Surface Triangulations Based on 3D Arbitrary Point-sets
三维散乱点集的曲面三角剖分

Surface triangulations based-on 3D arbitrary point-sets are widely applied in CAGD/CAD and reverse-engineering, etc. In the first place, this paper reviews two main methods in surface triangulations, named as plane-projection and direct triangulation. For the former, Delaunay triangulations are mainly enunciated. For the later, algorithm developed by B. K. Choi is particularized. Some typical algorithms are introduced in detail, as well as various data-structures built in these algorithms. Next, since the final result of triangulation is determined by the optimal criterion, some proverbial optimal criteria are specified and analyzed in this paper, and they are thoroughly compared with each other here through anatomizing an example. It is pointed that,in practical engineering, it is necessary to develop new algorithms with new criteria for triangulations of scattered points sampled from complicated surfaces so as to maintain the properties such as better smoothness and shape preserving. Finally the time and space complexities of various algorithms are briefly and concisely discussed, also the research trend of surface triangulations based-on 3D arbitrary point-sets.