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);
}
public void GenerateInternal(TilingConfig config, Polytope.Projection projection = Polytope.Projection.FaceCentered)
{
this.TilingConfig = config;
// Create a base tile.
Tile tile = CreateBaseTile(config);
// Handle edge/vertex centered projections.
if (projection == Polytope.Projection.VertexCentered)
{
Mobius mobius = config.VertexCenteredMobius();
tile.Transform(mobius);
}
else if (projection == Polytope.Projection.EdgeCentered)
{
Mobius mobius = config.EdgeMobius();
tile.Transform(mobius);
}
TransformAndAdd(tile);
List <Tile> tiles = new List <Tile>();
tiles.Add(tile);
Dictionary <Vector3D, bool> completed = new Dictionary <Vector3D, bool>();
completed[tile.Boundary.Center] = true;
ReflectRecursive(tiles, completed);
FillOutIsometries(tile, m_tiles, config.Geometry);
FillOutIncidences();
}
public static Tile CreateBaseTile(TilingConfig config)
{
Polygon boundary = new Polygon(), drawn = new Polygon();
boundary.CreateRegular(config.P, config.Q);
drawn = boundary.Clone();
//boundary.CreateRegular( 3, 10 );
//drawn.CreateRegular( 3, 8 );
//boundary.CreateRegular( 3, 7 );
//drawn = Heart();
//for( int i=0; i<drawn.NumSides; i++ )
// drawn.Segments[i].Center *= 0.1;
// Good combos:
// ( 5, 5 ), ( 10, 10 )
// ( 3, 10 ), ( 3, 9 )
// ( 6, 4 ), ( 6, 8 )
// ( 7, 3 ), ( 7, 9 )
Tile tile = new Tile(boundary, drawn, config.Geometry);
Tile.ShrinkTile(ref tile, config.Shrink);
return(tile);
}
/// <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 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 void Transform(double anim, IEnumerable <Tile> tetTiles)
{
//TilingConfig config = new TilingConfig( 8, 3, 4 ); // Reproduces Tolerance issues with {3,3,7}, though not actually correct to be applying hyperbolic transforms anyway (only spherical).
TilingConfig config = new TilingConfig(3, 3, 1);
Mobius m = new Mobius();
m = Mobius.Identity();
// Invert
Complex c1 = new Complex(0, 1);
Complex c2 = new Complex(1, 0);
Complex c3 = new Complex(0, -0.999999999999); // - 1 doesn't work
//m.MapPoints( c1, c2, c3, c3, c2, c1 );
//Mobius m = config.DualMobius();
//m.Isometry( Geometry.Spherical, 0, new Complex( 1.2345, -0.4321 ) ); // nice one
//m.Isometry( Geometry.Spherical, 0, new Complex( 0, 0.148125 ) ); // half plane
// Animation.
double p2 = DonHatch.e2hNorm(0.6);
double p2Interp = DonHatch.h2eNorm(p2 * anim);
//m.Isometry( Geometry.Spherical, 0, -p2Interp );
m.Isometry(Geometry.Hyperbolic, 0, new Complex(-p2Interp, 0));
Mobius m2 = new Mobius();
m2.Isometry(Geometry.Hyperbolic, 0, new Complex(-0.6, 0));
m2 = m_fixedCircleToStandardDisk.Inverse() * m2 * m_fixedCircleToStandardDisk;
bool firstAnim = false;
if (firstAnim)
{
m = m_fixedCircleToStandardDisk.Inverse() * m * m_fixedCircleToStandardDisk;
m_animMobius = m;
}
else
{
m = m_neighborToStandardDisk.Inverse() * m * m_neighborToStandardDisk;
m_animMobius = m2 * m;
}
m_animMobius.Normalize();
foreach (Tile t in tetTiles)
{
t.Transform(m_animMobius);
}
foreach (Tile t in m_tiles)
{
t.Transform(m_animMobius);
}
m_equator.Transform(m_animMobius);
m_neighborCircle.Transform(m_animMobius);
}
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);
}
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;
}
/// <summary>
/// Generate ourselves from a tiling config.
/// </summary>
public void Generate(TilingConfig config)
{
GenerateInternal(config);
}
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 Tile CreateBaseTile( TilingConfig config )
{
Polygon boundary = new Polygon(), drawn = new Polygon();
boundary.CreateRegular( config.P, config.Q );
drawn = boundary.Clone();
//boundary.CreateRegular( 3, 10 );
//drawn.CreateRegular( 3, 8 );
//boundary.CreateRegular( 3, 7 );
//drawn = Heart();
//for( int i=0; i<drawn.NumSides; i++ )
// drawn.Segments[i].Center *= 0.1;
// Good combos:
// ( 5, 5 ), ( 10, 10 )
// ( 3, 10 ), ( 3, 9 )
// ( 6, 4 ), ( 6, 8 )
// ( 7, 3 ), ( 7, 9 )
Tile tile = new Tile( boundary, drawn, config.Geometry );
Tile.ShrinkTile( ref tile, config.Shrink );
return tile;
}
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 );
}
/// <summary>
/// Generate ourselves from a tiling config.
/// </summary>
public void Generate( TilingConfig config )
{
GenerateInternal( config );
}
/// <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 );
*/
}
public void GenerateInternal( TilingConfig config, Polytope.Projection projection = Polytope.Projection.FaceCentered )
{
this.TilingConfig = config;
// Create a base tile.
Tile tile = CreateBaseTile( config );
// Handle edge/vertex centered projections.
if( projection == Polytope.Projection.VertexCentered )
{
Mobius mobius = config.VertexCenteredMobius();
tile.Transform( mobius );
}
else if( projection == Polytope.Projection.EdgeCentered )
{
Mobius mobius = config.EdgeMobius();
tile.Transform( mobius );
}
TransformAndAdd( tile );
List<Tile> tiles = new List<Tile>();
tiles.Add( tile );
Dictionary<Vector3D,bool> completed = new Dictionary<Vector3D,bool>();
completed[tile.Boundary.Center] = true;
ReflectRecursive( tiles, completed );
FillOutIsometries( tile, m_tiles, config.Geometry );
FillOutIncidences();
}
// 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 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 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 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();
}