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);
}
}
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 Sphere[] Simplex(ref Vector3D cen)
{
int p = 7;
int q = 3;
int r = 3;
// For vertex-centered.
//Vector3D v = SimplexCalcs.VertexPointBall( p, q, r );
//v = H3Models.BallToUHS( v );
bool ball = true;
Sphere[] simplex = SimplexCalcs.Mirrors(p, q, r, ref cen, moveToBall: ball /*, scaling: 1.0/v.Abs()*/);
return(simplex);
}
public static void OneImage(Settings config, double t = 0.0)
{
HoneycombDef imageData = new HoneycombDef(config.P, config.Q, config.R);
int p = imageData.P, q = imageData.Q, r = imageData.R;
string filename = imageData.FormatFilename();
//if( File.Exists( filename ) )
// return;
Sphere[] mirrors = SimplexCalcs.Mirrors(p, q, r);
double bounds = config.UhsBoundary.Bounds;
// 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;
}
Program.Log("\nGenerating full image...");
size = 500;
settings.Width = config.UhsBoundary.ImageWidth;
settings.Height = config.UhsBoundary.ImageHeight;
settings.FileName = filename;
imageCalculator.GenImage(settings, t);
}
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);
}
}
private static void OneAnimationFrame(HoneycombDef imageData, string filename, double colorScaling, double t = 0.0)
{
int p = imageData.P, q = imageData.Q, r = imageData.R;
Sphere[] mirrors = SimplexCalcs.Mirrors(p, q, r);
int size = 750;
size = 1024;
CoxeterImages.Settings settings = new CoxeterImages.Settings()
{
Honeycomb = imageData,
Width = size * 2,
Height = size,
Bounds = 1.0,
Mirrors = mirrors,
FileName = filename,
};
CoxeterImages imageCalculator = new CoxeterImages();
settings.ColorScaling = colorScaling;
imageCalculator.GenImage(settings, t);
}
// CHEAT! (would be better to do a geometrical construction)
// We are going to iterate to the starting point that will make all edge lengths the same.
public static Vector3D IterateToStartingPoint(HoneycombDef?def, int[] activeMirrors, Simplex simplex)
{
if (activeMirrors.Length == 1)
{
return(simplex.Verts[activeMirrors[0]]);
}
// We are minimizing the output of this function,
// because we want all edge lengths to be as close as possible.
// Input vector should be in the Ball Model.
Func <Vector3D, double> diffFunc = v =>
{
List <double> lengths = new List <double>();
for (int i = 0; i < activeMirrors.Length; i++)
{
Vector3D reflected = simplex.ReflectInFacet(v, activeMirrors[i]);
lengths.Add(H3Models.Ball.HDist(v, reflected));
}
double result = 0;
double average = lengths.Average();
foreach (double length in lengths)
{
result += Math.Abs(length - average);
}
if (Infinity.IsInfinite(result))
{
result = double.PositiveInfinity;
}
return(result);
};
// So that we can leverage Euclidean barycentric coordinates, we will first convert our simplex to the Klein model.
// We will need to take care to properly convert back to the Ball as needed.
Vector3D[] kleinVerts = simplex.Verts.Select(v => HyperbolicModels.PoincareToKlein(v)).ToArray();
if (def != null)
{
HoneycombDef d = def.Value;
Geometry vertexGeometry = Geometry2D.GetGeometry(d.Q, d.R);
if (vertexGeometry == Geometry.Hyperbolic)
{
kleinVerts[3] = SimplexCalcs.VertexPointKlein(d.P, d.Q, d.R);
}
}
// Normalizing barycentric coords amounts to making sure the 4 coords add to 1.
Func <Vector3D, Vector3D> baryNormalize = b =>
{
return(b / (b.X + b.Y + b.Z + b.W));
};
// Bary Coords to Euclidean
Func <Vector3D[], Vector3D, Vector3D> baryToEuclidean = (kv, b) =>
{
Vector3D result =
kv[0] * b.X + kv[1] * b.Y + kv[2] * b.Z + kv[3] * b.W;
return(result);
};
// Our starting barycentric coords (halfway between all active mirrors).
Vector3D bary = new Vector3D();
foreach (int a in activeMirrors)
{
bary[a] = 0.5;
}
bary = baryNormalize(bary);
// For each iteration, we'll shrink this search offset.
// NOTE: The starting offset and decrease factor I'm using don't guarantee convergence,
// but it seems to be working pretty well (even when varying these parameters).
