public void Gen()
{
Vector3D[] verts = Verts(m_m, m_k);
Sphere[] tet = Tetrahedron(verts);
Quad quad = new Quad()
{
Verts = verts
};
// We need to avoid infinities.
//tet = tet.Select( s => H3Models.UHSToBall( s ) ).ToArray();
//for( int i=0; i<quad.Verts.Length; i++ )
// quad.Verts[i] = H3Models.UHSToBall( quad.Verts[i] );
// Reflect it around.
//Quad[] quads = new Quad[] { quad };
Quad[] quads = CalcQuads(tet, quad);
List <H3.Cell.Edge> edges = new List <H3.Cell.Edge>();
foreach (Quad q in quads)
{
q.R3toS3();
edges.AddRange(q.GenEdges());
}
string filename = string.Format("lawson_{0}_{1}.pov", m_m, m_k);
PovRay.WriteEdges(new PovRay.Parameters()
{
AngularThickness = 0.01
},
Geometry.Spherical, edges.ToArray(), filename, append: false);
}
public static void Hypercube()
{
List <Vector3D> vertices = new List <Vector3D>();
vertices.Add(new Vector3D(1, 1, 1, 1));
vertices.Add(new Vector3D(1, 1, 1, -1));
vertices.Add(new Vector3D(1, 1, -1, 1));
vertices.Add(new Vector3D(1, 1, -1, -1));
vertices.Add(new Vector3D(1, -1, 1, 1));
vertices.Add(new Vector3D(1, -1, 1, -1));
vertices.Add(new Vector3D(1, -1, -1, 1));
vertices.Add(new Vector3D(1, -1, -1, -1));
vertices.Add(new Vector3D(-1, 1, 1, 1));
vertices.Add(new Vector3D(-1, 1, 1, -1));
vertices.Add(new Vector3D(-1, 1, -1, 1));
vertices.Add(new Vector3D(-1, 1, -1, -1));
vertices.Add(new Vector3D(-1, -1, 1, 1));
vertices.Add(new Vector3D(-1, -1, 1, -1));
vertices.Add(new Vector3D(-1, -1, -1, 1));
vertices.Add(new Vector3D(-1, -1, -1, -1));
HashSet <H3.Cell.Edge> edges = new HashSet <H3.Cell.Edge>(new H3.Cell.EdgeEqualityComparer());
foreach (Vector3D v1 in vertices)
{
foreach (Vector3D v2 in vertices)
{
if (v1.Dist(v2) == 2)
{
edges.Add(new H3.Cell.Edge(v1, v2));
}
}
}
// Radial project to S3, then stereographic to R3.
foreach (H3.Cell.Edge edge in edges)
{
edge.Start.Normalize();
edge.Start = Sterographic.S3toR3(edge.Start);
edge.End.Normalize();
edge.End = Sterographic.S3toR3(edge.End);
}
PovRay.WriteEdges(new PovRay.Parameters()
{
AngularThickness = .05
}, Geometry.Spherical, edges.ToArray(), "433.pov", append: false);
}
public static void ElevenCell()
{
Graph g = new Graph();
g.SetupCompleteGraph(11);
GraphRelaxation relaxer = new GraphRelaxation();
relaxer.Graph = g;
relaxer.NodeRepulsion = 0.01;
relaxer.EdgeAttraction = 0.0;
relaxer.EdgeRepulsion = 0.0;
relaxer.Relax(20000);
Vector3D northPole = new Vector3D(0, 0, 0, 1);
H3.Cell.Edge[] edges = g.Edges.Select(e =>
{
Vector3D v1 = g.Nodes[e.V1].Position.ToVec3D();
Vector3D v2 = g.Nodes[e.V2].Position.ToVec3D();
//if( v1.Compare( northPole, .5 ) || v2.Compare( northPole, 0.5 ) ) // Cull edges near north pole.
// return null;
v1 = Sterographic.S3toR3(v1);
v2 = Sterographic.S3toR3(v2);
return(new H3.Cell.Edge(v1, v2));
}).ToArray();
edges = edges.Where(e => e != null).ToArray();
bool povray = false;
if (povray)
{
string filename = "test.pov";
System.IO.File.Delete(filename);
using (StreamWriter sw = new StreamWriter(filename))
sw.WriteLine("#include \"C:\\Users\\hrn\\Documents\\roice\\povray\\H3\\horosphere\\633.pov\"");
PovRay.WriteEdges(new PovRay.Parameters {
AngularThickness = 0.03
}, Geometry.Spherical, edges, filename, append: true);
}
else
{
S3.EdgesToStl(edges);
}
}
private static void CreateSimplex(HoneycombDef imageData)
{
int p = imageData.P;
int q = imageData.Q;
int r = imageData.R;
Vector3D cen = InteriorPointBall;
bool ball = true;
Sphere[] simplex = SimplexCalcs.Mirrors(p, q, r, ref cen, moveToBall: ball);
// Offset as we do for the boundary images.
