 1.01;
Tile boundary = Tiling.CreateBaseTile(boundaryConfig);
AddSymmetryTriangles(mesh, tiling, boundary.Drawn);
//AddSymmetryTriangles( mesh, tiling, null );
return(mesh);
HashSet <Vector3D> completed = new HashSet <Vector3D>();
int count = 0;
foreach (Tile tile in tiling.Tiles)
{
MeshEdges(mesh, tile, completed, null);
count++;
if (count >= maxTiles)
{
break;
}
}
return(mesh);
}
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 List<H3.Cell.Edge> CopyAndProject( List<H3.Cell.Edge> regionEdges, Tiling tiling, double scale, Vector3D offset )
{
HashSet<H3.Cell.Edge> newEdges = new HashSet<H3.Cell.Edge>( new H3.Cell.EdgeEqualityComparer() );
//foreach( Tile tile in tiling.Tiles ) // Needed for doing full ball (rather than just half of it)
Tile tile = tiling.Tiles.First();
{
foreach( H3.Cell.Edge edge in regionEdges )
{
// Translation
// The isometry is necessary for the 363, but seems to mess up 636
Vector3D start = tile.Isometry.Apply( edge.Start ) + offset;
Vector3D end = tile.Isometry.Apply( edge.End ) + offset;
//Vector3D start = edge.Start + tile.Center + offset;
//Vector3D end = edge.End + tile.Center + offset;
// Scaling
start *= scale;
end *= scale;
// Projections
start = H3Models.UHSToBall( start );
end = H3Models.UHSToBall( end );
H3.Cell.Edge transformed = new H3.Cell.Edge( start, end );
if( EdgeOkBall( transformed ) )
newEdges.Add( transformed );
}
}
return newEdges.ToList();
}
private static Segment[] BaseTileSegments( int p, int q )
{
Tiling tiling = new Tiling();
TilingConfig config = new TilingConfig( p, q, 1 );
Tile baseTile = Tiling.CreateBaseTile( config );
//baseTile.Transform( Mobius.Scale( 2 ) ); // Only works in Euclidean case
return baseTile.Boundary.Segments.ToArray();
}
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>
/// Helper to do one step of reflections.
/// Returns a new list of region edges.
/// </summary>
private static List<H3.Cell.Edge> DoOneStep( List<H3.Cell.Edge> regionEdges, Tiling tiling, Circle region )
{
HashSet<H3.Cell.Edge> newEdges = new HashSet<H3.Cell.Edge>( new H3.Cell.EdgeEqualityComparer() );
foreach( Tile tile in tiling.Tiles )
{
foreach( H3.Cell.Edge edge in regionEdges )
{
H3.Cell.Edge toAdd = null;
if( !Tolerance.Zero( tile.Center.Abs() ) )
{
// Translate
// The isometry is necessary for the 363, but seems to mess up 636
Vector3D start = tile.Isometry.Apply( edge.Start );
Vector3D end = tile.Isometry.Apply( edge.End );
//Vector3D start = edge.Start + tile.Center;
//Vector3D end = edge.End + tile.Center;
// Reflect
start = region.ReflectPoint( start );
end = region.ReflectPoint( end );
toAdd = new H3.Cell.Edge( start, end );
}
else
toAdd = edge;
if( EdgeOkUHS( toAdd, region ) )
newEdges.Add( toAdd );
}
}
return newEdges.ToList();
}
private static void AddSymmetryTriangles(Mesh mesh, Tiling tiling, Polygon boundary)
{
// Assume template centered at the origin.
Polygon template = tiling.Tiles.First().Boundary;
List <Triangle> templateTris = new List <Triangle>();
foreach (Segment seg in template.Segments)
{
int num = 1 + (int)(seg.Length * m_divisions);
Vector3D a = new Vector3D();
Vector3D b = seg.P1;
Vector3D c = seg.Midpoint;
Vector3D centroid = (a + b + c) / 3;
Polygon poly = new Polygon();
Segment segA = Segment.Line(new Vector3D(), seg.P1);
Segment segB = seg.Clone();
segB.P2 = seg.Midpoint;
Segment segC = Segment.Line(seg.Midpoint, new Vector3D());
poly.Segments.Add(segA);
poly.Segments.Add(segB);
poly.Segments.Add(segC);
Vector3D[] coords = TextureHelper.TextureCoords(poly, Geometry.Hyperbolic);
int[] elements = TextureHelper.TextureElements(3, LOD: 3);
for (int i = 0; i < elements.Length / 3; i++)
{
int idx1 = i * 3;
int idx2 = i * 3 + 1;
int idx3 = i * 3 + 2;
Vector3D v1 = coords[elements[idx1]];
Vector3D v2 = coords[elements[idx2]];
Vector3D v3 = coords[elements[idx3]];
templateTris.Add(new Triangle(v1, v2, v3));
}
/*
*
* // Need to shrink a little, so we won't
* // get intersections among neighboring faces.
