Abstract
Motivated by the wide usage of the Tchebyshev basis and Legendre basis in the algebra polynomial space, we construct an orthogonal basis with the properties of the H-Bézier basis in the hyperbolic hybrid polynomial space, which is similar to the Legendre basis and holds remarkable properties. Moreover, we derive the transformation matrices that map the H-Bézier basis and the orthogonal basis forms into each other. An example for approximating the degree reduction of the H-Bézier curves is sketched to illustrate the utility of the orthogonal basis.
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Supported by the National Natural Science Foundation of China (Grant No. 60473130) and the National “973” Key Basic Research Project (Grant No. 2004CB318006)
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Huang, Y., Wang, G. An orthogonal basis for the hyperbolic hybrid polynomial space. SCI CHINA SER F 50, 21–28 (2007). https://doi.org/10.1007/s11432-007-0004-y
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DOI: https://doi.org/10.1007/s11432-007-0004-y