geometry - How to transform a plane into a sphere? [SOLVED]

Given a 2-dimensional array of MxN heights, how to transform it to a sphere? Every element of this array is just a 3D point (x,y,z) where z represents some height. One has to transform this array into a sphere, twisting it around the origin so, that only minimal distortions will happen.

Representing it by spherical coordinates is not very good, because of the severe distortions. It's probably better if there is no direct one-to-one mapping from 2D plane to a surface of 3D sphere - many plane's points will not be involved. But what is the best possible mapping and how to transform involved points (elements of array)?

This is for a 3D-planet terrain simulation. First, fractal landscape is produced, then, it is to be transformed to 3D sphere.

Thanks in advance!

SOLUTION: Map projection