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 Θ n = span {sinht, cosht, t n−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.
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Project supported by the National Natural Science Foundation of China (No. 60473130) and the National Basic Research Program (973) of China (No. G2004CB318000)
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Fan, Ft., Wang, Gz. Conversion matrix between two bases of the algebraic hyperbolic space. J. Zhejiang Univ. - Sci. A 7 (Suppl 2), 181–186 (2006). https://doi.org/10.1631/jzus.2006.AS0181
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DOI: https://doi.org/10.1631/jzus.2006.AS0181
Key words
- Matrix representation
- Hyperbolic polynomial B-spline basis
- Algebraic hyperbolic Bézier basis
- Conversion matrix