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A Discrete Approach to Multiresolution Curves and Surfaces

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Transactions on Computational Science VI

Part of the book series: Lecture Notes in Computer Science ((TCOMPUTATSCIE,volume 5730))

Abstract

Subdivision surfaces have been widely adopted in modeling in part because they introduce a separation between the surface and the underlying basis functions. This separation allows for simple general-topology subdivision schemes. Multiresolution representations based on subdivision, however, incongruently return to continuous functional spaces in their construction and analysis. In this paper, we propose a discrete multiresolution framework applicable to many subdivision schemes and based only on the subdivision rules. Noting that a compact representation can only afford to store a subset of the detail information, our construction enforces a constraint between adjacent detail terms. In this way, all detail information is recoverable for reconstruction, and a decomposition approach is implied by the constraint. Our framework is demonstrated with case studies in Dyn-Levin-Gregory curves and Catmull-Clark surfaces, each of which our method produces results on par with earlier methods. It is further shown that our construction can be interpreted as biorthogonal wavelet systems.

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Author information

Authors and Affiliations

  1. University of Calgary,  

    Luke Olsen & Faramarz Samavati

Authors
  1. Luke Olsen
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  2. Faramarz Samavati
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Calgary, 2500 University Drive N.W, T2N 1N4, Calgary, AB, Canada

    Marina L. Gavrilova

  2. OptimaNumerics Ltd., Cathedral House, 23-31 Waring Street, BT1 2DX, Belfast, UK

    C. J. Kenneth Tan

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Olsen, L., Samavati, F. (2009). A Discrete Approach to Multiresolution Curves and Surfaces. In: Gavrilova, M.L., Tan, C.J.K. (eds) Transactions on Computational Science VI. Lecture Notes in Computer Science, vol 5730. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10649-1_20

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  • DOI: https://doi.org/10.1007/978-3-642-10649-1_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-10648-4

  • Online ISBN: 978-3-642-10649-1

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