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General matrix representations for B-splines
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DOI：10.1007/s003710050206.png)
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Abstract
En 中文
In this paper, the concept of the basis matrix of B-splines is presented. A general matrix representation, which results in an explicitly recursive matrix formula, for nonuniform B-spline curves of an arbitrary degree is also presented by means of the Toeplitz matrix. New recursive matrix representations for uniform B-spline curves and Bezier curves of an arbitrary degree are obtained as special cases of that for nonuniform B-spline curves. The recursive formula for the basis matrix can be substituted for de Boor-Cox's formula for B-splines, and it has a better time complexity than de Boor-Cox's formula when used for computation and conversion of B-spline curves and surfaces between different CAD systems. Finally, some applications of the matrix representations are given in the paper.
Keywords:
B-splines
matrix representations
Toeplitz matrix
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2.9
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4.6K
Citations:
6.5K
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