//double searchOffset = 1.0 - bary[activeMirrors[0]];
//double searchOffset = bary[activeMirrors[0]];
double factor = 1.5; // Adjusting this helps get some to converge, e.g. 4353-1111
double searchOffset = bary[activeMirrors[0]] / factor;
double min = double.MaxValue;
int iterations = 1000;
for (int i = 0; i < iterations; i++)
{
min = diffFunc(HyperbolicModels.KleinToPoincare(baryToEuclidean(kleinVerts, bary)));
foreach (int a in activeMirrors)
{
Vector3D baryTest1 = bary, baryTest2 = bary;
baryTest1[a] += searchOffset;
baryTest2[a] -= searchOffset;
baryTest1 = baryNormalize(baryTest1);
baryTest2 = baryNormalize(baryTest2);
double t1 = diffFunc(HyperbolicModels.KleinToPoincare(baryToEuclidean(kleinVerts, baryTest1)));
double t2 = diffFunc(HyperbolicModels.KleinToPoincare(baryToEuclidean(kleinVerts, baryTest2)));
if (t1 < min)
{
min = t1;
bary = baryTest1;
}
if (t2 < min)
{
min = t2;
bary = baryTest2;
}
}
if (Tolerance.Equal(min, 0.0, 1e-14))
{
System.Console.WriteLine(string.Format("Converged in {0} iterations.", i));
break;
}
searchOffset /= factor;
}
if (!Tolerance.Equal(min, 0.0, 1e-14))
{
System.Console.WriteLine("Did not converge: " + min);
// Be a little looser before thrown an exception.
if (!Tolerance.Equal(min, 0.0, 1e-12))
{
System.Console.ReadKey(true);
//throw new System.Exception( "Boo. We did not converge." );
return(Vector3D.DneVector());
}
}
Vector3D euclidean = baryToEuclidean(kleinVerts, bary);
return(HyperbolicModels.KleinToPoincare(euclidean));
}
public static H3.Cell.Edge[] OneHoneycombOrthoscheme(HoneycombDef def, int[] active, int baseHue, Settings settings = null)
{
// Setup parameters.
int numEdges = 250000;
if (settings != null)
{
active = settings.PovRay.Active;
def = new HoneycombDef(settings.P, settings.Q, settings.R);
numEdges = settings.PovRay.NumEdges;
}
CalcThickness(active);
if (settings != null)
{
H3.m_settings.AngularThickness = settings.PovRay.EdgeWidth; // ZZZ - should really stop using that settings class.
}
string baseName = BaseName(def);
string mirrorsString = ActiveMirrorsString(active);
string suffix = "-" + mirrorsString;
string fileName = baseName + suffix;
if (ViewPath != null)
{
fileName += string.Format("_{0:D4}", ViewPath.Step);
}
if (File.Exists(fileName + ".pov"))
{
File.Delete(fileName + ".pov");
//Console.WriteLine( string.Format( "Skipping {0}", fileName ) );
//return;
}
Program.Log(string.Format("Building {0}", fileName));
// The wiki mirrors are labeled in the reverse of ours.
Func <int, int> mapMirror = i => 3 - i;
active = active.Select(i => mapMirror(i)).OrderBy(i => i).ToArray();
Simplex simplex = new Simplex();
simplex.Facets = SimplexCalcs.Mirrors(def.P, def.Q, def.R);
simplex.Verts = SimplexCalcs.VertsBall(def.P, def.Q, def.R);
Vector3D startingPoint = IterateToStartingPoint(def, active, simplex);
if (startingPoint.DNE)
{
return(null);
}
List <H3.Cell.Edge> startingEdges = new List <H3.Cell.Edge>();
foreach (int a in active)
{
Vector3D reflected = simplex.ReflectInFacet(startingPoint, a);
startingEdges.Add(new H3.Cell.Edge(startingPoint, reflected));
//startingEdges.Add( new H3.Cell.Edge( simplex.Verts[0], simplex.Verts[3] ) ); // Used for Borromean Rings complement image.
