| public static Mirrors ( Vector3D verts ) : R3.Geometry.Sphere[] | ||
| verts | Vector3D | |
| return | R3.Geometry.Sphere[] | |
public void InitializeGoursat()
{
//Vector3D[] test = SimplexCalcs.GoursatTetrahedron( 3.5, 3.8, 3.1, 2.2, 2.01, 2.1 ); // Example values from paper.
//Verts = SimplexCalcs.GoursatTetrahedron( 2, 4, 3, 2, 3, 3 ); // 4,3,3,3
//Verts = SimplexCalcs.GoursatTetrahedron( 2, 5, 3, 2, 3, 3 ); // 5,3,3,3
//Verts = SimplexCalcs.GoursatTetrahedron( 2, 4, 3, 2, 4, 3 ); // 4,3,4,3
//Verts = SimplexCalcs.GoursatTetrahedron( 2, 4, 3, 2, 5, 3 ); // 4,3,5,3
//Verts = SimplexCalcs.GoursatTetrahedron( 2, 5, 3, 2, 5, 3 ); // 5,3,5,3
//Verts = SimplexCalcs.GoursatTetrahedron( 3, 5, 3, 2, 2, 2 ); // 5,3^1,1
//Verts = SimplexCalcs.GoursatTetrahedron( 3, 2, 2, 2, 5, 3 ); // 5,3^1,1 alt (to avoid vertices at origin).
// Paracompact doesn't work :(
//Verts = SimplexCalcs.GoursatTetrahedron( 2, 6, 3, 2, 6, 3 ); // 6,3,6,3
// Regular
Verts = SimplexCalcs.GoursatTetrahedron(2, 5, 3, 2, 4, 2); // 5,3,4
//Verts = SimplexCalcs.GoursatTetrahedron( 2, 4, 3, 2, 5, 2 ); // 4,3,5
//Verts = SimplexCalcs.GoursatTetrahedron( 2, 5, 3, 2, 5, 2 ); // 5,3,5
//Verts = SimplexCalcs.GoursatTetrahedron( 2, 5, 2, 2, 5, 3 ); // 5,3,5 (Alt)
//Verts = SimplexCalcs.GoursatTetrahedron( 2, 3, 5, 2, 3, 2 ); // 3,5,3
// Spherical doesn't work :(
//Verts = SimplexCalcs.GoursatTetrahedron( 2, 5, 3, 2, 3, 2 ); // 5,3,3
Facets = SimplexCalcs.Mirrors(Verts);
}
/// <summary>
/// Returns the 6 simplex edges in the UHS model.
/// </summary>
public static H3.Cell.Edge[] SimplexEdgesUHS(int p, int q, int r)
{
// Only implemented for honeycombs with hyperideal cells right now.
if (!(Geometry2D.GetGeometry(p, q) == Geometry.Hyperbolic))
{
throw new System.NotImplementedException();
}
Sphere[] simplex = SimplexCalcs.Mirrors(p, q, r, moveToBall: false);
Circle[] circles = simplex.Select(s => H3Models.UHS.IdealCircle(s)).ToArray();
Vector3D[] defPoints = new Vector3D[6];
Vector3D dummy;
Euclidean2D.IntersectionLineCircle(circles[1].P1, circles[1].P2, circles[0], out defPoints[0], out dummy);
Euclidean2D.IntersectionLineCircle(circles[2].P1, circles[2].P2, circles[0], out defPoints[1], out dummy);
Euclidean2D.IntersectionLineCircle(circles[1].P1, circles[1].P2, circles[3], out defPoints[2], out dummy);
Euclidean2D.IntersectionLineCircle(circles[2].P1, circles[2].P2, circles[3], out defPoints[3], out dummy);
Circle3D c = simplex[0].Intersection(simplex[3]);
Vector3D normal = c.Normal;
normal.RotateXY(Math.PI / 2);
Vector3D intersection;
double height, off;
Euclidean2D.IntersectionLineLine(c.Center, c.Center + normal, circles[1].P1, circles[1].P2, out intersection);
off = (intersection - c.Center).Abs();
height = Math.Sqrt(c.Radius * c.Radius - off * off);
intersection.Z = height;
defPoints[4] = intersection;
Euclidean2D.IntersectionLineLine(c.Center, c.Center + normal, circles[2].P1, circles[2].P2, out intersection);
off = (intersection - c.Center).Abs();
height = Math.Sqrt(c.Radius * c.Radius - off * off);
intersection.Z = height;
defPoints[5] = intersection;
// Hyperideal vertex too?
bool order = false;
H3.Cell.Edge[] edges = null;
if (Geometry2D.GetGeometry(q, r) == Geometry.Hyperbolic)
{
edges = new H3.Cell.Edge[]
{
new H3.Cell.Edge(new Vector3D(), new Vector3D(0, 0, 10)),
new H3.Cell.Edge(defPoints[4], defPoints[5], order),
new H3.Cell.Edge(defPoints[0], defPoints[4], order),
new H3.Cell.Edge(defPoints[1], defPoints[5], order),
new H3.Cell.Edge(defPoints[2], defPoints[4], order),
new H3.Cell.Edge(defPoints[3], defPoints[5], order),
};
}
else
{
Vector3D vPointUHS = H3Models.BallToUHS(VertexPointBall(p, q, r));
defPoints[0] = defPoints[1] = vPointUHS;
edges = new H3.Cell.Edge[]
{
new H3.Cell.Edge(vPointUHS, new Vector3D(0, 0, 10)),
new H3.Cell.Edge(defPoints[4], defPoints[5], order),
new H3.Cell.Edge(defPoints[0], defPoints[4], order),
new H3.Cell.Edge(defPoints[1], defPoints[5], order),
new H3.Cell.Edge(defPoints[2], defPoints[4], order),
new H3.Cell.Edge(defPoints[3], defPoints[5], order),
};
}
return(edges);
}
public void InitializeGoursat(int[] dihedrals)
{
Verts = SimplexCalcs.GoursatTetrahedron(dihedrals[0], dihedrals[1], dihedrals[2], dihedrals[3], dihedrals[4], dihedrals[5]);
Facets = SimplexCalcs.Mirrors(Verts);
}