3D Sphere to 2D Stereographic Projection

Hey everyone,

Basically, I have some {x, y, z, f} data that represents a sphere (i.e. [x, y, z] = sphere(360) ) and data on the sphere f(x, y, z) = x. I would like to represent the data that is plotted on the sphere in the form of a 2D grid (i.e. a 1024x1024 matrix) with a stereographic projection. I looked at the mapping toolbox, but I don't see anything that is too conducive towards {x, y, z, f} coordinate inputs and 2D outputs. I would appreciate any sort of tips or places to look for reference.

Thank you for your help!