}
if (false)
{
Vector3D[] kv = simplex.Verts.Select(v => HyperbolicModels.PoincareToKlein(v)).ToArray();
kv[3] = SimplexCalcs.VertexPointKlein(def.P, def.Q, def.R);
Vector3D t = (kv[3] - kv[0]) * 0.5;
Sphere gSphere = H3Models.Ball.OrthogonalSphereInterior(HyperbolicModels.KleinToPoincare(t));
gSphere = H3Models.BallToKlein(gSphere);
Vector3D t2 = Euclidean3D.IntersectionPlaneLine(gSphere.Normal, gSphere.Offset, kv[3] - kv[2], kv[2]);
//t2 = kv[2] + ( kv[3] - kv[2]) * 0.5;
t = HyperbolicModels.KleinToPoincare(t);
t2 = HyperbolicModels.KleinToPoincare(t2);
startingEdges.Add(new H3.Cell.Edge(t, t2));
startingEdges.Add(new H3.Cell.Edge(t, simplex.ReflectInFacet(t, 3)));
}
// If we are doing a view path, transform our geometry.
if (ViewPath != null)
{
//Vector3D p = new Vector3D( 0, 0, .5 );
Vector3D p = new Vector3D(0.08, 0.12, 0.07);
simplex.Facets = simplex.Facets.Select(f => H3Models.Transform_PointToOrigin(f, p)).ToArray();
simplex.Verts = simplex.Verts.Select(v => H3Models.Transform_PointToOrigin(v, p)).ToArray();
startingEdges = startingEdges.Select(e => new H3.Cell.Edge(
H3Models.Transform_PointToOrigin(e.Start, p),
H3Models.Transform_PointToOrigin(e.End, p))).ToList();
}
SetupBaseHue(fileName, mirrorsString, baseHue);
Recurse.m_background = baseHue == -1 ? new Vector3D() : new Vector3D(baseHue, 1, .1);
H3.Cell.Edge[] edges = Recurse.CalcEdgesSmart2(simplex.Facets, startingEdges.ToArray(), numEdges);
//H3.Cell.Edge[] edges = Recurse.CalcEdges( simplex.Facets, startingEdges.ToArray(),
// new Recurse.Settings() { ThreshType = Recurse.EdgeThreshType.Radial, Threshold = H3Models.Ball.FindLocationForDesiredRadius( settings.PovRay.EdgeWidth, 0.8/100 ) } );
//edges = edges.Where( e => e.Depths[0] % 2 == 1 ).ToArray(); // Used for Borromean Rings complement image.
// Shapeways truncated 436.
if (false)
{
if (true)
{
Mobius m = Mobius.Scale(1.0 / H3Models.UHS.ToE(Honeycomb.InRadius(def.P, def.Q, def.R)));
double a = -Math.PI / 2 + Math.Asin(1 / Math.Sqrt(3));
edges = edges.Select(e =>
{
Vector3D v1 = e.Start;
Vector3D v2 = e.End;
v1.RotateAboutAxis(new Vector3D(1, 0, 0), a);
v2.RotateAboutAxis(new Vector3D(1, 0, 0), a);
v1 = H3Models.Ball.ApplyMobius(m, v1);
v2 = H3Models.Ball.ApplyMobius(m, v2);
return(new H3.Cell.Edge(v1, v2));
}).ToArray();
double thresh = -.01;
Vector3D looking = new Vector3D(0, 0, -1);
edges = edges.Where(e => e.Start.Dot(looking) > thresh && e.End.Dot(looking) > thresh).ToArray();
Dictionary <H3.Cell.Edge, int> edgeDict = edges.ToDictionary(e => e, e => 1);
H3.RemoveDanglingEdgesRecursive(edgeDict);
edges = edgeDict.Keys.ToArray();
}
else
{
Mobius m = Mobius.Scale(2);
edges = edges.Select(e =>
{
Vector3D v1 = e.Start;
Vector3D v2 = e.End;
v1 = H3Models.Ball.ApplyMobius(m, v1);
v2 = H3Models.Ball.ApplyMobius(m, v2);
return(new H3.Cell.Edge(v1, v2));
}).ToArray();
Dictionary <H3.Cell.Edge, int> edgeDict = edges.ToDictionary(e => e, e => 1);
H3.RemoveDanglingEdgesRecursive(edgeDict);
edges = edgeDict.Keys.ToArray();
}
}
//H3.m_settings.Output = H3.Output.STL;
//H3.m_settings.Scale = 50;
H3.SaveToFile(fileName, edges, finite: true, append: true);
bool doCells = false;
H3.Cell[] cellsToHighlight = null;
if (doCells)
{
int[] polyMirrors = new int[] { 1, 2, 3 };
active = active.Select(i => mapMirror(i)).OrderBy(i => i).ToArray();
H3.Cell startingCell = PolyhedronToHighlight(Geometry.Hyperbolic, polyMirrors, simplex, startingPoint);
cellsToHighlight = Recurse.CalcCells(simplex.Facets, new H3.Cell[] { startingCell });
H3.AppendFacets(fileName, cellsToHighlight);
}
return(edges);
}
public static void Test()
{
HoneycombDef def = new HoneycombDef(5, 3, 4);
Simplex simplex = new Simplex();
simplex.Facets = SimplexCalcs.Mirrors(def.P, def.Q, def.R);
// Simplices will be the "cells"
H3.Cell.Facet[] simplexFacets = simplex.Facets.Select(m => new H3.Cell.Facet(m)).ToArray();
H3.Cell startingCell = new H3.Cell(simplexFacets);
startingCell.AuxPoints = SimplexCalcs.VertsBall(def.P, def.Q, def.R);
startingCell.Center = HoneycombPaper.InteriorPointBall;
var cells = CalcCells(simplex.Facets, new H3.Cell[] { startingCell });
// Get all the cell centers
HashSet <Vector3D> centers = new HashSet <Vector3D>();
foreach (var cell in cells)
{
Vector3D cellCen = cell.AuxPoints[0];
centers.Add(cellCen);
}
// Colors.
