Surface height from surface normal function

[AndrewD]

If you are standing on the side of a mountain at a point (x,y) and you know where the peak is (Xp, Yp) and how high it is (Zp) and you have a function G(x,y) that defines the 3D normal vector to the mountain side at all points on the surface, how do you calculate your height?

OK it's a simple way to put it but it expresses the problem neatly. I know that from the surface function F(x,y,z)=0, ∇F(x,y,z) will get you the surface normal at any point on the surface but I haven't found a simple way to express the reverse process. Can anyone help me?

Thanks,

Andrew

 

[mathman]

If the mountain is conically shaped, the normal will be independent of height.