Curvilinear & Cartesian Conversions

[G4CKT]

I'm trying to create a program which will do these calculations. I am given Latitudes, Longitudes, and ellipsoidal heights for ellipsoids and another set of x, y, and z coordinates. I am so confused looking at how to convert these things. I know I need to iterate in order to go from cartesian to curvillinear I'm quite confused on the formulations though T_T.

Can anyone help me xD

PS: I need to take into account the height of the ellipsoid.

I made a bit of progress but I got stuck in the equation. I don't know how to find the eccentricity and the "N" value T_T

As well, I know I should be using these equations for the Curv -> Cart Transformation

X = (N+H) cos(phi) cos(lambda)
Y = (N+H) cos(phi) sin(lambda)
Z = [N(1-e^2)+H] sin(phi)

I just don't know how to get the "N" value or the eccentricity. I'm also still lost on the conversion back T_T

 

[G4CKT]

I figured out the curvilinear to cartesian conversion. Now I'm stuck on cartesian to curvilinear especially the convergence value T_T.