基于重新参数化的Bézier曲面求交算法  

Bézier parametric surface intersection algorithm based on reparameterization

作　　者：庞乾一 王振飞 陈小雕[1] PANG Qianyi;WANG Zhenfei;CHEN Xiaodiao(School of Computer,Hangzhou Dianzi Univrsity,Hangzhou Zhejiang 310018,China)

机构地区：[1]杭州电子科技大学计算机学院,浙江杭州310018

出　　处：《杭州电子科技大学学报（自然科学版）》2023年第3期24-29,共6页Journal of Hangzhou Dianzi University：Natural Sciences

基　　金：国家自然科学基金面上资助项目(61972120)。

摘　　要：现有的参数曲面求交算法在求得一系列交点之后,需要再次用B样条插值才能表示出交线,且求得的交线无法保证精确落在任一给定曲面上。针对这一问题,提出一种基于重新参数化的求交算法。首先,通过曲面升阶加密曲面的控制网格,并求2个曲面控制网格的交线;然后,将交线映射到参数域,通过分段B样条曲线拟合,将拟合结果作为牛顿迭代的初值;最后,运用牛顿迭代求得更精确的参数域交线。相比于传统跟踪算法,该算法可直接得到交线的有理多项式表示形式,且求得的交线严格落在其中一个曲面上,在计算的交点个数更少的同时获得更高的逼近精度,并通过仿真实验验证了算法的精确性和有效性。In prevailing parametric surface/surface intersection algorithms,after obtaining a set of intersection points,they need to represent the intersection curves by using B-spline interpolation,while the intersection curves cannot be guaranteed to fall on any given surface.In this paper,an intersection algorithm based on reparameterization is proposed to ensure that the intersection curves fall on one of the surfaces accurately.Firstly,the control mesh of the surface is encrypted by surface elevation,and the corresponding intersection lines of the two control meshes are obtained.Secondly,the intersection lines are mapped to the parameter domain,and the fitting results are taken as the initial value of Newton iteration through piecewise B-spline curve fitting.Finally,Newton iteration is applied to obtain more accurate intersection curves in the parameter domain.As a result,the algorithm can directly get the rational polynomial representations of the intersection curves without using interpolation,and the intersection curves are strictly on one of the two given surfaces.Simulation results show both accuracy and effectiveness of the proposed algorithm.

关 键 词：Bézier曲面求交 重新参数化 控制网格 B样条曲线拟合 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]