Polygonizing non-uniformly distributed 3D points by advancing mesh frontiers

3D digitization devices produce very large sets of 3D points sampled from the surfaces of the objects being scanned. A mesh construction procedure needs to be applied to derive polygon mesh from the 3D point sets. As the 3D points derived from digitization devices based on digital imaging technologies are inherently non-uniformly distributed over regions that may contain surface discontinuities, existing methods are not suitable for polygonizing them. This paper describes a novel polygonization algorithm for constructing triangle mesh from unorganized 3D points. In contrast to existing methods, this algorithm begins the mesh construction process from 3D points lying on smooth surfaces, and advances the mesh frontier towards 3D points lying near surface discontinuities. If 3D points along the edges and at the corners are sampled, then the algorithm will form an edge where two advancing frontiers meet, and a corner where three or more frontiers meet. Otherwise, the algorithm constructs approximations of the edges and corners. It can be shown that this frontier advancing algorithm performs 2D Delaunay triangulation of 3D points lying on a plane in 3D space.