带多形状参数的广义Bézier曲线曲面  

A Class of Generalized Bézier Curves and Surfaces with Multiple Shape Parameters

作　　者：刘植[1,2] 陈晓彦[1] 江平[1] 

机构地区：[1]合肥工业大学数学学院,合肥230009 [2]合肥工业大学计算机与信息学院,合肥230009

出　　处：《计算机辅助设计与图形学学报》2010年第5期838-844,共7页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(60773043);教育部博士点新教师基金(2008JYXJ0828);安徽省自然科学基金项目(090416232);安徽省高校优秀青年人才基金(2009SQRZ008)

摘　　要：为了在几何造型中更加灵活地调控曲线曲面的形状,提出一种带多形状参数的造型方法.首先构造一种带多形状参数的多项式调配函数,其中Bernstein基函数是它的特例;然后利用给出的调配函数定义一类形状可调的广义Bézier曲线曲面,并研究了它们的性质.对给定的控制多边形,可以通过改变形状参数的值整体或局部地调控曲线的形状.最后通过数值实例说明了文中方法的实用性.In order to control the shape of curves and surfaces more flexibly in geometric modeling,a new design technique with multiple shape parameters is presented in this paper.Firstly,a class of blending functions with multiple shape parameters is proposed.The common Bernstein basis function is a special case of proposed functions.Secondly,based on this blending function,we define a class of adjustable generalized Bézier curves and surfaces,and investigate their properties.We show that the shape of the generalized Bézier curves can be adjusted entirely or locally by changing the values of the shape parameters when the control polygon is maintained.Numerical examples are also given to illustrate the practicality of this method.

关 键 词：调配函数 形状参数 广义Bézier曲线曲面 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]