An Examination of New Paradigms for Spline Approximations.
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.
National Institute of Standards and Technology, Gaithersburg, MD 20899-8910.
Christoph
C
Witzgall
National Institute of Standards and Technology, Gaithersburg, MD 20899-8910.
David E
DE
Gilsinn
National Institute of Standards and Technology, Gaithersburg, MD 20899-8910.
Marjorie A
MA
McClain
Delaunay triangulation; Gauss-Seidel iteration; Hsieh-Clough-Tocher elements; Lavery splines; bivariate splines; curve fitting; irregular data; non-oscillatory splines; point clouds; surface fitting; thin beam; thin plate; triangulated irregular networks