A fundamental problem when representing or analyzing object is the following: given a set of points, generally produced by scanning some object (i.e. in applications such as motion capture,
facial recognition, medical imaging, etc.), reconstruct a triangulation
on these points which accurately represents the original object. We
will survey classical results and algorithms from this area, focusing
especially on the crust and powercrust algorithms, which were some of
the first to give provable guarantees on the quality of the
reconstruction, both from a topological and a geometric standpoint.