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 OneHoneycombGoursat(int[] active, string baseName, int baseHue, Settings settings = null)
{
// Setup parameters.
int numEdges = 250000;
if (settings != null)
{
active = settings.PovRay.Active;
numEdges = settings.PovRay.NumEdges;
baseName = string.Join("-", settings.Angles);
}
CalcThickness(active);
if (settings != null)
{
H3.m_settings.AngularThickness = settings.PovRay.EdgeWidth; // ZZZ - should really stop using that settings class.
}
// Create the simplex.
Simplex simplex = new Simplex();
if (settings != null)
{
simplex.InitializeGoursat(settings.Angles);
}
else
{
simplex.InitializeGoursat();
}
// Map of labels for mirrors consistent with input scheme to Goursat function.
// Map is from wikipedia labeling scheme to the indices our function generates.
//
// wiki == our index
// 0100 == 0
// 0001 == 1
// 1000 == 2
// 0010 == 3
Func <int, int> mapMirror = i =>
{
switch (i)
{
case 0: return(2);
case 1: return(0);
case 2: return(3);
case 3: return(1);
}
throw new System.ArgumentException();
};
// We need to set this up before converting the mirrors.
string mirrorsString = ActiveMirrorsString(active);
string suffix = "_" + mirrorsString;
// Convert our active mirrors into the Goursat tet indices.
int[] polyMirrors = new int[] { 1, 2, 3 };
active = active.Select(i => mapMirror(i)).OrderBy(i => i).ToArray();
polyMirrors = polyMirrors.Select(i => mapMirror(i)).OrderBy(i => i).ToArray();
Vector3D startingPoint = IterateToStartingPoint(null, active, simplex);
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));
}
bool doEdges = true;
bool doCells = false;
// Generate the honeycomb.
H3.Cell.Edge[] edges = null;
if (doEdges)
{
edges = Recurse.CalcEdgesSmart(simplex.Facets, startingEdges.ToArray(), numEdges);
}
// Highlighted cells.
H3.Cell[] cellsToHighlight = null;
if (doCells)
{
H3.Cell startingCell = PolyhedronToHighlight(Geometry.Hyperbolic, polyMirrors, simplex, startingPoint);
cellsToHighlight = Recurse.CalcCells(simplex.Facets, new H3.Cell[] { startingCell });
//cellsToHighlight = new H3.Cell[] { startingCell };
}
// plugin Wendy's nonuniform calcs here...
//Nonuniform.Wendy( simplex, edges );
// Trim out half the edges (the ones we won't see in our Pov-Ray view).
/*Vector3D lookFrom = new Vector3D( 1, 1, 1 ) * 0.7;
* Vector3D lookAt = new Vector3D(); // pov-ray lookat
* double thresh = -.01;
* if( doEdges )
* edges = edges.Where( e => e.Start.Dot( lookAt ) > thresh || e.End.Dot( lookAt ) > thresh ).ToArray();
* //if( doCells )
* // cellsToHighlight = cellsToHighlight.Where( c => c.Center.Dot( lookAt ) > thresh ).ToArray(); // I don't think this works right
*/
string fileName = baseName + suffix;
if (File.Exists(fileName + ".pov"))
{
File.Delete(fileName + ".pov");
//Console.WriteLine( string.Format( "Skipping {0}", fileName ) );
//return;
}
SetupBaseHueGoursat(fileName, mirrorsString, baseHue);
if (doEdges)
{
H3.SaveToFile(fileName, edges, finite: true, append: true);
}
if (doCells)
{
HashSet <H3.Cell.Edge> cellEdges = new HashSet <H3.Cell.Edge>(new H3.Cell.EdgeEqualityComparer());
foreach (H3.Cell cell in cellsToHighlight)
{
cell.AppendAllEdges(cellEdges);
}
edges = cellEdges.ToArray();
H3.SaveToFile(fileName, edges, finite: true, append: true);
H3.AppendFacets(fileName, cellsToHighlight);
}
}