A construction of edge B-spline functions for a C1 polynomial spline on two triangles and its application to Argyris type splines. (1st October 2021)

• Record Type: Journal Article
• Authors: Grošelj, Jan; Knez, Marjeta
• Is Part Of: Computers & mathematics with applications. Volume 99(2021)
• Page Start: 329
• Page End: 344
• Publication Date: 2021-10-01
• Subjects: Bernstein–Bézier form -- C1 splines on triangulations -- Argyris type splines -- B-spline-like basis; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2021.08.016
• Languages: English
• ISSNs: 0898-1221

Abstract

Highlights: A new construction of C1 continuous edge B-spline functions over two triangles is presented. The non-negativity of the derived splines is established provided the two triangles form a strictly convex quadrilateral. The introduced concept of edge B-splines is applied to construct a new basis for the Argyris type splines over triangulations. The basis functions are locally supported and non-negative C1 splines forming a partition of unity. The usability and stability of the basis is demonstrated on solving different least square problems. Abstract: Given two triangles in a planar domain sharing an edge and forming a convex quadrilateral, it is shown how to construct a non-negative basis for C 1 splines that restrict to polynomials of a total degree higher than one on each of the triangles. The representation may be seen as a generalization of the Bernstein–Bézier form of a spline on every separate triangle, and the main challenge in its development is the construction of basis functions associated with the common edge. This novel concept is aimed to be used in assembling B-spline-like bases for C 1 splines on triangulations, as it is demonstrated for Argyris type splines of degree higher than five on triangulations with flippable edges.