Semi-regular Interpolatory RBF-based Subdivision Schemes

Published: 26-07-2018| Version 1 | DOI: 10.17632/7fpccm8y9j.1
Alberto Viscardi


We present a MATLAB function to compute the subdivision matrices of semi-regular univariate interpolatory RBF-based binary subdivision schemes. The construction is the adaptation of the one presented in "Stationary binary subdivision schemes using radial basis function interpolation", B.-G. Lee, Y. J. Lee, J. Yoon (Adv. Comput. Math, 2006) and "Analysis of stationary subdivision schemes for curve design based on radial basis function interpolation", Y. J. Lee, J. Yoon (Appl. Math. Comput., 2010), to the semi-regular case, i.e. when the starting mesh is formed by two different uniform mesh that meet eachother at 0. The main function, RBFs_semi.m, given the stepsizes of the two uniform mesh, the family of radial basis function, the number of points used for the local computation, the required polynomial reproduction and, eventually, further parameters, determines the subdivision matrix of the scheme in the form of the regular mask on the left, the regular mask on the right and the irregular part of the matrix around 0. The supported families of RBFs are (inverse) multi-quadric, Gaussian, Wendland's functions, Wu's functions, Buhmann's functions, polyharmonic functions and Euclid's hat functions (see e.g. "Meshfree approximation methods with MATLAB", G. E. Fasshauer). For further information about how to choose the parameters for each family see the files in the Aux folder.