| public static SphereToPlane ( Vector3D spherePoint ) : Vector3D | ||
| spherePoint | Vector3D | |
| return | Vector3D | |
private Tile TemplateTile()
{
double inRadiusHyp = InRadius;
double inRadiusEuclidean = DonHatch.h2eNorm(inRadiusHyp);
double faceRadius = FaceRadius(inRadiusEuclidean);
// Calc the midpoint, and project to plane.
Vector3D midPoint = MidPoint(inRadiusEuclidean, faceRadius);
midPoint.Z *= -1;
midPoint = Sterographic.SphereToPlane(midPoint);
//double midPointSpherical = MidPoint( inRadiusEuclidean, faceRadius );
//double midPoint = Spherical2D.s2eNorm( midPointSpherical );
// Create and scale based on our midpoint.
Polygon poly = new Polygon();
poly.CreateRegular(Q, R);
double standardMidpointAbs = poly.Segments[0].Midpoint.Abs();
m_shrink = midPoint.Abs() / standardMidpointAbs;
poly.Scale(m_shrink);
Matrix4D m = Matrix4D.MatrixToRotateinCoordinatePlane(-Math.PI / Q, 0, 1);
poly.Rotate(m);
return(new Tile(poly, poly.Clone(), Geometry.Hyperbolic));
}
public static Vector3D SinusoidalToStereo(Vector3D v)
{
double lat = Math.PI / 2 * (1 - v.Y);
Vector3D spherical = new Vector3D(1, lat, Math.PI * v.X / Math.Cos(lat - Math.PI / 2));
Vector3D onBall = SphericalCoords.SphericalToCartesian(spherical);
return(Sterographic.SphereToPlane(onBall));
}
/// <summary>
/// 2-dimensional function.
/// http://archive.bridgesmathart.org/2013/bridges2013-217.pdf
/// </summary>
public static Vector3D MercatorToStereo(Vector3D v)
{
v *= Math.PI; // Input is [-1,1]
double lat = 2 * Math.Atan(Math.Exp(v.Y)) - Math.PI / 2;
double inclination = lat + Math.PI / 2;
Vector3D spherical = new Vector3D(1, inclination, v.X);
Vector3D onBall = SphericalCoords.SphericalToCartesian(spherical);
return(Sterographic.SphereToPlane(onBall));
}
public static Vector3D EquirectangularToStereo(Vector3D v)
{
// http://mathworld.wolfram.com/EquirectangularProjection.html
// y is the latitude
// x is the longitude
// Assume inputs go from -1 to 1.
Vector3D spherical = new Vector3D(1, Math.PI / 2 * (1 - v.Y), v.X * Math.PI);
Vector3D onBall = SphericalCoords.SphericalToCartesian(spherical);
return(Sterographic.SphereToPlane(onBall));
}
/// <summary>
/// 2-dimensional function.
/// ZZZ - Should make this general.
/// </summary>
public static Vector3D OrthographicToStereo(Vector3D v)
{
// We can only do the projection for half of the sphere.
double t = v.X * v.X + v.Y * v.Y;
if (t > 1)
{
t = 1;
}
v.Z = Math.Sqrt(1 - t);
return(Sterographic.SphereToPlane(v));
}
private static double EquidistantToStereo(double dist)
{
if (dist > 1)
{
throw new System.ArgumentException();
}
Vector3D v = new Vector3D(0, -1);
v.RotateXY(dist * Math.PI);
v = Sterographic.SphereToPlane(new Vector3D(v.X, 0, v.Y));
return(v.Abs());
}
/// <summary>
/// https://en.wikipedia.org/wiki/Lambert_azimuthal_equal-area_projection
/// </summary>
private static double EqualAreaToStereo(double dist)
{
if (dist > 1)
{
throw new System.ArgumentException();
}
// We have dist normalized between 0 and 1, so this formula is slightly
// different than on Wikipedia, where dist ranges up to 2.
Vector3D v = new Vector3D(1, 2 * Math.Acos(dist), 0);
v = Sterographic.SphereToPlane(SphericalCoords.SphericalToCartesian(v));
return(v.Abs());
}
