/// <summary>
/// Cozzi and Ring method using Newton Raphson from 3D Engine Design for Virtual Globes book
/// </summary
DVec3 ScaleToGeodeticSurface(DVec3 P)
{
double beta = 1.0 / Math.Sqrt(
(P.x * P.x) * ra2 +
(P.y * P.y) * rb2 +
(P.z * P.z) * rc2
);
double n = DVec3.length(new DVec3(beta * P.x * ra2, beta * P.y * rb2, beta * P.z * rc2));
double alpha = (1.0 - beta) * (DVec3.length(P) / n);
double x2 = P.x * P.x;
double y2 = P.y * P.y;
double z2 = P.z * P.z;
double da = 0.0;
double db = 0.0;
double dc = 0.0;
double s = 0.0;
double dSdA = 1.0;
do
{
alpha -= (s / dSdA);
da = 1.0 + (alpha * ra2);
db = 1.0 + (alpha * rb2);
dc = 1.0 + (alpha * rc2);
double da2 = da * da;
double db2 = db * db;
double dc2 = dc * dc;
double da3 = da * da2;
double db3 = db * db2;
double dc3 = dc * dc2;
s = x2 / (a2 * da2) + y2 / (b2 * db2) + z2 / (c2 * dc2) - 1.0;
dSdA = -2.0 * (x2 / (a4 * da3) + y2 / (b4 * db3) + z2 / (c4 * dc3));
} while (Math.Abs(s) > 1e-10);
return(new DVec3(P.x / da, P.y / db, P.z / dc));
}
/// <summary>
/// Normalise the vector and return the unit vector pointing in the same direction
/// </summary>
/// <param name="v"></param>
/// <returns></returns>
public static DVec3 normalize(DVec3 v)
{
double mag = DVec3.length(v);
return(new DVec3(v.x / mag, v.y / mag, v.z / mag));
}
