摘要
给出了2种分别带形状控制参数a、b、c和形状控制参数a、b、c、d的四次、五次基函数,是四次Bernstein基函数的扩展;分析了这2组基函数的性质,基于此2组基定义了2种四次扩展Bézier曲线。2种新曲线不仅具有与四次Bézier曲线类似的性质,而且具有灵活的形状可调性和更好的逼近性。造型实例表明,新扩展曲线为曲线/曲面的设计提供了2种有效的新方法。
The construction of Bezier curves with shape control parameters is one of the most popular areas in computer aided geometric design. Two classes of polynomial basis functions of 4th degree with shape control parameter a, b, c and 5th degree with shape control parameter a, b, c, d are presented. They are both extensions of quadric Bernstein basis functions. Properties of the proposed basis functions are analyzed and the corresponding polynomial curves are constructed accordingly. The constructed curves not only inherit the outstanding properties of the quadric Bezier curve, but also are adjustable in shape and fit close to the control polygon. Some examples illustrate the new curves are very valuable for the design of curves and surfaces.
出处
《武汉理工大学学报》
CAS
CSCD
北大核心
2009年第20期156-160,共5页
Journal of Wuhan University of Technology
基金
国家自然科学基金(90510017
50679073)
陕西省教育厅自然科学研究项目(08JK399)
