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>
/// 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);
}
}