private static H3.Cell.Facet GenFacet(Geometry g, int mirror1, int mirror2, Simplex simplex, Vector3D startingPoint)
{
List <Sphere> mirrors = new List <Sphere>();
mirrors.Add(simplex.Facets[mirror1]);
mirrors.Add(simplex.Facets[mirror2]);
List <H3.Cell.Edge> startingEdges = new List <H3.Cell.Edge>();
Vector3D reflected = simplex.ReflectInFacet(startingPoint, mirror1);
startingEdges.Add(new H3.Cell.Edge(startingPoint, reflected));
reflected = simplex.ReflectInFacet(startingPoint, mirror2);
startingEdges.Add(new H3.Cell.Edge(startingPoint, reflected));
startingEdges.RemoveAll(e => e.Start == e.End);
if (startingEdges.Count == 0)
{
return(null);
}
H3.Cell.Edge[] completedEdges = Recurse.CalcEdges(mirrors.ToArray(), startingEdges.ToArray(), new Recurse.Settings()
{
G = g
});
if (completedEdges.Length == 1)
{
return(null);
}
List <Vector3D> facetVerts = new List <Vector3D>();
H3.Cell.Edge edge = completedEdges.First();
Vector3D start = edge.Start;
Vector3D current = edge.End;
facetVerts.Add(edge.End);
while (current != start)
{
edge = completedEdges.First(e => e != edge && (e.Start == current || e.End == current));
current = edge.Start == current ? edge.End : edge.Start;
facetVerts.Add(current);
}
return(new H3.Cell.Facet(facetVerts.ToArray()));
}
private static void CreateCellPovRay(HoneycombDef def, string filename, double t = 0)
{
int p = def.P;
int q = def.Q;
int r = def.R;
//Vector3D trans = new Vector3D( 1.0/3, 0 ) * (2 + 2 * Math.Sin( Math.PI / 6 )) * t;
//double scale = 1.8;
Vector3D trans = new Vector3D();
double scale = 1.0;
Vector3D[] sVerts = null; // SimplexCalcs.VertsBall( p, q, r );
Vector3D vUHS = H3Models.BallToUHS(SimplexCalcs.VertexPointBall(p, q, r));
// Just did this for everything. Non-general position working better and will make all heads consistent.
scale = 2.0;
if (Geometry2D.GetGeometry(q, r) != Geometry.Hyperbolic) // Vertex-centered if possible
{
scale = 1.0 / vUHS.Z;
}
//else if( Geometry2D.GetGeometry( p, q ) == Geometry.Hyperbolic ) // Make the biggest head somewhat smaller.
// scale = 2.0;
Vector3D cen = InteriorPointBall;
/*var kleinVerts = sVerts.Select( v => HyperbolicModels.PoincareToKlein( v ) );
* Vector3D avg = new Vector3D();
* foreach( Vector3D v in kleinVerts )
* avg += v;
* avg /= kleinVerts.Count();
* Vector3D cen = HyperbolicModels.KleinToPoincare( avg );*/
cen = H3Models.BallToUHS(cen);
cen += trans;
//cen *= scale;
cen = H3Models.UHSToBall(cen);
Sphere[] simplex = SimplexCalcs.Mirrors(p, q, r, moveToBall: false);
// Apply transformations.
simplex = simplex.Select(s =>
{
Sphere.TranslateSphere(s, trans);
Sphere.ScaleSphere(s, scale);
return(H3Models.UHSToBall(s));
}).ToArray();
for (int i = 0; i < 4; i++)
{
if (simplex[i].IsPointInside(cen))
{
simplex[i].Invert = true;
}
}
Sphere[] simplexForColorScale = SimplexCalcs.Mirrors(p, q, r, moveToBall: true);
CoxeterImages.Settings temp = AutoCalcScale(def, simplexForColorScale);
int maxDepth = (int)temp.ColorScaling;
//Random rand = new Random( p+q+r );
//int randOffset = rand.Next( maxDepth );
bool ball = true;
bool dual = false;
H3.Cell[] simplicesFinal = GenCell(simplex, null, cen, ball, dual);
using (StreamWriter sw = File.CreateText(filename)) // We need to reuse this StreamWriter (vs. calling AppendSimplex) for performance.
{
sw.WriteLine("#include \"hyper_ball.pov\"");
//int[] include = new int[] { 0, 1, 2, 3 };
int[] include = new int[] { 0 };
if (dual)
{
include = new int[] { 3 }
}
;
// Output the facets.
foreach (H3.Cell cell in simplicesFinal)
{
Sphere[] facets = cell.Facets.Select(f => f.Sphere).ToArray();
if (m_toKlein)
{
facets = facets.Select(s => H3Models.BallToKlein(s)).ToArray();
}
int depth = cell.Depths[0] + 1;
Color c = Coloring.ColorAlongHexagon(maxDepth, depth);
if (cell.Depths.Sum() % 2 == 0)
{
c = Coloring.Inverse(c);
}
PovRay.AddSimplex(sw, facets, cell.Center, include, filename, Coloring.ToVec(c));
}
/*include = new int[] { 1, 2, 3 };
* foreach( H3.Cell cell in simplicesFinal )
* {
* Sphere[] facets = cell.Facets.Select( f => f.Sphere ).ToArray();
* Color c = Color.Red;
* Vector3D cv = Coloring.ToVec( c );
* cv.W = 0.9;
* PovRay.AddSimplex( sw, facets, cell.Center, include, filename, cv );
* }*/
}
// Output the edges/verts.
