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 hierarchical 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.
Original language | English |
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Article number | 101880 |
Pages (from-to) | 1-10 |
Number of pages | 10 |
Journal | Computer Aided Geometric Design |
Volume | 80 |
DOIs | |
Publication status | Published - 2020 |
Keywords
- Dimension formula
- Homological algebra
- Mixed smoothness
- Splines
- T-meshes