private H3.Cell.Edge[] GenEdgesInternal(Vector3D v1, Vector3D v2, Vector3D v3, Vector3D v4)
{
int div = 5;
List <H3.Cell.Edge> result = new List <H3.Cell.Edge>();
for (int i = 0; i <= div; i++)
{
Vector3D start = v1 + (v2 - v1) * i / div;
Vector3D end = v3 + (v4 - v3) * i / div;
start.Normalize();
end.Normalize();
start = Sterographic.S3toR3(start);
end = Sterographic.S3toR3(end);
if (Infinity.IsInfinite(start))
{
start = end * 10;
}
if (Infinity.IsInfinite(end))
{
end = start * 10;
}
result.Add(new H3.Cell.Edge(start, end));
}
return(result.ToArray());
}
/// <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 Vector3D Transform2(Vector3D p, Matrix4D mat)
{
p.Normalize();
p = mat.RotateVector(p);
p = Sterographic.S3toR3(p);
p = SphericalModels.StereoToEquidistant(p);
return(p);
}
private static Vector3D[] OneHopfCircleProjected(Vector3D s2Point, bool anti)
{
Vector3D[] circlePoints = S3.OneHopfCircle(s2Point, anti);
for (int i = 0; i < circlePoints.Length; i++)
{
circlePoints[i] = Sterographic.S3toR3(circlePoints[i]);
}
return(circlePoints);
}
public static void ElevenCell()
{
Graph g = new Graph();
g.SetupCompleteGraph(11);
GraphRelaxation relaxer = new GraphRelaxation();
relaxer.Graph = g;
relaxer.NodeRepulsion = 0.01;
relaxer.EdgeAttraction = 0.0;
relaxer.EdgeRepulsion = 0.0;
relaxer.Relax(20000);
Vector3D northPole = new Vector3D(0, 0, 0, 1);
H3.Cell.Edge[] edges = g.Edges.Select(e =>
{
Vector3D v1 = g.Nodes[e.V1].Position.ToVec3D();
Vector3D v2 = g.Nodes[e.V2].Position.ToVec3D();
//if( v1.Compare( northPole, .5 ) || v2.Compare( northPole, 0.5 ) ) // Cull edges near north pole.
// return null;
v1 = Sterographic.S3toR3(v1);
v2 = Sterographic.S3toR3(v2);
return(new H3.Cell.Edge(v1, v2));
}).ToArray();
edges = edges.Where(e => e != null).ToArray();
bool povray = false;
if (povray)
{
string filename = "test.pov";
System.IO.File.Delete(filename);
using (StreamWriter sw = new StreamWriter(filename))
sw.WriteLine("#include \"C:\\Users\\hrn\\Documents\\roice\\povray\\H3\\horosphere\\633.pov\"");
PovRay.WriteEdges(new PovRay.Parameters {
AngularThickness = 0.03
}, Geometry.Spherical, edges, filename, append: true);
}
else
{
S3.EdgesToStl(edges);
}
}
public static Circle3D GeodesicFrom2Points(Vector3D a, Vector3D b)
{
if (a == b || a == -b)
{
throw new System.Exception("Geodesic not unique");
}
System.Func <Vector3D, Circle3D> lineFunc = p =>
{
Circle3D circ = new Circle3D();
circ.Radius = double.PositiveInfinity;
p.Normalize();
circ.Normal = p; // Hacky representation of a line.
return(circ);
};
if (a.IsOrigin || b.IsOrigin)
{
Vector3D p = a.IsOrigin ? b : a;
return(lineFunc(p));
}
double mag1 = a.Abs(), mag2 = b.Abs();
if (Tolerance.Equal(mag1, 1) && Tolerance.Equal(mag2, 1))
{
return(new Circle3D(a, b, a * -1));
}
// The antipode in S^3 of a or b will give us a 3rd point.
