public static Vector3D VertexPointKlein(int p, int q, int r)
{
Geometry vertexGeometry = Geometry2D.GetGeometry(q, r);
if (vertexGeometry != Geometry.Hyperbolic)
{
throw new System.NotImplementedException();
}
Sphere[] mirrors = Mirrors(p, q, r);
Sphere klein = H3Models.BallToKlein(mirrors[0]);
Vector3D off = klein.Offset;
double h = off.Abs() / Math.Cos(off.AngleTo(new Vector3D(0, 0, -1)));
return(new Vector3D(0, 0, -h));
}
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);
}
}
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);
}
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);
}
}