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aht b zier curves and nuaht b-spline curves
Author(s): Gang Xu Guo-Zhao Wang 1 Institute of Computer Graphics and Image Processing, Zhejiang University, Hangzhou 310027, China 2 Department of Mathematics, Zhejiang University, Hangzhou 310027, China
Pages: 597-
607
Year: 2007
Issue:
4
Journal: Journal of Computer Science and Technology
Keyword: GetLinkList(KeywordFilter('CAD/CAM; AHT Bézier curve; NUAHT B-spline curves; transcendental curves'); 'kw'; 'CJFQ');
Abstract: <正>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.
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