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Dimension of polynomial splines of mixed smoothness on T-meshes
Computer Aided Geometric Design, Volume: 80, Start page: 101880
Swansea University Author:
Nelly Villamizar
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DOI (Published version): 10.1016/j.cagd.2020.101880
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 co...
| Published in: | Computer Aided Geometric Design |
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| ISSN: | 0167-8396 |
| Published: |
Elsevier BV
2020
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa54305 |
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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 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. |
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| Keywords: |
Splines; T-meshes; Mixed smoothness; Dimension formula; Homological algebra |
| Start Page: |
101880 |