//Sphere s = H3Models.UHSToBall( simplex[0] );
//s = CoxeterImages.GeodesicOffset( s, 0.02, ball: true );
if (m_toKlein)
{
simplex = simplex.Select(s => H3Models.BallToKlein(s)).ToArray();
}
int[] include = new int[] { 0, 1, 2, 3 }; // All facets
//int[] include = new int[] { 1 };
File.Delete("simplex.pov");
PovRay.AppendSimplex(simplex, cen, include, "simplex.pov");
bool includeEdges = false;
if (includeEdges)
{
H3.Cell.Edge[] edges = SimplexCalcs.SimplexEdgesUHS(p, q, r);
PovRay.WriteEdges(new PovRay.Parameters {
Halfspace = true, AngularThickness = 0.03
},
Geometry.Hyperbolic, edges, "simplex.pov", append: true);
}
}
/// <summary>
/// This generates a honeycomb by reflecting in 4 mirrors of the fundamental simplex.
/// This "new" method is now old.
/// </summary>
public static void OneHoneycombNew(HoneycombDef imageData)
{
int p = imageData.P;
int q = imageData.Q;
int r = imageData.R;
double thickness = 0.05;
double thicknessSpherical = Spherical2D.s2eNorm(thickness);
double thicknessHyperbolic = R3.Math.DonHatch.h2eNorm(thickness);
double threshold = 1;
H3.Cell.Edge[] edges = null;
H3.Cell[] cellsToHighlight = null;
Sphere[] simplex = null;
Vector3D vertex = new Vector3D();
Geometry g = Util.GetGeometry(p, q, r);
if (g == Geometry.Spherical)
{
thickness = thicknessSpherical /*.07 for 333*/ /* 0.05for 433*/ /*.025 for 533,335*/;
threshold = 10000;
simplex = SimplexCalcs.MirrorsSpherical(p, q, r);
vertex = SimplexCalcs.VertexSpherical(p, q, r);
// Ugly special casing for 333, since it has a vertex project to infinity.
if (p == 3 && q == 3 && r == 3)
{
SpecialCase333();
}
}
else if (g == Geometry.Euclidean)
{
thickness = thickness / 2;
threshold = 1 /*20*/;
//SimplexCalcs.CalcEScale();
simplex = SimplexCalcs.MirrorsEuclidean();
Vector3D[] verts = SimplexCalcs.VertsEuclidean();
vertex = verts[2];
}
else
{
thickness = thicknessHyperbolic;
threshold = 0.01;
simplex = SimplexCalcs.Mirrors(p, q, r);
Vector3D[] verts = SimplexCalcs.VertsBall(p, q, r);
vertex = verts[2];
//Vector3D[] simplexVerts = SimplexCalcs.VertsBall( p, q, r );
//H3.Cell.Edge edge = new H3.Cell.Edge( simplexVerts[2], simplexVerts[3] );
//H3.Cell.Edge edge = SimplexCalcs.HoneycombEdgeBall( p, q, r );
//H3.Cell.Edge[] startingEdges = new H3.Cell.Edge[] { edge };
//H3.Cell.Edge[] edges = Recurse.CalcEdgesSmart2( simplex, startingEdges );
// Vertex Centered.
