An incremental algorithm for reconstruction of surfaces of arbitrary codimension

A new algorithm is presented for surface reconstruction from unorganized points. Unlike many previous algorithms, this algorithm does not select a subcomplex of the Delaunay Triangulation of the points. Instead, it uses an incremental algorithm, adding one simplex of the surface at a time. As a result, the algorithm does not require the surface's embedding space to be R3; the dimension of the embedding space may vary arbitrarily without substantially affecting the complexity of the algorithm. One result of using this incremental algorithmic technique is that very little can be proven about the reconstruction; nonetheless, it is interesting from an experimental viewpoint, as it allows for a wider variety of surfaces to be reconstructed. In particular, the class of non-orientable surfaces, such as the Klein Bottle, may be reconstructed. Results are shown for surfaces of varying genus.