Surface Reconstruction Based on Lower Dimensional Localized Delaunay Triangulation

We present a fast, memory efficient algorithm that generates a manifold triangular mesh S passing through a set of unorganized points P R3. Nothing is assumed about the geometry, topology or presence of boundaries in the data set except that P is sampled from a real manifold surface. The speed of our algorithm is derived from a projection-based approach we use to determine the incident faces on a point. We define our sampling criteria to sample the surface and guarantee a topologically correct mesh after surface reconstruction for such a sampled surface. We also present a new algorithm to find the normal at a vertex, when the surface is sampled according our given criteria. We also present results of our surface reconstruction using our algorithm on unorganized point clouds of various models.