带形状参数的四次Bézier曲线曲面  

Quartic Bézier curves and surfaces with shape parameters

作　　者：陈晓彦[1] 刘植[1] 张莉[1] 

机构地区：[1]合肥工业大学数学学院,合肥230009

出　　处：《计算机工程与应用》2012年第9期172-175,共4页Computer Engineering and Applications

基　　金：高等学校博士学科点专项科研基金资助课题(No.20110111120026;20100111120023);安徽省自然科学基金(No.11040606Q42);合肥工业大学科学研究发展基金项目(No.2010HGXJ0084);合肥工业大学博士学位专项科研资助基金(No.2010HGBZ0563);中央高校基本科研业务费专项经费(No.2011HGXJ1076;2012HGXJ0039)

摘　　要：提出一种新的含参数的四次多项式基函数,四次Bernstein基函数是它的特例,给出其与四次Bernstein基的转换矩阵。分析了该组基函数的性质,定义了带有形状参数的四次Bézier曲线曲面,它们具有四次Bézier曲线曲面的特性,且当参数均取1时即为四次Bézier曲线曲面。对于给定的控制顶点,可以通过改变形状参数的值整体或局部调控曲线曲面的形状。实例表明,该方法应用于曲线曲面设计是有效的。A new polynomial base function of 4th degree with shape parameters is presented which includes the common quartic Bern- stein basis function. Properties of this new base function are analyzed and the corresponding polynomial curve and surface with shape pa- rameters are defined. They inherit the most properties of quartic Bezier curves and surfaces and degenerate to them when shape parame- ters are 1. Moreover the shape of the curve and surface can be adjusted entirely or locally through changing the values of the shape param- eters when the control points are maintained. Examples illustrate that this method of constructing curves and surfaces is useful in CAGD.

关 键 词：基函数 形状参数 线性无关 几何造型 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]