Points to Mesh Sphere

Hi All,

I am attempting to create a mesh from a set of points (elevation values).  However, these values are mapped to a sphere, which makes producing a mesh messy.  So far, when I try creating a Delaunay Mesh from one hemisphere, I get some seriously degraded mesh faces. (see photos)

Is there a tool that would help map points to a mesh surface with less degradation?  Do I need to break up the sphere into a smaller series of parts in order to improve the quality? Is there a tool other than the Delaunay Mesh that I could use?