三维散乱点集的曲面三角剖分

Surface Triangulations Based on 3D Arbitrary Point-sets

根据三维散乱点集构造曲面剖分在 CAGD/CAD、反求工程等方面有着十分广泛的应用 .本文回顾了三维散乱点集曲面三角剖分的两种主要方法即平面投影法和直接剖分法 ,对几种常用的算法作了较为详细的描述 ,同时对剖分算法中经常出现的数据结构作了详细的介绍 .由于剖分采用的优化准则决定了剖分结果 ,因此本文讨论了几种常用的剖分优化准则 ,并举例对几种优化准则进行了较详细的分析比较 .最后简要地讨论了算法复杂度以及目前剖分的主要研究方向 ,并指出在实际工程应用中对复杂曲面采样得到的散乱点集 ,要得到光顺和保形的三角剖分 ,需要新的剖分准则和算法 .

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.