AHT Bézier Curves and NUAHT B-Spline Curves

作     者：徐岗 汪国昭 

作者机构：Institute of Computer Graphics and Image ProcessingZhejiang University Department of MathematicsZhejiang University 

出 版 物：《Journal of Computer Science & Technology》 (计算机科学技术学报（英文版）)

年 卷 期：2007年第22卷第4期

页      面：597-607页

核心收录：

学科分类：081203[工学-计算机应用技术] 08[工学] 0835[工学-软件工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：This work is supported by the National Natural Science Foundation of China under Grant Nos.60473130,10371110 the National Grand Fundamental Research 973 Program of China under Grant No.2004CB318000 

主　　题：CAD/CAM AHT Bezier curve NUAHT B-spline curves transcendental curves 

摘      要：In this paper, we present two new unified mathematics models of conics and polynomial curves, called algebraic hyperbolic trigonometric （ AHT） Bezier curves and non-uniform algebraic hyperbolic trigonometric （ NUAHT） B-spline curves of order n, which are generated over the space span{sin t, cos t, sinh t, cosh t, 1, t,..., t^n-5}, n 7〉 5. The two kinds of curves share most of the properties as those of the Bezier curves and B-spline curves in polynomial space. In particular, they can represent exactly some remarkable transcendental curves such as the helix, the cycloid and the catenary. The subdivision formulae of these new kinds of curves are also given. The generations of the tensor product surfaces are straightforward. Using the new mathematics models, we present the control mesh representations of two classes of minimal surfaces.