/// <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);
}
private static string Edge(Parameters parameters, Geometry g, H3.Cell.Edge edge)
{
Vector3D v1 = edge.Start, v2 = edge.End;
Vector3D[] points = null;
Func <Vector3D, Sphere> sizeFunc = v => new Sphere()
{
Center = v, Radius = H3Models.SizeFuncConst(v, parameters.Scale)
};
//double minRad = 0.0005;
double minRad = 0.0004;
//double minRad = 0.0017;
// STL
//minRad = 0.8 / 100;
if (parameters.Halfspace)
{
//v1 = H3Models.BallToUHS( v1 );
//v2 = H3Models.BallToUHS( v2 );
points = H3Models.UHS.GeodesicPoints(v1, v2);
if (!parameters.ThinEdges)
{
sizeFunc = v =>
{
// XXX, inexact
return(new Sphere()
{
Center = v, Radius = Math.Max(H3Models.UHS.SizeFunc(v, parameters.AngularThickness), minRad)
});
}
}
;
}
else
{
if (g == Geometry.Hyperbolic)
{
points = H3Models.Ball.GeodesicPoints(v1, v2, edge.Color.Z);
}
else if (g == Geometry.Spherical)
{
points = S3.GeodesicPoints(v1, v2);
//points = points.Select( p => { p.Normalize(); return p; } ).ToArray();
}
else
{
//points = new Vector3D[] { v1, v2 };
List <Vector3D> interpolated = new List <Vector3D>();
int count = 20;
for (int i = 0; i <= count; i++)
{
interpolated.Add(v1 + (v2 - v1) * ((double)i / count));
}
points = interpolated.ToArray();
}
if (!parameters.ThinEdges)
{
sizeFunc = v =>
{
Vector3D c;
double r;
H3Models.Ball.DupinCyclideSphere(v, parameters.AngularThickness / 2, g, out c, out r);
return(new Sphere()
{
Center = c, Radius = Math.Max(r, minRad)
});
}
}
;
}
//if( g == Geometry.Euclidean )
// return EdgeCylinder( points, sizeFunc );
return(EdgeSphereSweep(points, sizeFunc, edge.Color));
}
