基于μ基有理可展曲面的参数化

摘要

Finding parametrization of a given curve or surface is an essential problem in CAGD and CG.It is still open to design an algorithm for a general given curve or surface.In this paper,we focus on rational developable surfaces which are widely used in manufacturing.%针对工程设计中常用的可展曲面,给出其有理参数化算法.给定一个隐式曲面,首先根据几何性质判定它是否是可展曲面,并给出判定算法；然后应用近年来新兴发展的隐式化代数工具——μ基方法,得到可展曲面的μ基的次数界.在此基础上,设计计算隐式曲面μ基的算法,并通过计算其对偶曲面的重新参数化,得到原隐式曲面的参数表示.结合已有的参数曲面隐式化算法,给出了有理可展曲面的代数交换算法图.