具有给定测地线的三次三角Bézier曲面的构造与拼接  

Construction and composite of cubic triangular Bézier surface from a given spatial cubic Bézier geodesic curve

作　　者：郭清伟.[1] 张官升 

机构地区：[1]合肥工业大学数学学院,安徽合肥230009

出　　处：《合肥工业大学学报（自然科学版）》2014年第1期125-128,共4页Journal of Hefei University of Technology：Natural Science

基　　金：安徽省高等学校省级自然科学研究资助项目(2011AJZR0071)

摘　　要：文章利用判定曲面上的曲线为其测地线的充要条件,研究如何在三角域上构造以给定空间三次Bézier曲线作为其边界测地线的三次三角Bézier曲面;通过给定三次Bézier曲线的控制顶点来表示所构造的三次三角Bézier曲面的控制顶点,从而确定了所构造的曲面;讨论了具有公共边界测地线的2个三次三角Bézier曲面的连续性。为了说明所给方法的有效性,给出了几个数值实例。Using the necessary and sufficient condition to determine a curve to be the geodesic curve of a surface, this paper deals with how to construct a cubic triangular B6zier surface with a given 3D cu- bic Bezier curve as geodesic boundary in a triangular region. The explicit expression of the control points for the constructed cubic triangular Bezier surface is obtained by using the control points of the given 3D cubic Bezier curve so as to determine the required surface. In addition, the continuity of two cubic triangular Bezier patches which possess common pregeodesic is discussed. Several numerical ex- amples are given to illustrate the effectiveness of the given method.

关 键 词：BEZIER曲面 三角BEZIER曲面 测地线 控制顶点 连续性 

分 类 号：O182.2[理学—数学]