Dimensions and bases of hierarchical tensor-product splines

• Autores: Dmitry Berdinsky, Tae Wan Kim, Cesare Bracco, Durkbin Cho, Bernard Mourrain
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 257, Nº 1, 2014, págs. 86-104
• Idioma: inglés
• DOI: 10.1016/j.cam.2013.08.019
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.