%'tps_eval': calculate the thin plate spline (tps) interpolation at a set of points % see tps_coeff.m for more information and test_tps.m for an example %------------------------------------------------------------------------ % function EM = tps_eval(dsites,ctrs) %------------------------------------------------------------------------ % OUTPUT: % EM: Mx(N+s) matrix representing the contributions at the M sites % from unit sources located at each of the N centers, + (s+1) columns % representing the contribution of the linear gradient part. % use : U_interp=EM*U_tps % % INPUT: % dsites: Mxs matrix representing the postions of the M 'observation' sites, with s the space dimension % ctrs: Nxs matrix representing the postions of the N centers, sources of the tps, % % RELATED FUNCTIONS: % tps_coeff, tps_eval_dxy % tps_coeff_field, set_subdomains, filter_tps, calc_field %======================================================================= % Copyright 2008-2016, LEGI UMR 5519 / CNRS UGA G-INP, Grenoble, France % http://www.legi.grenoble-inp.fr % Joel.Sommeria - Joel.Sommeria (A) legi.cnrs.fr % % This file is part of the toolbox UVMAT. % % UVMAT is free software; you can redistribute it and/or modify % it under the terms of the GNU General Public License as published % by the Free Software Foundation; either version 2 of the license, % or (at your option) any later version. % % UVMAT is distributed in the hope that it will be useful, % but WITHOUT ANY WARRANTY; without even the implied warranty of % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the % GNU General Public License (see LICENSE.txt) for more details. %======================================================================= function EM = tps_eval(dsites,ctrs) [M,s] = size(dsites); [N,s] = size(ctrs); EM = zeros(M,N); % calculate distance matrix: accumulate sum of squares of coordinate differences % The ndgrid command produces two MxN matrices: % Dsite, consisting of N identical columns (each containing % the d-th coordinate of the M data sites) % Ctrs, consisting of M identical rows (each containing % the d-th coordinate of the N centers) for d=1:s [Dsites,Ctrs] = ndgrid(dsites(:,d),ctrs(:,d)); EM = EM + (Dsites-Ctrs).^2;%EM=square of distance matrices end % calculate tps np=find(EM~=0); EM(np) = EM(np).*log(EM(np))/2;%= tps formula r^2 log(r) (EM=r^2) % add linear gradient part: EM = [EM ones(M,1) dsites];