任意拓朴网上构造高阶连续曲面的方法及应用

METHOD AND APPLICATION FOR GENERATING CONTINUOUS SURFACES OF HIGHER ORDER OVER ARBITRARY TOPOLOGICAL MESHES

本文提出了一种任意拓朴网上构造高阶连续曲面的QB(Quartic B-spline)方法。理论分析表明,曲面除个别“超常点”外,均可达到C^3连续,在超常点处曲面至少达到一阶几何连续。在引入了内边界的概念及边界控制的新方法后,实现了任意拓朴网上构造多连通域曲面的设想。实际应用表明,该方法具有简单,构造曲面灵活,计算效率高等优点。

In this paper,a new method QB(Quartic B-spline)for generating continuous surfaces of higher order over arbitrary topological meshes is presented.The results prove that except some extraordinary points,surface as a whole gain C^3 continuity,and gain at least C^1 continu- ity at those points.By introducing concept of internal boundary,an approach for controlling boundary curves is discussed as well.