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Beta-Function B-splines and Subdivision Schemes, a Preliminary Study

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Large-Scale Scientific Computing (LSSC 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10665))

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Abstract

This paper is an initial study of subdivision schemes in connection with blending technics such as Expo Rational B-splines, see [1]. The study is done on curves, but surfaces are a natural next step. It turns out that blending two second degree polynomial curves, which interpolates three points, generate a 4-point subdivision scheme for Catmull Rom Splines, see [2]. It can be shown that different subdivision schemes can be developed from a blending spline construction using different types of local curves and/or blending functions. We will show examples, as circular arcs, and discuss some problems and properties.

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References

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Authors and Affiliations

  1. University of Tromsø - The Arctic University of Norway, Narvik, Norway

    Arne Lakså

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  1. Arne Lakså
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Correspondence to Arne Lakså .

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Editors and Affiliations

  1. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Lirkov

  2. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Svetozar Margenov

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Lakså, A. (2018). Beta-Function B-splines and Subdivision Schemes, a Preliminary Study. In: Lirkov, I., Margenov, S. (eds) Large-Scale Scientific Computing. LSSC 2017. Lecture Notes in Computer Science(), vol 10665. Springer, Cham. https://doi.org/10.1007/978-3-319-73441-5_65

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  • DOI: https://doi.org/10.1007/978-3-319-73441-5_65

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-73440-8

  • Online ISBN: 978-3-319-73441-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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