How much Geometry it takes to Reconstruct a 2-Manifold in R^3

Known algorithms for reconstructing a 2-manifold from a point
sample in R3 are naturally based on geometric decisions/predicates,
facing the always present problem of round-off errors that
easily compromise their exactness; an exact and robust
implementation of these algorithms is far from being trivial
and typically requires the employment of advanced datatypes
for exact arithmetic.
We present a new reconstruction algorithm, one of
whose main novelties is to throw away geometry information
early on in the reconstruction process and to mainly
operate combinatorially on a graph structure.