摘要
为了弥补以四点插值细分方法为代表的线性细分方法在形状控制方面的缺陷,提出一种基于几何的插值型保凸细分方法.细分过程每一步中,每条边所对应的新控制顶点由原控制顶点及其切向共同确定;每点处的切向由其邻近的点所确定,并且随细分过程逐步调整.理论分析表明,该方法的极限曲线是G1连续的保凸曲线.如果所有的初始点取自圆弧段,则极限曲线就是该圆弧段.数值实例表明,采用文中方法得到的曲线较为光顺.
A geometric driven subdivision scheme for curve interpolation is proposed. For the initial control polygon, the newly generating points are determined by the old control points as well as their tangent vectors, and the tangent vector at a point is determined by its adjacent points. In each subdivision step, the tangent vectors are adjusted adaptively and the limit curve is G1 continuous and convexity preserving. It can reproduce circular arc segment if all the initial points are sampled from a circular arc. Numerical examples show that curves generated by this subdivision scheme are fair curves.
出处
《计算机辅助设计与图形学学报》
EI
CSCD
北大核心
2009年第8期1042-1046,共5页
Journal of Computer-Aided Design & Computer Graphics
基金
国家自然科学基金(60773179)
国家"九七三"重点基础研究发展计划项目(2004CB318000)
杭州电子科技大学校科研启动项目(KYS075608073)
关键词
细分方法
曲线插值
保凸
subdivision scheme
curve interpolation
convexity preserving