* a = Shrink( a, centroid );
* b = Shrink( b, centroid );
* c = Shrink( c, centroid );
*
* Vector3D[] list = seg.Subdivide( num * 2 );
* list[0] = b;
* list[list.Length / 2] = c;
* for( int i = 0; i < list.Length / 2; i++ )
* templateTris.Add( new Triangle( centroid, list[i], list[i + 1] ) );
*
* for( int i = num - 1; i >= 0; i-- )
* templateTris.Add( new Triangle( centroid, a + (c - a) * (i + 1) / num, a + (c - a) * i / num ) );
*
* for( int i = 0; i < num; i++ )
* templateTris.Add( new Triangle( centroid, a + (b - a) * i / num, a + (b - a) * (i + 1) / num ) );
*/
}
foreach (Tile tile in tiling.Tiles)
{
Vector3D a = tile.Boundary.Segments[0].P1;
Vector3D b = tile.Boundary.Segments[1].P1;
Vector3D c = tile.Boundary.Segments[2].P1;
Mobius m = new Mobius();
if (tile.Isometry.Reflected)
{
m.MapPoints(template.Segments[0].P1, template.Segments[1].P1, template.Segments[2].P1, c, b, a);
}
else
{
m.MapPoints(template.Segments[0].P1, template.Segments[1].P1, template.Segments[2].P1, a, b, c);
}
foreach (Triangle tri in templateTris)
{
Triangle transformed = new Triangle(
m.Apply(tri.a),
m.Apply(tri.b),
m.Apply(tri.c));
CheckAndAdd(mesh, transformed, boundary);
}
}
}
/// <summary>
/// A static helper to generate two dual tilings.
/// </summary>
/// <remarks>{p,q} will have a vertex at the center.</remarks>
/// <remarks>{q,p} will have its center at the center.</remarks>
public static void MakeDualTilings( out Tiling tiling1, out Tiling tiling2, int p, int q )
{
tiling1 = new Tiling();
tiling2 = new Tiling();
int maxTiles = 2000;
TilingConfig config1 = new TilingConfig( p, q, maxTiles );
TilingConfig config2 = new TilingConfig( q, p, maxTiles );
tiling1.GenerateInternal( config1, Polytope.Projection.FaceCentered );
tiling2.GenerateInternal( config2, Polytope.Projection.VertexCentered );
/*
Circle c = new Circle();
c.Radius = .9;
tiling1.Clip( c );
tiling2.Clip( c );
*/
}
private static void AddSymmetryTriangles( Mesh mesh, Tiling tiling, Polygon boundary )
{
// Assume template centered at the origin.
Polygon template = tiling.Tiles.First().Boundary;
List<Triangle> templateTris = new List<Triangle>();
foreach( Segment seg in template.Segments )
{
int num = 1 + (int)(seg.Length * m_divisions);
Vector3D a = new Vector3D();
Vector3D b = seg.P1;
Vector3D c = seg.Midpoint;
Vector3D centroid = ( a + b + c ) / 3;
Polygon poly = new Polygon();
Segment segA = Segment.Line( new Vector3D(), seg.P1 );
Segment segB = seg.Clone();
segB.P2 = seg.Midpoint;
Segment segC = Segment.Line( seg.Midpoint, new Vector3D() );
poly.Segments.Add( segA );
poly.Segments.Add( segB );
poly.Segments.Add( segC );
Vector3D[] coords = TextureHelper.TextureCoords( poly, Geometry.Hyperbolic );
int[] elements = TextureHelper.TextureElements( 3, LOD: 3 );
for( int i = 0; i < elements.Length / 3; i++ )
{
int idx1 = i * 3;
int idx2 = i * 3 + 1;
int idx3 = i * 3 + 2;
Vector3D v1 = coords[elements[idx1]];
Vector3D v2 = coords[elements[idx2]];
Vector3D v3 = coords[elements[idx3]];
templateTris.Add( new Triangle( v1, v2, v3 ) );
}
/*
// Need to shrink a little, so we won't
// get intersections among neighboring faces.