Dictionary <double, Color> colors = new Dictionary <double, Color>(new DoubleEqualityComparer());
System.Random rand = new System.Random(0);
// Get all the in-spheres
double inRad = startingCell.AuxPoints[1].Abs();
//inRad *= 1.16;
List <Sphere> inSpheres = new List <Sphere>();
foreach (Vector3D c in centers)
{
Vector3D p = c;
//SphericalModels.GnomonicToStereo( c );
Geometry g = Geometry.Hyperbolic;
Vector3D cen;
double rad;
H3Models.Ball.DupinCyclideSphere(p, inRad, g, out cen, out rad);
Sphere i = new Sphere(cen, rad);
Color color;
if (!colors.TryGetValue(c.Abs(), out color))
{
Vector3D rgb = ColorUtil.CHSL2RGB(new Vector3D(rand.NextDouble() * 360, .5, .5));
rgb *= 255;
color = Color.FromArgb(255, (int)rgb.X, (int)rgb.Y, (int)rgb.Z);
colors[c.Abs()] = color;
}
i.Color = color;
inSpheres.Add(i);
}
// Project sphere to unit sphere.
List <Circle3D> circlesOnUnitSphere = new List <Circle3D>();
foreach (Sphere i in inSpheres)
{
if (i.Center.IsOrigin || i.Center.DNE || Infinity.IsInfinite(i.Center))
{
continue;
}
Sphere orthogonal = new Sphere(new Vector3D(), RadiusOrthogonal(i));
Circle3D c = orthogonal.Intersection(i);
// We need to scale this based on the size of the orthogonal sphere.
c.Center /= orthogonal.Radius;
c.Radius /= orthogonal.Radius;
c.Color = i.Color;
circlesOnUnitSphere.Add(c);
}
Circle3D unit = new Circle3D();
//circlesOnUnitSphere.Add( unit );
ProjectAndSave(circlesOnUnitSphere);
}
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>
/// 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();
}
}
}
private static void CompoundOfFive24Cells(ref H3.Cell.Edge[] edges)
{
List <H3.Cell.Edge> allEdges = new List <H3.Cell.Edge>();
Vector3D v600 = Sterographic.R3toS3(SimplexCalcs.VertexSpherical(3, 3, 5));
Vector3D v24 = Sterographic.R3toS3(SimplexCalcs.VertexSpherical(3, 4, 3));
Sphere[] mirrors600 = SimplexCalcs.MirrorsSpherical(3, 3, 5);
double a24 = v24.AngleTo(Sterographic.R3toS3(new Vector3D()));
double a600 = v600.AngleTo(Sterographic.R3toS3(new Vector3D()));
Matrix4D m600 = Matrix4D.MatrixToRotateinCoordinatePlane(a600, 2, 3);
Matrix4D m600_ = Matrix4D.MatrixToRotateinCoordinatePlane(-a600, 2, 3);
Matrix4D m24 = Matrix4D.MatrixToRotateinCoordinatePlane(a24, 2, 3);
Matrix4D m24_ = Matrix4D.MatrixToRotateinCoordinatePlane(-a24, 2, 3);
double eLength = 2 * Math.PI / 10; // 600-cell edge length
double a_id = Math.Asin(Math.Sin(eLength / 2) / Math.Sin(Math.PI / 3) * Math.Sin(Math.PI / 2));
eLength = 1.0 / Math.Sin(2 * Math.PI / 5); // icosahedron edge length
double a_i = Math.Asin(Math.Sin(eLength / 2) / Math.Sin(Math.PI / 3) * Math.Sin(Math.PI / 5));
Func <Vector3D, Vector3D> rot600 = v =>
{
v = Sterographic.R3toS3(v);
v = m600.RotateVector(v);
v = Sterographic.S3toR3(v);
return(v);
};
Func <Vector3D, int, Vector3D> rotOne = (v, idx) =>
{
v = Sterographic.R3toS3(v);
v = m24.RotateVector(v);
v = Sterographic.S3toR3(v);
v.RotateAboutAxis(new Vector3D(1, 0, 0), -a_id);
// Vertex to cell center.
