We prove that the dimension of trivariate tensor-product spline space of tri-degree (m,m,m) with maximal order of smoothness over a three-dimensional domain coincides with the number of tensor-product B-spline basis functions acting effectively on the domain considered. A domain is required to belong to a certain class. This enables us to show that, for a certain assumption about the configuration of a hierarchical mesh, hierarchical B-splines span the spline space. This paper presents an extension to three-dimensional hierarchical meshes of results proposed recently by Giannelli and Jüttler for two-dimensional hierarchical meshes.

Dimensions and bases of hierarchical tensor-product splines / Berdinsky, Dmitry; Kim, Tae-Wan; Bracco, Cesare; Cho, Durkbin; Mourrain, Bernard; Min-Jae, Oh; Kiatpanichgij, Sutipong. - In: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. - ISSN 0377-0427. - STAMPA. - 257:(2014), pp. 86-104. [10.1016/j.cam.2013.08.019]

Dimensions and bases of hierarchical tensor-product splines

Bracco, Cesare;
2014

Abstract

We prove that the dimension of trivariate tensor-product spline space of tri-degree (m,m,m) with maximal order of smoothness over a three-dimensional domain coincides with the number of tensor-product B-spline basis functions acting effectively on the domain considered. A domain is required to belong to a certain class. This enables us to show that, for a certain assumption about the configuration of a hierarchical mesh, hierarchical B-splines span the spline space. This paper presents an extension to three-dimensional hierarchical meshes of results proposed recently by Giannelli and Jüttler for two-dimensional hierarchical meshes.
2014
257
86
104
Berdinsky, Dmitry; Kim, Tae-Wan; Bracco, Cesare; Cho, Durkbin; Mourrain, Bernard; Min-Jae, Oh; Kiatpanichgij, Sutipong
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1104129
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