Open Access

ARTICLE

Subdivision of Uniform ωB-Spline Curves and Two Proofs of Its Ck−2-Continuity

Jing Tang¹, Mei-e Fang^1,*, Guozhao Wang²

1 School of Computer Sciences and Educational Softwares, Guangzhou University, Guangzhou, China.
2 Department of Mathematics, Zhejiang University, Hangzhou, China .

*Corresponding Author: Mei-e Fang. Email: .

Computer Modeling in Engineering & Sciences 2018, 115(2), 263-280. https://doi.org/10.3970/cmes.2018.01702

Abstract

ωB-splines have many optimal properties and can reproduce plentiful commonly-used analytical curves. In this paper, we further propose a non-stationary subdivision method of hierarchically and efficiently generating ωB-spline curves of arbitrary order of ωB-spline curves and prove its Ck−2-continuity by two kinds of methods. The first method directly prove that the sequence of control polygons of subdivision of order k converges to a Ck−2-continuousωB-spline curve of order k. The second one is based on the theories upon subdivision masks and asymptotic equivalence etc., which is more convenient to be further extended to the case of surface subdivision. And the problem of approximation order of this non-stationary subdivision scheme is also discussed. Then a uniform ωB-spline curve has both perfect mathematical representation and efficient generation method, which will benefit the application of ωB-splines.

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Keywords

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