A Class of Generalized Bézier Curves and Surfaces with Multiple Shape Parameters

In order to control the shape of curves and surfaces more flexibly in geometric modeling,a new design technique with multiple shape parameters is presented in this paper.Firstly,a class of blending functions with multiple shape parameters is proposed.The common Bernstein basis function is a special case of proposed functions.Secondly,based on this blending function,we define a class of adjustable generalized Bézier curves and surfaces,and investigate their properties.We show that the shape of the generalized Bézier curves can be adjusted entirely or locally by changing the values of the shape parameters when the control polygon is maintained.Numerical examples are also given to illustrate the practicality of this method.