A novel generalization of Bezier curve and surface

作者：Han Xi An^*; Ma YiChen; Huang XiLi

来源：Journal of Computational and Applied Mathematics, 2008, 217(1): 180-193.

DOI：10.1016/j.cam.2007.06.027

• Computer aided geometric design
• Generalized Bernstein basis functions
• Bezier curve/surface patches
• Q-Bezier curve/surface patches
• Shape parameters

A new formulation for the representation and designing of curves and surfaces is presented. It is a novel generalization of Bezier curves and surfaces. Firstly, a class of polynomial basis functions with n adjustable shape parameters is present. It is a natural extension to classical Bernstein basis functions. The corresponding Bezier curves and surfaces, the so-called Quasi-Bezier (i.e., Q-Bezier, for short) curves and surfaces, are also constructed and their properties studied. It has been shown that the main advantage compared to the ordinary Bezier curves and surfaces is that after inputting a set of control points and values of newly introduced n shape parameters, the desired curve or surface can be flexibly chosen from a set of curves or surfaces which differ either locally or globally by suitably modifying the values of the shape parameters, when the control polygon is maintained. The Q-Bezier curve and surface inherit the most properties of Bezier curve and surface and can be more approximated to the control polygon. It is visible that the properties of end-points on Q-Bezier curve and surface can be locally controlled by these shape parameters. Some examples are given by figures.

• 出版日期2008-7-15
• 单位西安交通大学; 中国人民解放军装备学院