带双参数的五次Said-Ball型曲线曲面  

Quintic Said-Ball Type Curves and Surfaces with Two Parameters

作　　者：陈辉[1] 王成伟[1] 

机构地区：[1]北京服装学院基础教学部,北京100029

出　　处：《北京服装学院学报（自然科学版）》2014年第2期67-75,共9页Journal of Beijing Institute of Fashion Technology：Natural Science Edition

基　　金：2014年度北京服装学院科学研究项目资助(2014A-14);北京服装学院科学研究创新基金项目资助(2014AL-32)

摘　　要：文章构造了1组带有2个形状参数α、β的五次Said-Ball型基函数,它是四次Said-Ball基函数的扩展.基于Said-Ball型基函数定义了带双参数的Said-Ball型曲线和张量积曲面,这种曲线不仅具有四次Ball曲线的特性,还能够实现五次Said-Ball曲线到四次Bézier曲线的过渡.文中分析了基函数及曲线的性质和2个形状参数的几何意义;给出了2条Said-Ball型曲线的G0、G1、G2连续拼接条件;最后以实例表明构造的新曲线为曲线曲面造型提供了一种有效方法.Abstract： A class of quintic Said-Ball type blending functions with two shape parameters α,β is presented in this paper, which is an extension of quartic Said-Ball blending functions. Based on Said-Ball type blending functions , the quintic Said-Ball type curves and surfaces with two shape pa-rameters are defined. This class of curves not only inherits the outstanding properties of the quartic Ball curve, but also realizes the transition from quintic Said-Ball curve to quartic Bezier curve. Theproperties of the blending functions and curves, and the geometrical property of shape parameters are analyzed. The G^0-continuity, G^1-continuity and G^2-continuity conditions of two pieces of curves arealso given. Some examples illustrate that this method of constructing curves and surfaces is useful for curves and surfaces design.

关 键 词：SAID-BALL曲线 BÉZIER曲线 形状参数 曲线设计 连续性 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]