On Smooth Bicubic Surfaces from Quad Meshes

  • Jianhua Fan
  • Jörg Peters
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5358)

Abstract

Determining the least m such that one m×m bi-cubic macro-patch per quadrilateral offers enough degrees of freedom to construct a smooth surface by local operations regardless of the vertex valences is of fundamental interest; and it is of interest for computer graphics due to the impending ability of GPUs to adaptively evaluate polynomial patches at animation speeds.

We constructively show that m = 3 suffices, show that m = 2 is unlikely to always allow for a localized construction if each macro-patch is internally parametrically C 1 and that a single patch per quad is incompatible with a localized construction. We do not specify the GPU implementation.

Keywords

Subdivision Scheme Black Disk Localize Construction Vertex Valence Quad Mesh 
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 2008

Authors and Affiliations

  • Jianhua Fan
    • 1
  • Jörg Peters
    • 1
  1. 1.Dept CISEUniversity of FloridaUSA

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