how map 2d grid points (x,y) onto sphere as 3d points (x,y,z)
I have a set of 2d grid points (x,y) that I want to map/project onto a sphere as 3d points (x,y,z). I realize there will be some warping towards the poles as abs(y) increases but my grid patch will only cover a portion of the sphere near the equator so severe warping will be avoided. I'm having trouble finding the right equations for that. Paraphrased from the wikipedia article on Mercator projection: Given a "mapping sphere" of radius R, the Mercator projection (x,y) of a given latitude and longitude is: x = R * longitude y = R * log( tan( (latitude + pi/2)/2 ) ) and the inverse mapping of a