/// <summary>
/// Hopf Link between two points on S^2.
/// </summary>
public static void HopfLink(StreamWriter sw, Vector3D s2_1, Vector3D s2_2, bool anti)
{
Vector3D[] circlePoints;
string circleString;
circlePoints = OneHopfCircleProjected(s2_1, anti);
circleString = PovRay.EdgeSphereSweep(circlePoints, SizeFunc);
sw.WriteLine(circleString);
circlePoints = OneHopfCircleProjected(s2_2, anti);
circleString = PovRay.EdgeSphereSweep(circlePoints, SizeFunc);
sw.WriteLine(circleString);
Mesh mesh = new Mesh();
Vector3D[] interpolated = S3.GeodesicPoints(s2_1, s2_2);
for (int i = 0; i < interpolated.Length - 1; i++)
{
Vector3D v1 = interpolated[i];
Vector3D v2 = interpolated[i + 1];
Vector3D[] p1 = OneHopfCircleProjected(v1, anti);
Vector3D[] p2 = OneHopfCircleProjected(v2, anti);
for (int j = 0; j < p1.Length - 1; j++)
{
Mesh.Triangle t1 = new Mesh.Triangle(p1[j], p1[j + 1], p2[j]);
Mesh.Triangle t2 = new Mesh.Triangle(p2[j], p1[j + 1], p2[j + 1]);
mesh.Triangles.Add(t1);
mesh.Triangles.Add(t2);
}
}
PovRay.WriteMesh(sw, mesh, append: true);
}
public static void HopfOrbit()
{
List <Vector3D> s2Points = new List <Vector3D>();
for (double theta = Math.PI * .1; theta <= Math.PI * .9; theta += Math.PI * .2)
{
for (double lon = -Math.PI; lon <= Math.PI; lon += Math.PI / 10)
{
s2Points.Add(SphericalCoords.SphericalToCartesian(new Vector3D(1.0, theta, lon)));
}
}
using (StreamWriter sw = File.CreateText(@".\out.pov"))
{
System.Func <Vector3D, Sphere> sizeFunc = v => new Sphere()
{
Center = v, Radius = 0.01
};
foreach (Vector3D s2Point in s2Points)
{
Vector3D[] circlePoints = OneHopfCircle(s2Point);
//for( int i = 0; i < circlePoints.Length; i++ )
// circlePoints[i] = circlePoints[i].ProjectTo3DSafe( 1.0 );
// Note: effectively orthogonal projects here because EdgeSphereSweep doesn't write W coord.
string circleString = PovRay.EdgeSphereSweep(circlePoints, sizeFunc);
sw.WriteLine(circleString);
}
}
}
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");
}
}