v = Sterographic.R3toS3(v);
v = m600_.RotateVector(v);
v = Sterographic.S3toR3(v);
List <int> reflections = new List <int>();
if (idx == 0)
{
reflections.Add(2);
reflections.Add(1);
reflections.Add(2);
reflections.Add(0);
reflections.Add(1);
reflections.Add(2);
reflections.Add(1);
reflections.Add(2);
}
if (idx != 0)
{
reflections.Add(3);
}
if (idx == 2)
{
reflections.Add(1);
reflections.Add(2);
}
if (idx == 3)
{
reflections.Add(2);
reflections.Add(1);
}
if (idx == 4)
{
reflections.Add(1);
reflections.Add(0);
reflections.Add(1);
reflections.Add(2);
reflections.Add(0);
reflections.Add(1);
reflections.Add(0);
reflections.Add(1);
}
foreach (int reflection in reflections)
{
v = mirrors600[reflection].ReflectPoint(v);
}
v = Sterographic.R3toS3(v);
v = m600.RotateVector(v);
v = Sterographic.S3toR3(v);
//v.RotateAboutAxis( new Vector3D( 0, 0, 1 ), Math.PI/3 );
//v.RotateAboutAxis( new Vector3D( 1, 0, 0 ), -a_i*2 );
v = Sterographic.R3toS3(v);
//v = m24_.RotateVector( v );
v = Sterographic.S3toR3(v);
return(v);
};
for (int i = 0; i < 5; i++)
{
//if( i == 0 )
// continue;
allEdges.AddRange(edges.Select(e =>
{
H3.Cell.Edge newEdge = new H3.Cell.Edge(rotOne(e.Start, i), rotOne(e.End, i));
//H3.Cell.Edge newEdge = new H3.Cell.Edge( rot600( e.Start ), rot600( e.End ) );
switch (i)
{
case 0:
newEdge.Color = new Vector3D(1, 0, 0, 1);
//newEdge.Color = new Vector3D( 1, 1, 1, 0 );
break;
case 1:
newEdge.Color = new Vector3D(0, 1, 0, 2);
break;
case 2:
newEdge.Color = new Vector3D(0, 0, 1, 3);
break;
case 3:
newEdge.Color = new Vector3D(1, 0, 1, 4);
break;
case 4:
newEdge.Color = new Vector3D(0, 1, 1, 5);
break;
}
return(newEdge);
}));
}
edges = allEdges.ToArray();
//edges = edges.Where( e => Tolerance.Equal( 1, e.Start.Abs() ) || Tolerance.Equal( 1, e.End.Abs() ) ).ToArray();
HashSet <Vector3D> uniqueVerts = new HashSet <Vector3D>();
foreach (H3.Cell.Edge e in edges)
{
uniqueVerts.Add(e.Start);
uniqueVerts.Add(e.End);
}
System.Diagnostics.Trace.WriteLine("Number of verts = " + uniqueVerts.Count);
/*edges = edges.Where( e =>
* {
* Vector3D v = Tolerance.Equal( 1, e.Start.Abs() ) ? e.End : e.Start;
* if( v.Abs() >= 0.8 || v.Abs() <= 0.7 )
* return false;
*
* if( Tolerance.LessThanOrEqual( v.X, 0 ) || Tolerance.GreaterThanOrEqual( v.Y, 0 ) || Tolerance.GreaterThanOrEqual( v.Z, 0 ) )
* return false;
*
* return true;
* } ).ToArray();
*
* edges = edges.OrderBy( e => Tolerance.Equal( 1, e.Start.Abs() ) ? e.End.Abs() : e.Start.Abs() ).ToArray();*/
}
/// <summary>
/// Create an STL file for a cell.
/// Currently only works for cells with both hyperideal vertices and cells.
/// </summary>
public static void HoneycombHyperidealLegs(HoneycombDef def, int lod, Dictionary <Vector3D, H3.Cell> complete)
{
int p = def.P;
int q = def.Q;
int r = def.R;
m_div = TextureHelper.SetLevels(lod);
bool ball = false;
Sphere[] simplex = SimplexCalcs.Mirrors(p, q, r, moveToBall: ball);
H3.Cell.Edge[] edges;
if (ball)
{
edges = SimplexCalcs.SimplexEdgesBall(p, q, r);
}
else
{
edges = SimplexCalcs.SimplexEdgesUHS(p, q, r);
}
// Two edges of one simplex facet.