bool vertexCentered = false;
if (vertexCentered)
{
Vector3D v = SimplexCalcs.VertexPointBall(p, q, r);
v = H3Models.BallToUHS(v);
double scale = 1.0 / v.Abs();
edges = edges.Select(e =>
{
Vector3D start = H3Models.UHSToBall(H3Models.BallToUHS(e.Start) * scale);
Vector3D end = H3Models.UHSToBall(H3Models.BallToUHS(e.End) * scale);
return(new H3.Cell.Edge(start, end));
}).ToArray();
}
// Code to show endpoints of 535
/*using( StreamWriter sw = File.CreateText( "535_points.pov" ) )
* {
* HashSet<Vector3D> verts = new HashSet<Vector3D>();
* foreach( H3.Cell.Edge e in edges )
* {
* verts.Add( Sterographic.SphereToPlane( e.Start ) );
* verts.Add( Sterographic.SphereToPlane( e.End ) );
* }
*
* foreach( Vector3D vert in verts )
* if( !Infinity.IsInfinite( vert ) )
* sw.WriteLine( PovRay.Sphere( new Sphere() { Center = vert, Radius = 0.01 } ) );
* }*/
}
// Recurse
bool dual = false;
{
H3.Cell.Edge[] startingEdges = null;
if (dual)
{
startingEdges = new H3.Cell.Edge[] { SimplexCalcs.DualEdgeBall(simplex) }
}
;
else
{
//startingEdges = new H3.Cell.Edge[] { SimplexCalcs.HoneycombEdgeBall( simplex, vertex ) };
Vector3D[] verts = SimplexCalcs.VertsEuclidean();
Vector3D v1 = verts[0] + 2 * verts[2]; // adjacent cube center
Vector3D corner = verts[3];
startingEdges = new H3.Cell.Edge[] { new H3.Cell.Edge(v1, corner) };
}
edges = Recurse.CalcEdges(simplex, startingEdges, new Recurse.Settings()
{
G = g, Threshold = threshold
});
edges = edges.Where(e =>
{
int sum = e.Depths.Count(d => d == 0);
return(true);
}).ToArray();
//CullHalfOfEdges( ref edges );
// No need to cull edges in spherical case.
// This was just to generate some images for 350-cell paper.
//edges = Cull120Cell( edges );
Simplex tet = new Simplex();
tet.Facets = simplex;
if (dual)
{
H3.Cell.Edge[] oneDualCell = edges.Where(e => e.Depths[2] == 0).ToArray();
simplex = simplex.Skip(1).ToArray();
edges = Recurse.CalcEdges(simplex, oneDualCell, new Recurse.Settings()
{
G = g, Threshold = threshold
});
int[] polyMirrors = new int[] { 0, 1, 3 };
H3.Cell startingCell = HoneycombGen.PolyhedronToHighlight(g, polyMirrors, tet, new Vector3D());
cellsToHighlight = Recurse.CalcCells(simplex, new H3.Cell[] { startingCell });
//cellsToHighlight = new H3.Cell[] { startingCell };
//cellsToHighlight = cellsToHighlight.Skip( 7 ).ToArray();
}
else
{
int[] polyMirrors = new int[] { 1, 2, 3 };
H3.Cell startingCell = HoneycombGen.PolyhedronToHighlight(g, polyMirrors, tet, vertex);
//cellsToHighlight = Recurse.CalcCells( simplex, new H3.Cell[] { startingCell } );
cellsToHighlight = new H3.Cell[] { startingCell };
}
// Include just one cell?
bool includeOne = false;
if (includeOne)
{
edges = edges.Where(e => e.Depths[0] == 0).ToArray();
//cellsToHighlight = cellsToHighlight.Where( c => c.Depths[0] == 0 ).ToArray();
}
}
// Rotate
bool rotate = false;
if (rotate)
{
CompoundOfFive24Cells(ref edges);
}
// Write the file
bool pov = true;
if (pov)
{
string filename = string.Format("{0}{1}{2}.pov", p, q, r);
PovRay.WriteEdges(new PovRay.Parameters()
{
AngularThickness = thickness
}, g, edges,
filename, append: false);
//File.Delete( filename );
//PovRay.AppendFacets( cellsToHighlight, filename );
HashSet <Vector3D> verts = new HashSet <Vector3D>();
foreach (H3.Cell.Edge e in edges)
{
verts.Add(e.Start);
verts.Add(e.End);
}
/*foreach( Vector3D v in verts )
* {
* Vector3D t = v;
* t.Normalize();
* t *= 0.9;
* System.Diagnostics.Trace.WriteLine( string.Format( "light_source {{ <{0},{1},{2}> White*.2 }}", t.X, t.Y, t.Z ) );
* }*/
/*
* // Include the standard pov stuff, so we can batch this.
* string fileName = imageData.FormatFilename( string.Empty );
* using( StreamWriter sw = File.CreateText( fileName + ".pov" ) )
* {
* sw.WriteLine( "#include \"C:\\Users\\hrn\\Documents\\roice\\povray\\paper\\H3.pov\"" );
* }
*
* bool dummy = true; // Doesn't matter for Pov-Ray, just Shapeways meshes.
* H3.SaveToFile( fileName, edges, dummy, append: true );
*/
}
else
{
if (g == Geometry.Spherical)
{
edges = edges.Where(e => e.Start.Valid() && e.End.Valid() && !Infinity.IsInfinite(e.Start) && !Infinity.IsInfinite(e.End)).ToArray();
S3.EdgesToStl(edges);
}
else
{
throw new System.NotImplementedException();
}
}
}
