A simple strategy for defining polynomial spline spaces over hierarchical T-meshes. (March 2016)

• Record Type: Journal Article
• Authors: Brovka, M.; López, J.I.; Escobar, J.M.; Montenegro, R.; Cascón, J.M.
• Is Part Of: Computer aided design. Volume 72(2016)
• Page Start: 140
• Page End: 156
• Publication Date: 2016-03
• Subjects: Isogeometric analysis -- Multivariate splines -- Local refinement -- T-mesh -- Nested spaces; Computer-aided design -- Periodicals; Engineering design -- Data processing -- Periodicals; Computer graphics -- Periodicals; Conception technique -- Informatique -- Périodiques; Infographie -- Périodiques; Computer graphics; Engineering design -- Data processing; Periodicals; Electronic journals; 620.00420285
• DOI: 10.1016/j.cad.2015.06.008
• Languages: English
• ISSNs: 0010-4485

Abstract

Abstract: We present a new strategy for constructing spline spaces over hierarchical T-meshes with quad- and octree subdivision schemes. The proposed technique includes some simple rules for inferring local knot vectors to define C 2 -continuous cubic tensor product spline blending functions. Our conjecture is that these rules allow to obtain, for a given T-mesh, a set of linearly independent spline functions with the property that spaces spanned by nested T-meshes are also nested, and therefore, the functions can reproduce cubic polynomials. In order to span spaces with these properties applying the proposed rules, the T-mesh should fulfill the only requirement of being a 0-balanced mesh. The straightforward implementation of the proposed strategy can make it an attractive tool for its use in geometric design and isogeometric analysis. In this paper we give a detailed description of our technique and illustrate some examples of its application in isogeometric analysis performing adaptive refinement for 2D and 3D problems. Highlights: A strategy for defining cubic tensor product spline functions is proposed. Simple rules for inferring local knot vectors to define blending functions for a given T-mesh. Examples of application of the strategy for adaptive refinement in isogeometric analysis and CAD.