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arXiv · 1912.13118

Dimension of polynomial splines of mixed smoothness on T-meshes

Deepesh Toshniwal·Nelly Villamizar
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Abstract

In this paper we study the dimension of splines of mixed smoothness on axis-aligned T-meshes. This is the setting when different orders of smoothness are required across the edges of the mesh. Given a spline space whose dimension is independent of its T-mesh's geometric embedding, we present constructive and sufficient conditions that ensure that the smoothness across a subset of the mesh edges can be reduced while maintaining stability of the dimension. The conditions have a simple geometric interpretation. Examples are presented to show the applicability of the results on both hierarchical and non-hierarchical T-meshes. For hierarchal T-meshes it is shown that mixed smoothness spline spaces that contain the space of PHT-splines (Deng et al., 2008) always have stable dimension.

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Deepesh Toshniwal, Nelly Villamizar. 2019-12-30. Dimension of polynomial splines of mixed smoothness on T-meshes. https://doi.org/10.1016/j.cagd.2020.101880

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