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Dimension of polynomial splines of mixed smoothness on T-meshes / Deepesh Toshniwal, Nelly Villamizar

Computer Aided Geometric Design, Volume: 80, Start page: 101880

Swansea University Author: 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 co...

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Published in: Computer Aided Geometric Design
ISSN: 0167-8396
Published: Elsevier BV 2020
Online Access: Check full text

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.
Keywords: Splines; T-meshes; Mixed smoothness; Dimension formula; Homological algebra
Start Page: 101880