An Examination of New Paradigms for Spline Approximations

Published

May 1, 2006

Author(s)

Christoph J. Witzgall, David E. Gilsinn, Marjorie A. McClain

Abstract

Lavery splines are examined in the univariate and bivariate cases. In both instances relaxation based algorithms for approximate calculation of Lavery splines are proposed. Following previous work Gilsinn, et al. [7] addressing the bivariate case, a rotationally invariant functional is assumed. The version of bivariate splines proposed in this paper also aims at irregularly spaced data and uses Hseih-Clough-Tocher elements based on the triangulated irregular network (TIN) concept. In this paper, the univariate case, however, is investigated in greater detail so as to further the understanding of the bivariate case.

Citation

Journal of Research (NIST JRES) -

Volume

111 No. 2

NIST Pub Series

Journal of Research (NIST JRES)

Pub Type

NIST Pubs

Keywords

bivariate splines, curve fitting, Delaunay triangulation, Gauss-Seidel iteration, Hsieh-Clough-Tocher elements, irregular data, Lavery splines, non-oscillatory splines, point clouds

Citation

Witzgall, C. , Gilsinn, D. and McClain, M. (2006), An Examination of New Paradigms for Spline Approximations, Journal of Research (NIST JRES), National Institute of Standards and Technology, Gaithersburg, MD (Accessed October 22, 2025)