/// <summary> /// Allow a hyperbolic transformation using an absolute offset. /// offset is specified in the respective geometry. /// </summary> public void Hyperbolic2(Geometry g, Complex fixedPlus, Complex point, double offset) { // To the origin. Mobius m = new Mobius(); m.Isometry(g, 0, fixedPlus * -1); double eRadius = m.Apply(point).Magnitude; double scale = 1; switch (g) { case Geometry.Spherical: double sRadius = Spherical2D.e2sNorm(eRadius); sRadius += offset; scale = Spherical2D.s2eNorm(sRadius) / eRadius; break; case Geometry.Euclidean: scale = (eRadius + offset) / eRadius; break; case Geometry.Hyperbolic: double hRadius = DonHatch.e2hNorm(eRadius); hRadius += offset; scale = DonHatch.h2eNorm(hRadius) / eRadius; break; } Hyperbolic(g, fixedPlus, scale); }
public void AnimationSections(Settings config) { HoneycombDef imageData = new HoneycombDef(config.P, config.Q, config.R); int p = imageData.P, q = imageData.Q, r = imageData.R; string filename = imageData.FormatFilename(); Sphere[] mirrors = SimplexCalcs.Mirrors(p, q, r); double bounds = 1.0; //config.UhsBoundary.Bounds; bounds = 9.0; // Calculate the color scale. int size = 200; CoxeterImages.Settings settings = new CoxeterImages.Settings() { Honeycomb = imageData, Width = size, Height = size, Bounds = bounds, Mirrors = mirrors, FileName = imageData.FormatFilename(), }; CoxeterImages imageCalculator = new CoxeterImages(); //imageCalculator.AutoCalcScale( settings ); if (settings.ColorScaling < 1) { settings.ColorScaling = 15; } settings.ColorScaling = 11; Program.Log("\nGenerating sections..."); size = 500; settings.Width = size; settings.Height = size; settings.FileName = filename; double max = Spherical2D.e2sNorm(15); double min = Spherical2D.e2sNorm(1.0 / 15); DonHatch.e2hNorm(max); int numSteps = 1800; // 1 minute double step = (max - min) / numSteps; for (int i = 0; i < 1; i++) { Program.Log("\nSection " + i); imageCalculator.m_z = 1.0 / 0.5; Spherical2D.s2eNorm(min + step * i); DonHatch.h2eNorm(step * i); settings.FileName = string.Format("533_{0:D4}.png", i); imageCalculator.GenImage(settings); } }
/// <summary> /// Equally subdivides a segment with a startpoint at the origin, in the respective geometry. /// </summary> private static Vector3D[] SubdivideRadialInGeometry(Segment radial, int divisions, Geometry g) { List <Vector3D> result = new List <Vector3D>(); if (radial.Type != SegmentType.Line) { Debug.Assert(false); return(result.ToArray()); } switch (g) { case Geometry.Spherical: { double eLength = radial.Length; double sLength = Spherical2D.e2sNorm(eLength); double divLength = sLength / divisions; for (int i = 0; i <= divisions; i++) { double temp = Spherical2D.s2eNorm(divLength * i); result.Add(radial.P2 * temp / eLength); } break; } case Geometry.Euclidean: return(radial.Subdivide(divisions)); case Geometry.Hyperbolic: { double eLength = radial.Length; double hLength = DonHatch.e2hNorm(eLength); double divLength = hLength / divisions; for (int i = 0; i <= divisions; i++) { double temp = DonHatch.h2eNorm(divLength * i); result.Add(radial.P2 * temp / eLength); } break; } } return(result.ToArray()); }
static public double OffsetInModel(Tiler.Settings settings, double p = 0, double q = 0, double r = 1) { double off = OffsetInSpace(settings, p, q, r); switch (settings.Geometry) { case Geometry.Spherical: off = Spherical2D.s2eNorm(off); break; case Geometry.Hyperbolic: off = DonHatch.h2eNorm(off); break; } return(off); }
/// <summary> /// Calculate the 4 points defining the fundamental geodesic quadrilateral. /// </summary> private static Vector3D[] Verts(int m, int k) { double dist1 = Math.PI / (m + 1); double dist2 = Math.PI / (k + 1); Vector3D p4 = new Vector3D(1, 0); p4.RotateXY(dist2); return(new Vector3D[] { new Vector3D(), new Vector3D(1, 0), new Vector3D(0, 0, Spherical2D.s2eNorm(dist1)), p4 }); }
public static Sphere GeodesicOffset(Sphere s, double offset, bool ball = true) { Sphere offsetSphere; if (ball) { // Geodesic offset (ball). { // Hyperbolic honeycomb double mag = s.Center.Abs() - s.Radius; mag = s.IsPlane ? DonHatch.h2eNorm(offset) : DonHatch.h2eNorm(DonHatch.e2hNorm(mag) - offset); Vector3D closestPointToOrigin = s.IsPlane ? s.Normal : s.Center; closestPointToOrigin.Normalize(); closestPointToOrigin *= mag; offsetSphere = H3Models.Ball.OrthogonalSphereInterior(closestPointToOrigin); // There are multiple ultraparallel spheres. // This experiments with picking others. Mobius m = new Mobius(); m.Isometry(Geometry.Hyperbolic, 0, new Vector3D(0, -0.2)); //H3Models.TransformInBall2( offsetSphere, m ); } { // Spherical honeycomb //offset *= -1; double mag = -s.Center.Abs() + s.Radius; Spherical2D.s2eNorm(Spherical2D.e2sNorm(mag) + offset); offsetSphere = s.Clone(); offsetSphere.Radius += offset * 10; } } else { // Geodesic offset (UHS). // XXX - not scaled right. offsetSphere = s.Clone(); offsetSphere.Radius += offset; } return(offsetSphere); }
/// <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(); } } }