Surface Reconstruction based on Lower Dimensional Localized Delaunay Triangulation

TLDR

The data set consists of unorganized points sampled from a real manifold surface, with no assumptions about geometry, topology, or boundary presence. The authors propose a fast, memory‑efficient algorithm that constructs a manifold triangular mesh from unorganized point clouds, defines sampling criteria guaranteeing topologically correct reconstruction, and introduces a method for computing vertex normals. The algorithm’s speed derives from a projection‑based approach that identifies incident faces on each point, supplemented by the sampling criteria and vertex‑normal computation. Experiments on diverse unorganized point clouds show that the algorithm successfully reconstructs surfaces.

Abstract

We present a fast, memory efficient algorithm that generates a manifold triangular mesh S passing through a set of unorganized points P R 3 . 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.