Given several points that belong to a surface, how do I reconstruct and render the complete surface using OpenGL. Pointers to existing code would be of great help to me. Thanks.
You might want to try bezier surface or b-spline surface(NURBS). In order to create these surface, you need at least 4 points though. The red book(OpenGL Programming Guide) explains about it in chapter 11.
if you don’t have the book, just google-search for the programming guide. There should be a lot of websites which have the entire book on the site.
If this is getting input from a 3D scanner in form of a point cloud, search for Delaunay triangulation or tetrahedralization