H3.Cell.Edge e1 = edges[2];
H3.Cell.Edge e2 = edges[3];
Vector3D[] points1, points2;
if (ball)
{
points1 = H3Models.Ball.GeodesicPoints(e1.Start, e1.End, 2 * m_div);
points2 = H3Models.Ball.GeodesicPoints(e2.Start, e2.End, 2 * m_div);
}
else
{
points1 = H3Models.UHS.GeodesicPoints(e1.Start, e1.End, 2 * m_div);
points2 = H3Models.UHS.GeodesicPoints(e2.Start, e2.End, 2 * m_div);
}
Sphere cellSphere = simplex[0];
Sphere vertexSphere = simplex[3];
// Because one vertex the facet triangle is hyperideal, it will actually look like a square.
List <Vector3D[]> allPoints = new List <Vector3D[]>();
for (int i = 0; i < points1.Length; i++)
{
Vector3D p1 = points1[i];
Vector3D p2 = points2[i];
Vector3D[] arcPoints;
if (i == points1.Length - 1)
//if( false )
{
// NOTE: This arc is not generally geodesic!
// Or is it?
arcPoints = ball ?
H3Models.Ball.GeodesicPoints(p1, p2, m_div) :
H3Models.UHS.GeodesicPoints(p1, p2, m_div);
/*Circle3D arc = cellSphere.Intersection( vertexSphere );
* double angleTot = (p1 - arc.Center).AngleTo( p2 - arc.Center );
* arcPoints = Shapeways.CalcArcPoints( arc.Center, arc.Radius, p1, arc.Normal, -angleTot, div );*/
}
else
{
Circle3D c = Circle3D.FromCenterAnd2Points(cellSphere.Center, p1, p2);
double angleTot = (p1 - c.Center).AngleTo(p2 - c.Center);
arcPoints = Shapeways.CalcArcPoints(cellSphere.Center, cellSphere.Radius, p1, c.Normal, -angleTot, m_div);
}
//Vector3D[] arcPoints = new Vector3D[] { p1, p2 };
allPoints.Add(arcPoints);
}
// Create the triangles for the patch.
Mesh mesh = new Mesh();
for (int i = 0; i < allPoints.Count - 1; i++)
{
Vector3D[] arc1 = allPoints[i];
Vector3D[] arc2 = allPoints[i + 1];
for (int j = 0; j < arc1.Length - 1; j++)
{
// Points of (i,j) box;
Vector3D p1 = arc1[j];
Vector3D p2 = arc2[j];
Vector3D p3 = arc1[j + 1];
Vector3D p4 = arc2[j + 1];
Mesh.Triangle tri1 = new Mesh.Triangle(p1, p2, p3);
Mesh.Triangle tri2 = new Mesh.Triangle(p2, p4, p3);
// We need to thicken after reflecting around, otherwise we can't apply a min thickness.
/*Sphere normal = cellSphere;
* Mesh.Triangle[] thickened1 = Thicken( tri1, normal );
* Mesh.Triangle[] thickened2 = Thicken( tri2, normal );
* mesh.Triangles.AddRange( thickened1 );
* mesh.Triangles.AddRange( thickened2 );*/
mesh.Triangles.Add(tri1);
mesh.Triangles.Add(tri2);
}
}
// AuxPoints will be used for multiple things.
// - The first two points are for an an that will fill the gap where there is a missing face.
// - We'll also store the points for the 4 edges of our fundamental triangle.
List <Vector3D> auxPoints = new List <Vector3D>();
{
var edge1 = allPoints.First();
var edge2 = allPoints.Last();
List <Vector3D> edge3 = new List <Vector3D>(), edge4 = new List <Vector3D>();
for (int i = 0; i < allPoints.Count; i++)
{
edge3.Add(allPoints[i][0]);
edge4.Add(allPoints[i][allPoints[i].Length - 1]);
}
edge4.Reverse();
auxPoints.Add(e1.Start);
auxPoints.Add(e1.End);
auxPoints.AddRange(edge1.Reverse());
auxPoints.AddRange(edge2);
auxPoints.AddRange(edge3);
auxPoints.AddRange(edge4);
}
Vector3D cen = HoneycombPaper.InteriorPointBall;
/* Reorientation code. Move this elsewhere.
*
* // Face centered orientation.
