NURBS曲线的无自交近似等距曲线计算  

Computing Approximation Offsets of Non-Self-Intersecting NURBS Curves

作　　者：赵轩艺 贺仕琪 朱春钢[2] Zhao Xuanyi;He Shiqi;Zhu Chungang(School of Science,Dalian Maritime University,Dalian 116026;School of Mathematical Sciences,Dalian University of Technology,Dalian 116024)

机构地区：[1]大连海事大学理学院,大连116026 [2]大连理工大学数学科学学院,大连116024

出　　处：《计算机辅助设计与图形学学报》2022年第9期1362-1371,共10页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(11801053,12071057);中央高校基本科研业务费专项资金(3132021195)。

摘　　要：NURBS曲线是CAGD中的标准工具,其等距曲线的计算是CAGD中的重要内容,对异常情况包括自交(或自交环)、奇点等的处理是等距曲线计算的关键技术.基于2阶导数采样和NURBS曲线的单值性,提出一种NURBS曲线的无自交近似等距曲线计算算法.首先提出并证明了NURBS曲线无自交等距曲线的最大偏移距离;然后通过计算最大偏移距离,以NURBS曲线的单值性为约束条件计算NURBS曲线的无自交近似等距曲线.2次和3次NURBS曲线无自交近似等距曲线计算的数值实例的结果表明,所提算法可以快速、有效地生成无自交的NURBS曲线的近似等距曲线,保证剩余控制顶点数尽量少且不依赖于权因子的选择,保留了NURBS曲线的权因子对曲线形状的调整性.The NURBS curve is a standard tool in CAGD.The calculation of the offset curve is an important research component in CAGD.The processing of abnormal situations,including self-intersections(or self-intersection loops)and singularities,is a key technology of offset curve calculation.Based on the second-derivative sampling and injectivity of the NURBS curve,an algorithm for computing non-self-intersecting approximate offset curve of the NURBS curve is proposed.First,the maximum offset distance of the non-self-intersecting offset curve of the NURBS curve is proposed and proved.Second,using the injectivity of the NURBS curve as a constraint condition,the non-self-intersecting offset curve of the NURBS curve is computed.Examples of computing non-self-intersecting offset curves of NURBS curves with degrees of 2 and 3 are presented.It is verified through examples that the proposed algorithm can quickly and effectively generate the approximate offset curves of the non-self-intersecting NURBS curve.Furthermore,the proposed algorithm does not depend on the choice of weights,and retains the adjustment of the weights of the NURBS curve to the curve shape.

关 键 词：NURBS曲线 等距曲线 移除自交 单值性 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]