Here's a nice article with pictures on sphere point picking[0]. Here is another [1]. The surface of a sphere in 3-dimensional space has only two dimensions. You can specify any point on the sphere with two coordinates (spherical coordinates). The mathematical expression for this sphere is S-2. If you're using three coordinates to generate the point, you're using more than you need. It's straight algebra to convert from spherical to linear coordinates if you need those for your work.

[0] http://mathworld.wolfram.com/SpherePointPicking.html [1] http://stats.stackexchange.com/questions/7977/how-to-generat...