/// <summary>
/// Returns a stereographically sphere representing us.
/// </summary>
public Sphere ToSphere()
{
// Equatorial sphere?
if (Pole == new Vector3D(0, 0, 0, 1))
{
return(new Sphere());
}
// A plane?
Vector3D poleR3 = Sterographic.S3toR3(Pole);
if (Tolerance.Equal(poleR3.Abs(), 1))
{
return(Sphere.Plane(poleR3));
}
// Get 4 points on the sphere.
Vector3D e1 = new Vector3D(1, 0, 0, 0);
Vector3D e2 = new Vector3D(0, 1, 0, 0);
Vector3D e3 = new Vector3D(0, 0, 1, 0);
Vector3D e4 = new Vector3D(0, 0, 0, 1);
System.Func <Vector3D, Vector3D> one = v =>
{
v = Euclidean3D.ProjectOntoPlane(Pole, new Vector3D(), v);
v.Normalize();
return(Sterographic.S3toR3(v));
};
return(Sphere.From4Points(one(e1), one(e2), one(e3), one(e4)));
}
private static Circle3D ConstructRotationCircle(Edge hinge, Vector3D hingePoint, Vector3D polyPoint)
{
Vector3D hingeAxis = EdgeAxis(hinge);
Circle3D c = new Circle3D
{
Center = Euclidean3D.ProjectOntoLine(hingeAxis, hingePoint, polyPoint),
Normal = hingeAxis,
Radius = Euclidean3D.DistancePointLine(hingeAxis, hingePoint, polyPoint)
};
if (c.Normal.Dot(c.Center) < 0)
{
c.Normal *= -1;
}
return(c);
}
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);
}
