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.