一类带形状参数的DP-NTP曲线及其应用

A New Type of DP-NTP Curve with Shape Parameters and its Application

摘要: 为使得求值简单且具保形性的DP-NTP曲线增加一个形状调节的功能,将文献(Delgado J,Pe a J M.Ashape preserving representation with an evaluation algorithm of linear complexity.Computer Aided GeometricDesign,2003,20(1):1-10)中给出的一类全新的标准全正(NTP)基进行推广,提出了带多个形状参数的DP-NTP基,并在此基础上定义了带形状参数的DP-NTP曲线.在分析DP-NTP曲线基本几何性质的同时,给出了这类带形状参数的DP-NTP基到Bernstein基的转换公式,并对各个形状参数的几何意义进行讨论,给出了形状调节的一些实例.实例结果表明,形状参数可以较好地起到外形调节的作用.

Abstract: In order to improve the effects of shape control,we extended the normalized totally positive(NTP) basis,in literature(Delgado J,Pea J M.A shape preserving representation with an evaluation algorithm of linear complexity.Computer Aided Geometric Design,2003,20(1): 1-10) and obtained a new type of DP-NTP basis with multiple shape parameters.Then the DP-NTP curves with shape parameters are defined,some basic geometric properties and the conversion formulae from the new basis to the Bernstein basis are derived.At last,the geometric meaning of each shape parameter is discussed,some examples are given to show the effects of shape control.Moreover,some examples are illustrated to show the effective shape control by shape parameters.