交互外形设计中的有理插值方法

RATIONAL INTERPOLATION METHOD FOR INTERACTIVE SHAPE DESIGN

在CAGD中,构造光滑曲线通过给定的二维或三维点集是非常重要的问题。广泛釆用的方法是Hermite技术,但是依照这种方法,插值曲线的形状过多地依赖于切矢的模长,且形状的修改不能依几何的方式交互完成。本文提出了一种结合交互技术和插值技术于一体的曲线插值方法,插值基函数为有理函数,在此基础上讨论了形状参数在几何修形中的作用,

An important problem in CAGD is to pass a smooth curve through a set of two or three dimensional points. Hermite scheme is used widely [in CAGD. But the shape of the interpolant largely depends on the tangent vectors as well as the parametric knots, and the shape modifying can not be implemented interactively in term of geometry. A method that combines interactive techniques with interpolation methods is presented to allow user intervention. Rational interpolation curves are used as local interpolants, and an approach is discussed for exploiting shape parameters.