Journal of Zhejiang University SCIENCE A
(Monthly)

2006   Vol. 7   Suppl. II   p. 181-186

Conversion matrix between two bases of the algebraic hyperbolic space

Fan Feng-Tao^†, Wang Guo-Zhao

(Institute of Computer Graphics and Image Processing, Department of Mathematics, Zhejiang University, Hangzhou 310027, China)
^†E-mail: ftfan@163.com
Received Dec. 27, 2005 revision accepted Mar. 31, 2006

Abstract: This paper presents the matrix representation for the hyperbolic polynomial B-spline basis and the algebraic hyperbolic Bézier basis in a recursive way, which are both generated over the space Ω_n=span{sinht, cosht, tⁿ⁻³, …, t, 1} in which n is an arbitrary integer larger than or equal to 3. The conversion matrix from the hyperbolic polynomial B-spline basis of arbitrary order to the algebraic hyperbolic Bézier basis of the same order is also given by a recursive approach. As examples, the specific expressions of the matrix representation for the hyperbolic polynomial B-spline basis of order 4 and the algebraic hyperbolic Bézier basis of order 4 are given, and we also construct the conversion matrix between the two bases of order 4 by the method proposed in the paper. The results in this paper are useful for the evaluation and conversion of the curves and surfaces constructed by the two bases.

Key words: Matrix representation, Hyperbolic polynomial B-spline basis, Algebraic hyperbolic Bézier basis, Conversion matrix
doi:10.1631/jzus.2006.AS0181             CLC number: TP391.72

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