private static Vector3D Transform2(Vector3D p, Matrix4D mat)
{
p.Normalize();
p = mat.RotateVector(p);
p = Sterographic.S3toR3(p);
p = SphericalModels.StereoToEquidistant(p);
return(p);
}
public static Vector3D ToConformal(Geometry g, Vector3D[] kv, Vector3D b)
{
Vector3D klein = Util.BaryToEuclidean(kv, b);
switch (g)
{
case Geometry.Spherical:
return(SphericalModels.GnomonicToStereo(klein));
case Geometry.Euclidean:
return(klein);
case Geometry.Hyperbolic:
return(HyperbolicModels.KleinToPoincare(klein));
}
throw new System.ArgumentException();
}
// So that we can leverage Euclidean barycentric coordinates, we will first convert our simplex to the Klein model.
// We will need to take care to properly convert back to the Ball as needed.
public static Vector3D[] KleinVerts(Geometry g, Vector3D[] conformalVerts)
{
return(conformalVerts.Select(v =>
{
switch (g)
{
case Geometry.Spherical:
return SphericalModels.StereoToGnomonic(v);
case Geometry.Euclidean:
return v;
case Geometry.Hyperbolic:
return HyperbolicModels.PoincareToKlein(v);
}
throw new System.ArgumentException();
}).ToArray());
}
public static Circle3D GetCircleForBallPoint(Vector3D p)
{
Sphere ball = new Sphere();
p = SphericalModels.GnomonicToStereo(p);
if (Tolerance.GreaterThanOrEqual(p.Abs(), 1))
{
return(null);
}
Sphere t = H3Models.Ball.OrthogonalSphereInterior(p);
//return H3Models.Ball.IdealCircle( t );
// Get the corresponding point on the exterior (our inversion).
p = HyperbolicModels.PoincareToKlein(p);
p = HyperbolicModels.PoincareToKlein(p);
p = ball.ReflectPoint(p);
return(GetCircle(p));
}
/// <summary>
/// Helper to transform to standard model if needed.
/// </summary>
private Vector3D ToStandardIfNeeded(Vector3D point)
{
if (m_geometry == Geometry.Hyperbolic &&
m_settings.HyperbolicModel == HModel.Klein)
{
return(HyperbolicModels.KleinToPoincare(point));
}
if (m_geometry == Geometry.Spherical)
{
if (m_settings.SphericalModel == SphericalModel.Gnomonic)
{
return(SphericalModels.GnomonicToStereo(point));
}
if (m_settings.SphericalModel == SphericalModel.Fisheye)
{
return(SphericalModels.StereoToGnomonic(point));
}
}
return(point);
}