Algorithm for simplifying 3d surface?

Question

I have a set of 3d points that approximate a surface. Each point, however, are subject to some error. Furthermore, the set of points contain a lot more points than is actually n

Answer 1

Instead of dealing with it as a point cloud, I would recommend triangulating a mesh using Delaunay triangulation: http://en.wikipedia.org/wiki/Delaunay_triangulation

Then decimate the mesh. You can research decimation algorithms, but you can get pretty good quick and dirty results with an algorithm that just merges adjacent tris that have similar normals.