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Dimension of polynomial splines of mixed smoothness on T-meshes

Deepesh Toshniwal, Nelly Villamizar Orcid Logo

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

Swansea University Author: Nelly Villamizar Orcid Logo

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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...

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Published in: Computer Aided Geometric Design
ISSN: 0167-8396
Published: Elsevier BV 2020
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URI: https://cronfa.swan.ac.uk/Record/cronfa54305
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first_indexed 2020-05-24T19:07:49Z
last_indexed 2020-06-19T13:10:27Z
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spelling 2020-06-19T10:31:54.3338346 v2 54305 2020-05-24 Dimension of polynomial splines of mixed smoothness on T-meshes 41572bcee47da6ba274ecd1828fbfef4 0000-0002-8741-7225 Nelly Villamizar Nelly Villamizar true false 2020-05-24 SMA 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. Journal Article Computer Aided Geometric Design 80 101880 Elsevier BV 0167-8396 Splines; T-meshes; Mixed smoothness; Dimension formula; Homological algebra 1 6 2020 2020-06-01 10.1016/j.cagd.2020.101880 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2020-06-19T10:31:54.3338346 2020-05-24T13:58:02.4201912 Deepesh Toshniwal 1 Nelly Villamizar 0000-0002-8741-7225 2 54305__17547__f74565eb368b4b80b6105fb087be2e0b.pdf 54305VOR.pdf 2020-06-19T10:28:54.7033390 Output 562364 application/pdf Version of Record true Released under the terms of a Creative Commons Attribution License (CC-BY). true eng http://creativecommons.org/licenses/by/4.0/
title Dimension of polynomial splines of mixed smoothness on T-meshes
spellingShingle Dimension of polynomial splines of mixed smoothness on T-meshes
Nelly Villamizar
title_short Dimension of polynomial splines of mixed smoothness on T-meshes
title_full Dimension of polynomial splines of mixed smoothness on T-meshes
title_fullStr Dimension of polynomial splines of mixed smoothness on T-meshes
title_full_unstemmed Dimension of polynomial splines of mixed smoothness on T-meshes
title_sort Dimension of polynomial splines of mixed smoothness on T-meshes
author_id_str_mv 41572bcee47da6ba274ecd1828fbfef4
author_id_fullname_str_mv 41572bcee47da6ba274ecd1828fbfef4_***_Nelly Villamizar
author Nelly Villamizar
author2 Deepesh Toshniwal
Nelly Villamizar
format Journal article
container_title Computer Aided Geometric Design
container_volume 80
container_start_page 101880
publishDate 2020
institution Swansea University
issn 0167-8396
doi_str_mv 10.1016/j.cagd.2020.101880
publisher Elsevier BV
document_store_str 1
active_str 0
description 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.
published_date 2020-06-01T04:07:46Z
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score 10.998048

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