Constrained visualisation using Shepard-Bernoulli interpolation operator
DOI:
https://doi.org/10.24193/subbmath.2020.2.08Keywords:
Scattered data, Shepard operator, constrained interpolation.Abstract
We consider Shepard-Bernoulli operator in order to solve a problem of interpolation of scattered data that is constrained to preserve positivity, using the technique described by K.W. Brodlie, M.R. Asim and K. Unsworth (2005). We also give some numerical examples.
Mathematics Subject Classification (2010): 41A29, 41A05, 41A25, 41A35.
References
Asim, M.R., Mustafa, G., Brodlie, K.W., Constrained Visualization of 2D Positive Data using Modified Quadratic Shepard Method, WSCG, 2004.
Brodlie, K.W., Asim, M.R., Unsworth, K., Constrained Visualization Using the Shepard Interpolation Family, Computer Graphics Forum, 24(2005), 809-820.
Caira, R., Dell’Accio, F., Shepard-Bernoulli operators, Math. Comp., 76(2007), 299-321. [4] C˘atina¸s, T., The bivariate Shepard operator of Bernoulli type, Calcolo, 44(2007), 189-202.
Coman, Gh., The remainder of certain Shepard type interpolation formulas, Stud. Univ. Babe¸s-Bolyai Math., 32(1987), no. 4, 24-32.
Costabile, F.A., Dell’Accio, F., Expansion Over a Rectangle of Real Functions in Bernoulli Polynomials and Applications, BIT, 41(2001), no. 3, 451-464.
Franke, R., Scattered data interpolation: tests of some methods, Math. Comp., 38(1982), 181-200.
Franke, R., Nielson, G., Smooth interpolation of large sets of scattered data, Int. J. Numer. Meths. Engrg., 15(1980), 1691-1704.
Lazzaro, D., Montefusco, L.B., Radial basis functions for multivariate interpolation of large scattered data sets, J. Comput. Appl. Math., 140(2002), 521-536.
Renka, R.J., Multivariate interpolation of large sets of scattered data, ACM Trans. Math. Software, 14(1988), 139-148.
Renka, R.J., Cline, A.K., A triangle-based C1 interpolation method, Rocky Mountain J. Math., 14(1984), 223-237.
Shepard, D., A two dimensional interpolation function for irregularly spaced data, Proc. 23rd Nat. Conf. ACM, 1968, 517-523.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2020 Studia Universitatis Babeș-Bolyai Mathematica
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
