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Bases of T-meshes and the refinement of hierarchical B-splines

机译:Bases of T-meshes and the refinement of hierarchical B-splines

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摘要

In this paper we consider spaces of bivariate splines of bi-degree (m, n) with maximal order of smoothness over domains associated to a two-dimensional grid. We define admissible classes of domains for which suitable combinatorial technique allows us to obtain the dimension of such spline spaces and the number of tensor-product B-splines acting effectively on these domains. Following the strategy introduced recently by Giannelli and Juettler, these results enable us to prove that under certain assumptions about the configuration of a hierarchical T-mesh the hierarchical B-splines forma basis of bivariate splines of bi-degree (m, ti) with maximal order of smoothness over this hierarchical T-mesh. In addition, we derive a sufficient condition about the configuration of a hierarchical T-mesh that ensures a weighted partition of unity property for hierarchical B-splines with only positive weights.

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  • 作者单位

    Research Institute of Marine Systems Engineering, Seoul National University, Seoul 151-744, Republic of Korea,Department of Computer Science, The University of Auckland, Auckland 1142, New Zealand,Department of Physics, Novosibirsk State University, Pirog;

    Research Institute of Marine Systems Engineering, Seoul National University, Seoul 151-744, Republic of Korea,Department of Naval Architecture and Ocean Engineering, Seoul National University, Seoul 151-744, Republic of Korea;

    Department of Mathematics, Dongguk University, Pil-dong 3-ga, Jung-gu, Seoul 100-715, Republic of KoreaDepartment of Mathematics 'Giuseppe Peano', University of Turin, v. Carlo Alberto 10, 10123, Turin, ItalySchool of Engineering and Technology, Asian Institute of Technology, Palhumlhani 12120, Thailand;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 英语
  • 中图分类 自动化基础理论;工程基础科学;
  • 关键词

    T-mesh; Spline space; Local refinement; Hierarchical B-splines;

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