Delaunay-based triangular surface reconstruction from points via Umbrella Facet Matching

Abstract

This paper presents an effective algorithm to reconstruct a closed 3D triangular surface mesh from a set of unorganized points based on Delaunay triangles. The algorithm essentially seeks to construct an optimal local 2D manifold surface (umbrella) at each individual point in parallel. The underlying principle is that for any point, there always exists a cluster of triangular facets, selected from the Delaunay triangles at the point, to constitute the shape of an opened umbrella. If a triangular facet belongs to all three umbrellas of its three vertices, the triangular facet is considered as a matched facet. When all triangular facets of an umbrella are matched facets, the umbrella is regarded as a matched umbrella which fully overlaps with its neighboring umbrellas. A topologically correct triangular surface mesh is then constructed when the matched umbrella for every individual point is found. The proposed Umbrella Facet Matching (UFM) algorithm has been implemented and validated using many publicly available point cloud data sets. The algorithm is seen to be of good convergence and without the need for further hole-filling post-processing. And the reconstructed surface meshes only contain minor shape approximation errors, when compared to the original surfaces of the sampled points.