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A Discrete Approach to Multiresolution Curves and Surfaces

  • Luke Olsen
  • Faramarz Samavati
Part of the Lecture Notes in Computer Science book series (LNCS, 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.

Keywords

Subdivision Scheme Discrete Approach Subdivision Surface Subdivision Rule Edge Vertex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Luke Olsen
    • 1
  • Faramarz Samavati
    • 1
  1. 1.University of Calgary 

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