Vector3D antipode = Sterographic.S3toR3(Sterographic.R3toS3(a) * -1);
// If the antipode is also an an antipode in R3, the points are colinear
// (or they are on the equatorial 2-sphere, but that is checked above).
if (a == antipode * -1)
{
return(lineFunc(a));
}
return(new Circle3D(a, b, antipode));
}
private static void Relax(Vector3D[] coordsR3, int[] elementIndices, Vector3D[] locks)
{
int dim = 4;
Graph g = new Graph();
for (int i = 0; i < coordsR3.Length; i++)
{
Vector3D v = coordsR3[i];
GraphNode node = new GraphNode(new VectorND(Sterographic.R3toS3(v)), new VectorND(dim));
node.Lock = new VectorND(locks[i]);
g.Nodes.Add(node);
}
for (int i = 0; i < elementIndices.Length; i += 3)
{
int a = elementIndices[i];
int b = elementIndices[i + 1];
int c = elementIndices[i + 2];
g.AddEdge(new GraphEdge(a, b));
g.AddEdge(new GraphEdge(b, c));
g.AddEdge(new GraphEdge(c, a));
}
GraphRelaxation relaxer = new GraphRelaxation();
relaxer.Graph = g;
relaxer.NodeRepulsion = 0;
relaxer.EdgeAttraction = 0.5;
relaxer.EdgeRepulsion = 0;
relaxer.Relax(1000);
for (int i = 0; i < coordsR3.Length; i++)
{
GraphNode node = g.Nodes[i];
coordsR3[i] = Sterographic.S3toR3(node.Position.ToVec3D());
}
}
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();*/
}
public static void S3BiHelicoid()
{
double cutoff = 8.0;
int div = 500;
Matrix4D mat = Matrix4D.MatrixToRotateinCoordinatePlane(1 * Math.PI / 4, 0, 3);
Mesh m1 = S3Helicoid(div, mat, reciprocal: false);
//m1.Triangles = m1.Triangles.Where( t => t.a.Abs() < cutoff && t.b.Abs() < cutoff && t.c.Abs() < cutoff ).ToList();
Mesh m2 = S3Helicoid(div, mat, reciprocal: true);
//m2.Triangles = m2.Triangles.Where( t => t.a.Abs() < cutoff && t.b.Abs() < cutoff && t.c.Abs() < cutoff ).ToList();
Mesh m3 = new Mesh();
System.Action <bool> addCore = recip =>
{
List <Vector3D> circlePoints = new List <Vector3D>();
double aOffset = 2 * Math.PI / div;
for (int i = 0; i <= div; i++)
{
double x = Math.Sin(aOffset * i);
double y = Math.Cos(aOffset * i);
circlePoints.Add(recip ?
new Vector3D(x, y) : new Vector3D(0, 0, x, y));
}
// partial transform to R3 here.
circlePoints = circlePoints.Select(p =>
{
p = mat.RotateVector(p);
p = Sterographic.S3toR3(p);
return(p);
}).ToList();
List <Vector3D> ePoints = new List <Vector3D>();
List <double> eRadii = new List <double>();
foreach (Vector3D pNE in circlePoints)
{
Sphere sphere = SphereFuncBall(Geometry.Spherical, pNE, false);
ePoints.Add(sphere.Center);
eRadii.Add(sphere.Radius);
}
Shapeways shapeways = new Shapeways();
shapeways.AddClosedCurve(ePoints.ToArray(), eRadii.ToArray());
m3.Append(shapeways.Mesh);
};
addCore(false);
addCore(true);
for (int i = 0; i < m3.Triangles.Count; i++)
{
Mesh.Triangle t = m3.Triangles[i];
m3.Triangles[i] = Transform(t, SphericalModels.StereoToEquidistant);
}
string filename = "helicoid.stl";
File.Delete(filename);
using (StreamWriter sw = File.AppendText(filename))
{
STL.AppendMeshToSTL(m1, sw);
STL.AppendMeshToSTL(m2, sw);
STL.AppendMeshToSTL(m3, sw);
}
//HelicoidHelper( thinMesh, boundaryPoints );
}
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");
}
}
