Abstract Determining the least m such that one mxm 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. © Springer-Verlag Berlin Heidelberg 2008.
CITATION STYLE
Fan, J., & Peters, J. (2008). On smooth bicubic surfaces from quad meshes. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5358 LNCS, pp. 87–96). https://doi.org/10.1007/978-3-540-89639-5_9
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