* bool faceCentered = false;
* if( faceCentered )
* SimplexCalcs.PrepForFacetCentering( p, q, simplex, ref cen );
*
* Mobius mUHS = SimplexCalcs.FCOrientMobius( p, q );
* Mobius mBall = HoneycombPaper.FCOrientMobius( H3Models.UHSToBall( cellSphere ) );
*
* simplex = simplex.Select( s =>
* {
* s = H3Models.UHSToBall( s );
* //H3Models.TransformInBall2( s, mBall );
* return s;
* } ).ToArray();
*
*
* {
* for( int i = 0; i < mesh.Triangles.Count; i++ )
* {
* Mesh.Triangle tri = mesh.Triangles[i];
*
* if( faceCentered )
* {
* tri.a = mUHS.ApplyToQuaternion( tri.a );
* tri.b = mUHS.ApplyToQuaternion( tri.b );
* tri.c = mUHS.ApplyToQuaternion( tri.c );
* }
*
* tri.a = H3Models.UHSToBall( tri.a );
* tri.b = H3Models.UHSToBall( tri.b );
* tri.c = H3Models.UHSToBall( tri.c );
*
* if( faceCentered )
* {
* tri.a = H3Models.TransformHelper( tri.a, mBall );
* tri.b = H3Models.TransformHelper( tri.b, mBall );
* tri.c = H3Models.TransformHelper( tri.c, mBall );
* }
* mesh.Triangles[i] = tri;
* }
*
* if( faceCentered )
* cen = H3Models.TransformHelper( cen, mBall );
* }
*/
// Now we need to reflect around this fundamental patch.
H3.Cell[] simplices = GenCell(simplex, mesh, cen, auxPoints.ToArray(), ball);
// Existing cells take precedence.
foreach (H3.Cell c in simplices)
{
Vector3D t = c.Center;
H3.Cell dummy;
if (!complete.TryGetValue(t, out dummy))
{
complete[t] = c;
}
}
}
private static void HoneycombFiniteVertexFig(HoneycombDef def, int lod, Dictionary <Vector3D, H3.Cell> complete)
{
int p = def.P;
int q = def.Q;
int r = def.R;
double scale = 1.0;
Vector3D vUHS = H3Models.BallToUHS(SimplexCalcs.VertexPointBall(p, q, r));
if (Geometry2D.GetGeometry(q, r) != Geometry.Hyperbolic) // Vertex-centered if possible
{
scale = 1.0 / vUHS.Z;
}
System.Func <Vector3D, Vector3D> trans = v =>
{
v = H3Models.BallToUHS(v);
v *= scale;
v = H3Models.UHSToBall(v);
return(v);
};
bool ball = true;
Sphere[] simplex = SimplexCalcs.Mirrors(p, q, r, moveToBall: ball);
simplex = simplex.Select(s =>
{
s = H3Models.BallToUHS(s);
Sphere.ScaleSphere(s, scale);
s = H3Models.UHSToBall(s);
return(s);
}).ToArray();
H3.Cell.Edge[] edges = SimplexCalcs.SimplexEdgesBall(p, q, r);
// Two edges of the simplex facet.
// NOTE: This contruction only works for material triangles, and matches the construction in the TextureHelper.
m_div = TextureHelper.SetLevels(lod);
int[] elementIndices = TextureHelper.TextureElements(1, lod);
List <Vector3D> points = new List <Vector3D>();
H3.Cell.Edge e1 = edges[2];
H3.Cell.Edge e2 = edges[3];
Vector3D p1 = trans(e1.Start), p2 = trans(e1.End), p3 = trans(e2.End);
Vector3D[] points1 = H3Models.Ball.GeodesicPoints(p2, p1, m_div);
Vector3D[] points2 = H3Models.Ball.GeodesicPoints(p3, p1, m_div);
for (int i = 0; i < m_div; i++)
{
points.AddRange(H3Models.Ball.GeodesicPoints(points1[i], points2[i], m_div - i));
}
points.Add(p1);
Mesh mesh = new Mesh();
for (int i = 0; i < elementIndices.Length / 3; i++)
{
int idx1 = i * 3;
int idx2 = i * 3 + 1;
int idx3 = i * 3 + 2;
Vector3D v1 = points[elementIndices[idx1]];
Vector3D v2 = points[elementIndices[idx2]];
Vector3D v3 = points[elementIndices[idx3]];
mesh.Triangles.Add(new Mesh.Triangle(v1, v2, v3));
}
// AuxPoints will be used for multiple things.
// - The first is a definition point for a face, so we can check for duplicates.
