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.
出处
《计算机工程与应用》
CSCD
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)
关键词
基函数
形状参数
线性无关
几何造型
base function
shape parameter
linearly independent
geometric modeling
