On Smooth Bicubic Surfaces from Quad Meshes

Authors:
Jianhua Fan;Jörg Peters
Affiliations:
Dept CISE, University of Florida,;Dept CISE, University of Florida,
Venue:
ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing
Year:
2008

Citing 3
Cited 2

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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.