a = Shrink( a, centroid );
b = Shrink( b, centroid );
c = Shrink( c, centroid );
Vector3D[] list = seg.Subdivide( num * 2 );
list[0] = b;
list[list.Length / 2] = c;
for( int i = 0; i < list.Length / 2; i++ )
templateTris.Add( new Triangle( centroid, list[i], list[i + 1] ) );
for( int i = num - 1; i >= 0; i-- )
templateTris.Add( new Triangle( centroid, a + (c - a) * (i + 1) / num, a + (c - a) * i / num ) );
for( int i = 0; i < num; i++ )
templateTris.Add( new Triangle( centroid, a + (b - a) * i / num, a + (b - a) * (i + 1) / num ) );
*/
}
foreach( Tile tile in tiling.Tiles )
{
Vector3D a = tile.Boundary.Segments[0].P1;
Vector3D b = tile.Boundary.Segments[1].P1;
Vector3D c = tile.Boundary.Segments[2].P1;
Mobius m = new Mobius();
if( tile.Isometry.Reflected )
m.MapPoints( template.Segments[0].P1, template.Segments[1].P1, template.Segments[2].P1, c, b, a );
else
m.MapPoints( template.Segments[0].P1, template.Segments[1].P1, template.Segments[2].P1, a, b, c );
foreach( Triangle tri in templateTris )
{
Triangle transformed = new Triangle(
m.Apply( tri.a ),
m.Apply( tri.b ),
m.Apply( tri.c ) );
CheckAndAdd( mesh, transformed, boundary );
}
}
}
/// <summary>
/// Helper to do one step of reflections.
/// Returns a new list of region edges.
/// </summary>
private static List <H3.Cell.Edge> DoOneStep(List <H3.Cell.Edge> regionEdges, Tiling tiling, Circle region)
{
HashSet <H3.Cell.Edge> newEdges = new HashSet <H3.Cell.Edge>(new H3.Cell.EdgeEqualityComparer());
foreach (Tile tile in tiling.Tiles)
{
foreach (H3.Cell.Edge edge in regionEdges)
{
H3.Cell.Edge toAdd = null;
if (!Tolerance.Zero(tile.Center.Abs()))
{
// Translate
// The isometry is necessary for the 363, but seems to mess up 636
Vector3D start = tile.Isometry.Apply(edge.Start);
Vector3D end = tile.Isometry.Apply(edge.End);
//Vector3D start = edge.Start + tile.Center;
//Vector3D end = edge.End + tile.Center;
// Reflect
start = region.ReflectPoint(start);
end = region.ReflectPoint(end);
toAdd = new H3.Cell.Edge(start, end);
}
else
{
toAdd = edge;
}
if (EdgeOkUHS(toAdd, region))
{
newEdges.Add(toAdd);
}
}
}
return(newEdges.ToList());
}
private static Sphere[] SphericalCellFacetMirrors( HoneycombDef imageData )
{
int p = imageData.P;
int q = imageData.Q;
int r = imageData.R;
double inRadius = Honeycomb.InRadius( p, q, r );
//inRadius *= 1.4; // Experimenting with {3,3,u}
Tiling tiling = new Tiling();
TilingConfig config = new TilingConfig( p, q );
tiling.GenerateInternal( config, imageData.Projection );
Sphere[] mirrors = H3.GenFacetSpheres( tiling, inRadius )
.Select( f => f.Sphere ).ToArray();
return mirrors;
}
private static List <H3.Cell.Edge> CopyAndProject(List <H3.Cell.Edge> regionEdges, Tiling tiling, double scale, Vector3D offset)
{
HashSet <H3.Cell.Edge> newEdges = new HashSet <H3.Cell.Edge>(new H3.Cell.EdgeEqualityComparer());
//foreach( Tile tile in tiling.Tiles ) // Needed for doing full ball (rather than just half of it)
Tile tile = tiling.Tiles.First();
{
foreach (H3.Cell.Edge edge in regionEdges)
{
// Translation
// The isometry is necessary for the 363, but seems to mess up 636
Vector3D start = tile.Isometry.Apply(edge.Start) + offset;
Vector3D end = tile.Isometry.Apply(edge.End) + offset;
//Vector3D start = edge.Start + tile.Center + offset;
//Vector3D end = edge.End + tile.Center + offset;
// Scaling
start *= scale;
end *= scale;
// Projections
start = H3Models.UHSToBall(start);
end = H3Models.UHSToBall(end);
H3.Cell.Edge transformed = new H3.Cell.Edge(start, end);
if (EdgeOkBall(transformed))
{
newEdges.Add(transformed);
}
}
}
return(newEdges.ToList());
}
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");
}
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" );
}
// 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 } ) );
}
}
}