// - We'll also store the points for the 3 edges of our fundamental triangle.
List <Vector3D> auxPoints = new List <Vector3D>();
{
auxPoints.Add((p1 + p2 + p3) / 3);
auxPoints.AddRange(points1);
auxPoints.AddRange(points2.Reverse());
auxPoints.AddRange(H3Models.Ball.GeodesicPoints(points2[0], points1[0], m_div));
}
Vector3D cen = HoneycombPaper.InteriorPointBall;
H3.Cell[] simplices = GenCell(simplex, mesh, cen, auxPoints.ToArray(), ball);
// Existing cells take precedence.
foreach (H3.Cell c in simplices)
{
Vector3D t = c.AuxPoints[0];
H3.Cell dummy;
if (!complete.TryGetValue(t, out dummy))
{
complete[t] = c;
}
}
}
public void Gen(int p, int q, int r)
{
Geometry g = Util.GetGeometry(p, q, r);
if (g != Geometry.Spherical)
{
throw new System.Exception("Point group code only for spherical geometry.");
}
Simplex simplex = new Simplex();
simplex.Facets = SimplexCalcs.Mirrors(p, q, r);
Vector3D cen = new Vector3D();
Vector3D faceCenter = SimplexCalcs.FaceCenterSpherical(p, q, r);
Vector3D edgeMid = SimplexCalcs.EdgeMidpointSpherical(p, q, r);
Vector3D vertex = SimplexCalcs.VertexSpherical(p, q, r);
List <Vector3D> startingPoles = new List <Vector3D>();
startingPoles.Add(Sterographic.S3toR3(GreatSphere.FromSphere(simplex.Facets[0]).Pole));
GreatSphere[] spheres = CalcSpheres(simplex.Facets, startingPoles.ToArray());
string filename = "point_group.pov";
using (StreamWriter sw = File.CreateText(filename))
{
//foreach( var greatSphere in spheres )
//sw.WriteLine( PovRay.Sphere( greatSphere.ToSphere() ) );
}
/*
* List<H3.Cell.Edge> startingEdges = new List<H3.Cell.Edge>();
* startingEdges.Add( new H3.Cell.Edge( cen, faceCenter ) );
* H3.Cell.Edge[] edges = Recurse.CalcEdges( simplex.Facets, startingEdges.ToArray(), new Recurse.Settings() { G = Geometry.Spherical, Threshold = 0.001 } );
* //edges = edges.Where( e => !( Infinity.IsInfinite( e.Start ) || Infinity.IsInfinite( e.End ) ) ).ToArray();
*
* PovRay.WriteEdges( new PovRay.Parameters() { AngularThickness = 0.01 }, Geometry.Spherical, edges, filename, append: true );
*/
double minRad = 0;
double thick = 0.005;
System.Func <Vector3D, Sphere> sizeFunc = v =>
{
Vector3D c;
double rad;
H3Models.Ball.DupinCyclideSphere(v, thick / 2, g, out c, out rad);
return(new Sphere()
{
Center = c, Radius = Math.Max(rad, minRad)
});
};
// All geodesics
List <Circle3D> startingCircles = new List <Circle3D>();
startingCircles.Add(GeodesicFrom2Points(cen, edgeMid));
Circle3D[] geodesics = CalcGeodesics(simplex.Facets, startingCircles.ToArray());
Vector3D color = new Vector3D(0, 0, 1);
using (StreamWriter sw = File.CreateText(filename))
{
Shapeways shapeways = new Shapeways();
foreach (Circle3D geodesic in geodesics)
{
Vector3D[] points;
if (Infinity.IsInfinite(geodesic.Radius))
{
double cutoff = 15;
Segment seg = Segment.Line(geodesic.Normal * cutoff, geodesic.Normal * -cutoff);
points = seg.Subdivide(42);
}
else
{
List <Vector3D> tempPoints = geodesic.Subdivide(150).ToList();
tempPoints.Add(tempPoints[0]);
tempPoints.Add(tempPoints[1]);
points = tempPoints.ToArray();
}
List <Vector3D> ePoints = new List <Vector3D>();
List <double> eRadii = new List <double>();
foreach (Vector3D pNE in points)
{
Sphere sphere = sizeFunc(pNE);
ePoints.Add(sphere.Center);
eRadii.Add(sphere.Radius);
}
shapeways.AddCurve(ePoints.ToArray(), eRadii.ToArray());
sw.WriteLine(PovRay.EdgeSphereSweep(points, sizeFunc, color));
}
STL.SaveMeshToSTL(shapeways.Mesh, "533.stl");
}
}
