SPS参数化有理Bézier曲线的几何性质  

Geometric Properties of Rational Bézier Curves with SPS Parameter

作　　者：朱如媛 徐晨东[1] 

机构地区：[1]宁波大学理学院,浙江宁波315211

出　　处：《宁波大学学报（理工版）》2016年第1期59-63,共5页Journal of Ningbo University：Natural Science and Engineering Edition

基　　金：国家自然科学基金(11101230;11371209);浙江省自然科学基金(LY13A010013);宁波大学学科项目(XKL11D2051)

摘　　要：SPS(Scalar Projection Scale)参数化有理Bézier曲线在几何造型中有重要应用.为研究其几何性质,首先分析了当SPS参数化有理Bézier曲线退化为Bézier曲线时,其所具有的几何性质;其次证明了SPS参数化有理Bézier曲线升阶后仍为SPS参数化;最后在求导的基础上利用笛卡尔符号法则分析SPS参数化二次有理Bézier曲线曲率的单调性,并得到了其曲率分布的规律.Rational Bézier curves with SPS（scalar projection scale） parameterization are useful in geometric molding. In order to study their geometric properties, the following three steps are carried out. In the first step, we note that, when a rational Bézier curve degenerates into Bézier curve, it will present an intuitive geometric character. In the second step, we demonstrate that a rational Bézier curve with SPS parameterization is still SPS parameterized after degree elevation. Finally, by Descartes＇ rule of signs, the monotonicity of curvature is discussed for a rational quadratic Bézier curve parameterized by SPS in a bid to obtain the curvature distribution.

关 键 词：有理BÉZIER曲线 SPS参数化 升阶 曲率 

分 类 号：O183.1[理学—数学]