AHT Bézier Curves and NUAHT B-Spline Curves

In this paper, we present two new unified mathematics models of conics and polynomial curves, called algebraic hyperbolic trigonometric (AHT) Bézier 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 5. The two kinds of curves share most of the properties as those of the Bézier 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. Electronic Supplementary Material The online version of this article (doi:) contatins supplementary material, which is available to authorized users. This work is supported by the National Natural Science Foundation of China under Grant Nos. 60473130, 10371110 and the National Grand Fundamental Research 973 Program of China under Grant No. 2004CB318000.