Journal of Computer Science and Technology

, Volume 22, Issue 4, pp 597–607 | Cite as

AHT Bézier Curves and NUAHT B-Spline Curves

  • Gang XuEmail author
  • Guo-Zhao Wang
Regular Paper


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.


CAD/CAM AHT Bézier curve NUAHT B-spline curves transcendental curves 


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Supplementary material

11390_2007_9073_MOESM1_ESM.pdf (112 kb)
Supplementary material - Chinese Abstract (PDF 111 Kb).


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Copyright information

© Science Press, Beijing, China and Springer Science + Business Media, LLC, USA 2007

Authors and Affiliations

  1. 1.Institute of Computer Graphics and Image ProcessingZhejiang UniversityHangzhouChina
  2. 2.Department of MathematicsZhejiang UniversityHangzhouChina

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