Conversion matrix between two bases of the algebraic hyperbolic space |
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| Authors: | Fan Feng-tao Wang Guo-zhao |
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| Institution: | 1.Unstitute of Computer Graphics and Image Processing, Department of Mathematics,Zhejiang University,Hangzhou,China |
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| 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 Θn = 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. |
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