[356] | 1 | %'tps_eval_dxy': calculate the derivatives of thin plate spline (tps) interpolation at a set of points (limited to the 2D case) |
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| 2 | %------------------------------------------------------------------------ |
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| 3 | % function [DMX,DMY] = tps_eval_dxy(dsites,ctrs) |
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| 4 | %------------------------------------------------------------------------ |
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| 5 | % OUTPUT: |
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[811] | 6 | % DMX: Mx(N+3) matrix representing the contributions to the X |
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| 7 | % derivatives at the M sites from unit sources located at each of the N |
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| 8 | % centers, + 3 columns representing the contribution of the linear gradient part. |
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| 9 | % DMY: idem for Y derivatives |
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[246] | 10 | % |
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| 11 | % INPUT: |
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[811] | 12 | % dsites: M x s matrix of interpolation site coordinates (s=space dimension=2 here) |
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| 13 | % ctrs: N x s matrix of centre coordinates (initial data) |
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[246] | 14 | % |
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[811] | 15 | % RELATED FUNCTIONS: |
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| 16 | % tps_coeff, tps_eval |
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| 17 | % tps_coeff_field, set_subdomains, filter_tps, calc_field |
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[356] | 18 | |
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[809] | 19 | %======================================================================= |
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[924] | 20 | % Copyright 2008-2016, LEGI UMR 5519 / CNRS UGA G-INP, Grenoble, France |
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[809] | 21 | % http://www.legi.grenoble-inp.fr |
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| 22 | % Joel.Sommeria - Joel.Sommeria (A) legi.cnrs.fr |
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| 23 | % |
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| 24 | % This file is part of the toolbox UVMAT. |
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| 25 | % |
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| 26 | % UVMAT is free software; you can redistribute it and/or modify |
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| 27 | % it under the terms of the GNU General Public License as published |
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| 28 | % by the Free Software Foundation; either version 2 of the license, |
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| 29 | % or (at your option) any later version. |
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| 30 | % |
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| 31 | % UVMAT is distributed in the hope that it will be useful, |
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| 32 | % but WITHOUT ANY WARRANTY; without even the implied warranty of |
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| 33 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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| 34 | % GNU General Public License (see LICENSE.txt) for more details. |
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| 35 | %======================================================================= |
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| 36 | |
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| 37 | function [DMX,DMY] = tps_eval_dxy(dsites,ctrs) |
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[246] | 38 | %% matrix declarations |
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| 39 | [M,s] = size(dsites); [N,s] = size(ctrs); |
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[247] | 40 | Dsites=zeros(M,N); |
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[246] | 41 | DM = zeros(M,N); |
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[247] | 42 | % DMXY = zeros(M,N+1+s); |
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[246] | 43 | |
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| 44 | %% Accumulate sum of squares of coordinate differences |
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| 45 | % The ndgrid command produces two MxN matrices: |
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| 46 | % Dsites, consisting of N identical columns (each containing |
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| 47 | % the d-th coordinate of the M interpolation sites) |
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| 48 | % Ctrs, consisting of M identical rows (each containing |
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| 49 | % the d-th coordinate of the N centers) |
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| 50 | |
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[247] | 51 | [Dsites,Ctrs] = ndgrid(dsites(:,1),ctrs(:,1));%d coordinates of interpolation points (Dsites) and initial points (Ctrs) |
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[434] | 52 | DX=Dsites-Ctrs;% set of x wise distances between sites and centres |
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[247] | 53 | [Dsites,Ctrs] = ndgrid(dsites(:,2),ctrs(:,2));%d coordinates of interpolation points (Dsites) and initial points (Ctrs) |
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[434] | 54 | DY=Dsites-Ctrs;% set of y wise distances between sites and centres |
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[247] | 55 | DM = DX.*DX + DY.*DY;% add d component squared |
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| 56 | |
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| 57 | %% calculate matrix of tps derivatives |
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| 58 | DM(DM~=0) = log(DM(DM~=0))+1; %=2 log(r)+1 derivative of the tps r^2 log(r) |
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| 59 | |
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| 60 | DMX=[DX.*DM zeros(M,1) ones(M,1) zeros(M,1)];% effect of mean gradient |
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[434] | 61 | DMY=[DY.*DM zeros(M,1) zeros(M,1) ones(M,1)];% effect of mean gradient |
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[247] | 62 | |
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