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.
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© 2008 Springer-Verlag Berlin Heidelberg
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Fan, J., Peters, J. (2008). On Smooth Bicubic Surfaces from Quad Meshes. In: Bebis, G., et al. Advances in Visual Computing. ISVC 2008. Lecture Notes in Computer Science, vol 5358. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89639-5_9
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DOI: https://doi.org/10.1007/978-3-540-89639-5_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-89638-8
Online ISBN: 978-3-540-89639-5
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