// Functions assumes ellipsoid scaled coordinates
public static Double ComputeMagnitude(Vector3 point, Vector3 sphereCenter)
{
var magnitudeSquared = Cartesian3D.MagnitudeSquared(point);
var magnitude = Math.Sqrt(magnitudeSquared);
var direction = Cartesian3D.MultiplyByScalar(point, 1 / magnitude);
magnitudeSquared = Math.Max(1.0, magnitudeSquared);
magnitude = Math.Max(1.0, magnitude);
var cosAlpha = DotProduct(direction, sphereCenter);
var sinAlpha = Cartesian3D.Magnitude(CrossProduct(direction, sphereCenter));
var cosBeta = 1.0 / magnitude;
var sinBeta = Math.Sqrt(magnitudeSquared - 1.0) * cosBeta;
return(1.0 / (cosAlpha * cosBeta - sinAlpha * sinBeta));
}
public static Vector3 CrossProduct(Vector3 A, Vector3 B)
{
return(new Vector3(A.Y * B.Z - B.Y * A.Z, A.Z * B.X - B.Z * A.X, A.X * B.Y - B.X * A.Y));
}
/*
* wgs84_a = radiusX # Semi-major axis
* wgs84_b = radiusZ # Semi-minor axis
* wgs84_e2 = 0.0066943799901975848 # First eccentricity squared
* wgs84_a2 = wgs84_a** 2 # To speed things up a bit
* wgs84_b2 = wgs84_b** 2
*/
public static Double DotProduct(Vector3 pt1, Vector3 pt2)
{
return(pt1.X * pt2.X + pt1.Y * pt2.Y + pt1.Z * pt2.Z);
}
