On Smooth Bicubic Surfaces from Quad Meshes

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


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.


Subdivision Scheme Black Disk Localize Construction Vertex Valence Quad Mesh 
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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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