public static void Create(HoneycombDef def, string filename) { int p = def.P; int q = def.Q; int r = def.R; double scale = 5.0; Vector3D cen = HoneycombPaper.InteriorPointBall; Sphere[] simplex = SimplexCalcs.Mirrors(p, q, r, moveToBall: false); // Apply transformations. simplex = simplex.Select(s => { 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 = HoneycombPaper.AutoCalcScale(def, simplexForColorScale); int maxDepth = (int)temp.ColorScaling; bool ball = true; bool dual = false; H3.Cell[] simplicesFinal = HoneycombPaper.GenCell(simplex, null, cen, ball, dual); simplicesFinal = simplicesFinal.Where(s => s.Depths[0] < 1).ToArray(); //simplicesFinal = simplicesFinal.Where( s => s.) // Output the facets. 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 }; foreach (H3.Cell cell in simplicesFinal) { Sphere[] facets = cell.Facets.Select(f => f.Sphere).ToArray(); int depth = cell.Depths[0] + 1; Color c = Coloring.ColorAlongHexagon(maxDepth, depth); PovRay.AddSimplex(sw, facets, cell.Center, include, filename, Coloring.ToVec(c)); } } }
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); } }