We propose a new approach for reconstructing a 2-manifold from a point
sample in R3. Compared to previous algorithms our approach is novel in
that it throws away geometry information early on in the reconstruction
process and mainly operates combinatorially on a graph structure.
Furthermore it is very conservative in creating adjacencies between
samples in the vicinity of slivers, still we can prove that the resulting
reconstruction faithfully resembles the original 2-manifold. While the
theoretical proof requires an extremely high sampling density our
prototype implementation of the approach produces surprisingly good
results on typical sample sets and seems to have great potential.