private static Vector3D[] CalcViaProjections(Vector3D p1, Vector3D p2, Vector3D p3, int divisions, Geometry g)
{
Vector3D h1 = Sterographic.PlaneToHyperboloid(p1);
Vector3D h2 = Sterographic.PlaneToHyperboloid(p2);
Vector3D h3 = Sterographic.PlaneToHyperboloid(p3);
List <Vector3D> temp = new List <Vector3D>();
Segment seg1 = Segment.Line(h1, h2);
Segment seg2 = Segment.Line(h3, h2);
Vector3D[] s1 = seg1.Subdivide(divisions);
Vector3D[] s2 = seg2.Subdivide(divisions);
for (int i = 0; i < divisions; i++)
{
Segment seg = Segment.Line(s1[i], s2[i]);
temp.AddRange(seg.Subdivide(divisions - i));
}
temp.Add(h2);
List <Vector3D> result = new List <Vector3D>();
foreach (Vector3D v in temp)
{
Vector3D copy = v;
Sterographic.NormalizeToHyperboloid(ref copy);
result.Add(Sterographic.HyperboloidToPlane(copy));
}
return(result.ToArray());
}
public static Vector3D[] CalcViaProjections(Vector3D p1, Vector3D p2, Vector3D p3, int divisions, Geometry g)
{
if (g == Geometry.Euclidean)
{
throw new System.NotImplementedException();
}
Vector3D h1 = new Vector3D(), h2 = new Vector3D(), h3 = new Vector3D();
if (g == Geometry.Hyperbolic)
{
h1 = Sterographic.PlaneToHyperboloid(p1);
h2 = Sterographic.PlaneToHyperboloid(p2);
h3 = Sterographic.PlaneToHyperboloid(p3);
}
else if (g == Geometry.Spherical)
{
h1 = Sterographic.PlaneToSphereSafe(p1);
h2 = Sterographic.PlaneToSphereSafe(p2);
h3 = Sterographic.PlaneToSphereSafe(p3);
}
List <Vector3D> temp = new List <Vector3D>();
Segment seg1 = Segment.Line(h1, h2);
Segment seg2 = Segment.Line(h3, h2);
Vector3D[] s1 = seg1.Subdivide(divisions);
Vector3D[] s2 = seg2.Subdivide(divisions);
for (int i = 0; i < divisions; i++)
{
Segment seg = Segment.Line(s1[i], s2[i]);
temp.AddRange(seg.Subdivide(divisions - i));
}
temp.Add(h2);
List <Vector3D> result = new List <Vector3D>();
foreach (Vector3D v in temp)
{
Vector3D copy = v;
if (g == Geometry.Hyperbolic)
{
Sterographic.NormalizeToHyperboloid(ref copy);
result.Add(Sterographic.HyperboloidToPlane(copy));
}
else if (g == Geometry.Spherical)
{
copy.Normalize();
result.Add(Sterographic.SphereToPlane(copy));
}
}
return(result.ToArray());
}
public static Vector3D Centroid(Geometry g, Vector3D[] conformalVerts)
{
if (g == Geometry.Euclidean)
{
Vector3D result = new Vector3D();
foreach (Vector3D v in conformalVerts)
{
result += v;
}
return(result / conformalVerts.Length);
}
Vector3D[] verts = conformalVerts.Select(v =>
{
switch (g)
{
case Geometry.Spherical:
return(Sterographic.PlaneToSphereSafe(v));
case Geometry.Hyperbolic:
return(Sterographic.PlaneToHyperboloid(v));
}
throw new System.ArgumentException();
}).ToArray();
// https://math.stackexchange.com/a/2173370/300001
Vector3D sum = new Vector3D();
for (int i = 0; i < verts.Length; i++)
{
sum += verts[i];
}
Vector3D centroid = sum / Math.Sqrt(DotInGeometry(g, sum, sum));
NormalizeInGeometry(g, ref centroid);
switch (g)
{
case Geometry.Spherical:
return(Sterographic.SphereToPlane(centroid));
case Geometry.Hyperbolic:
return(Sterographic.HyperboloidToPlane(centroid));
}
throw new System.ArgumentException();
}