Quartic Bézier curves and surfaces with shape parameters

Computer Engineering and Applications ›› 2012, Vol. 48 ›› Issue (9): 172-175.

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Quartic Bézier curves and surfaces with shape parameters

CHEN Xiaoyan, LIU Zhi, ZHANG Li

School of Mathematics, Hefei University of Technology, Hefei 230009, China

Received:1900-01-01 Revised:1900-01-01 Online:2012-03-21 Published:2012-04-11

带形状参数的四次Bézier曲线曲面

陈晓彦，刘植，张莉

合肥工业大学数学学院，合肥 230009

Abstract

Abstract: A new polynomial base function of 4th degree with shape parameters is presented which includes the common quartic Bernstein basis function. Properties of this new base function are analyzed and the corresponding polynomial curve and surface with shape parameters are defined. They inherit the most properties of quartic Bézier curves and surfaces and degenerate to them when shape parameters are 1. Moreover the shape of the curve and surface can be adjusted entirely or locally through changing the values of the shape parameters when the control points are maintained. Examples illustrate that this method of constructing curves and surfaces is useful in CAGD.

Key words: base function, shape parameter, linearly independent, geometric modeling

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。

关键词: 基函数, 形状参数, 线性无关, 几何造型

CHEN Xiaoyan, LIU Zhi, ZHANG Li. Quartic Bézier curves and surfaces with shape parameters[J]. Computer Engineering and Applications, 2012, 48(9): 172-175.

陈晓彦，刘植，张莉. 带形状参数的四次Bézier曲线曲面[J]. 计算机工程与应用, 2012, 48(9): 172-175.

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Quartic Bézier curves and surfaces with shape parameters

带形状参数的四次Bézier曲线曲面

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