基于离散网格的流形曲面构造综述

基于离散网格的流形曲面构造技术不仅能够生成具有高阶光滑性的曲面,并且该曲面可以是任意拓扑结构的.此外,在构造流形曲面时,无需进行额外的拼接操作,克服了传统曲面造型技术在进行面片之间的拼接时,计算量增大以及曲面光滑性难以保证的难题.本文介绍了流形曲面构造的流程以及构造过程中的难点,然后将目前已有的流形曲面构造技术分为三大类:传统意义上的流形构造方法;基于规范区域的流形构造方法;基于样条曲面推广的流形构造方法.并对每一类都进行详细地分类介绍.最后,对其作一个总结以及对未来的展望.

Survey on Manifold Construction Based on Polygonal Mesh

Manifold construction method based on polygonal mesh can generate surfaces with high orders of smoothness and the surface can be of arbitrary topology.Besides, there is no need of extra patching or trimming operations which increases computational cost and results in low orders of smoothness for traditional surface construction methods.Manifold construction theory and difficulties when constructing surfaces with the method are presented in this paper.We have surveyed geometric computing researches in manifold construction.The researches are classified into three categories according to the characteristics of the methods: traditional manifold construction, canonical surfaces based construction, and manifold spline.Each category is introduced in detail.Finally, we come to a conclusion and present a few future directions of manifold construction.