bool includeEdges = false;
if (includeEdges)
{
sVerts = sVerts.Select(v =>
{
v = H3Models.BallToUHS(v);
v += trans;
v *= scale;
return(H3Models.UHSToBall(v));
}).ToArray();
H3.Cell.Edge[] edges = Recurse.CalcEdges(simplex.Skip(1).ToArray(),
new H3.Cell.Edge[] { new H3.Cell.Edge(sVerts[2], sVerts[3], order: false) },
new Recurse.Settings()
{
Threshold = 0.01
});
PovRay.WriteH3Edges(new PovRay.Parameters {
AngularThickness = 0.01
}, edges, filename, append: true);
HashSet <Vector3D> verts = new HashSet <Vector3D>();
foreach (H3.Cell.Edge e in edges)
{
verts.Add(e.End);
}
PovRay.WriteVerts(new PovRay.Parameters {
AngularThickness = 0.02
}, Geometry.Hyperbolic, verts.ToArray(), filename, append: true);
}
}
/// <summary>
/// Wendy's 77
/// </summary>
public static void Wendy(Simplex simplex, H3.Cell.Edge[] edges)
{
H3.Cell startingCell = null;
Vector3D start = startingCell.Verts.First();
Func <Vector3D, Vector3D> findAntipode = input =>
{
Vector3D antipode = new Vector3D();
double max = double.MinValue;
foreach (Vector3D v in startingCell.Verts)
{
double d = H3Models.Ball.HDist(v, input);
if (d > max)
{
max = d;
antipode = v;
}
}
return(antipode);
};
H3.Cell.Edge[] diagonals = new H3.Cell.Edge[] { new H3.Cell.Edge(start, findAntipode(start)) };
diagonals = Recurse.CalcEdges(simplex.Facets, diagonals, new Recurse.Settings()
{
Threshold = 0.9983
});
// diagonals includes too much at this point (it includes all icosahedra diagonals, but we only want one diagonal from each cell).
// We need to begin at 4 start points, and branch out from each to find the ones we want.
var vertsToDiagonals = FindConnectedEdges(diagonals);
var connectedEdges = FindConnectedEdges(edges);
// Get all edges (not diagonals) connected to start.
List <H3.Cell.Edge> connectedToStart = connectedEdges[start];
Vector3D startOpp = connectedToStart[0].Opp(start);
List <H3.Cell.Edge> connectedToStartOpp = connectedEdges[startOpp];
// We need to pick 4 of these edges, arranged in a tetrahedron for our starting points.
List <Vector3D> startingPoints = new List <Vector3D>();
List <double> distances = new List <double>();
// View1
//startingPoints.Add( start );
//foreach( Vector3D v in connectedToStartOpp.Select( e => e.Opp( startOpp ) ) )
// distances.Add( H3Models.Ball.HDist( startingPoints.First(), v ) );
//startingPoints.Add( connectedToStartOpp[10].Opp( startOpp ) );
//startingPoints.Add( connectedToStartOpp[13].Opp( startOpp ) );
//startingPoints.Add( connectedToStartOpp[14].Opp( startOpp ) );
// View2
startingPoints.Add(startOpp);
foreach (Vector3D v in connectedToStart.Select(e => e.Opp(start)))
{
distances.Add(H3Models.Ball.HDist(startingPoints.First(), v));
}
startingPoints.Add(connectedToStart[10].Opp(start));
startingPoints.Add(connectedToStart[13].Opp(start));
startingPoints.Add(connectedToStart[14].Opp(start));
distances.Clear();
distances.Add(H3Models.Ball.HDist(startingPoints[1], startingPoints[2]));
distances.Add(H3Models.Ball.HDist(startingPoints[1], startingPoints[3]));
distances.Add(H3Models.Ball.HDist(startingPoints[2], startingPoints[3]));
distances.Add(H3Models.Ball.HDist(startingPoints[0], startingPoints[1]));
distances.Add(H3Models.Ball.HDist(startingPoints[0], startingPoints[2]));
distances.Add(H3Models.Ball.HDist(startingPoints[0], startingPoints[3]));
double dist = 3.097167;
Func <Vector3D[], H3.Cell.Edge[]> RemoveVerts = starting =>
{
List <H3.Cell.Edge> keepers = new List <H3.Cell.Edge>();
HashSet <Vector3D> removedVerts = new HashSet <Vector3D>();
Recurse.BranchAlongVerts(starting.ToArray(), vertsToDiagonals, removedVerts);
foreach (H3.Cell.Edge e in edges)
{
if (removedVerts.Contains(e.Start) || removedVerts.Contains(e.End))
{
continue;
}
keepers.Add(e);
}
return(keepers.ToArray());
};
edges = RemoveVerts(startingPoints.ToArray());
bool done = false;
while (!done)
{
done = true;
var newConnectedEdges = FindConnectedEdges(edges);
foreach (Vector3D v in newConnectedEdges.Keys)
{
List <H3.Cell.Edge> oldEdgeList = connectedEdges[v];
List <H3.Cell.Edge> newEdgeList = newConnectedEdges[v];
// Only work edges that were full originally.
if (oldEdgeList.Count != 20)
{
continue;
}
// We need at least two to find the rest.
int newCount = newEdgeList.Count;
if (newCount > 16 && newCount < 19)
{
List <H3.Cell.Edge> removed = oldEdgeList.Except(newEdgeList, new H3.Cell.EdgeEqualityComparer()).ToList();
H3.Cell.Edge[] toTrim = newEdgeList.FindAll(e =>
{
foreach (H3.Cell.Edge alreadyRemoved in removed)
{
double d = H3Models.Ball.HDist(alreadyRemoved.Opp(v), e.Opp(v));
if (!Tolerance.Equal(dist, d, 0.00001))
{
return(false);
}
}
return(true);
}).ToArray();
edges = RemoveVerts(toTrim.Select(e => e.Opp(v)).ToArray());
done = false;
}
if (newCount == 20)
{
done = false;
}
}
}
}
/// <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();
}
}
}