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AHT Bézier Curves and NUAHT B-Spline Curves

Gang Xu and Guo-Zhao Wang   

  1. 1Institute of Computer Graphics and Image Processing, Zhejiang University, Hangzhou 310027, China {2}Department of Mathematics, Zhejiang University, Hangzhou 310027, China
  • Received:2006-02-21 Revised:2006-12-20 Online:2007-07-10 Published:2007-07-10

In this paper, we present two new unified mathematics models of conics and polynomial curves, called {\it algebraic hyperbolic trigonometric} ({\it AHT}) {\it B\'{e}zier curves} and {\it non-uniform algebraic hyperbolic trigonometric $($NUAHT$)$ B-spline curves of order n}, which are generated over the space ${\rm span}\{\sin t,\cos t,\sinh t,\cosh t,1,t,\ldots,t^{n-5}\}$, $n\ge 5$. The two kinds of curves share most of the properties as those of the B\'{e}zier 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.

Key words: distributed system; checkpointing and rollback recovery; storage management; thorough garbage collection;



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