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Published in:
2008 | OriginalPaper | Chapter
On Smooth Bicubic Surfaces from Quad Meshes
Authors : Jianhua Fan, Jörg Peters
Published in: Advances in Visual Computing
Publisher: Springer Berlin Heidelberg
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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.