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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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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10 | % |
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11 | % INPUT: |
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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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14 | % |
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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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18 | |
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19 | %======================================================================= |
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20 | % Copyright 2008-2020, LEGI UMR 5519 / CNRS UGA G-INP, Grenoble, France |
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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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38 | %% matrix declarations |
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39 | [M,s] = size(dsites); [N,s] = size(ctrs); |
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40 | Dsites=zeros(M,N); |
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41 | DM = zeros(M,N); |
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42 | % DMXY = zeros(M,N+1+s); |
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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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51 | [Dsites,Ctrs] = ndgrid(dsites(:,1),ctrs(:,1));%d coordinates of interpolation points (Dsites) and initial points (Ctrs) |
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52 | DX=Dsites-Ctrs;% set of x wise distances between sites and centres |
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53 | [Dsites,Ctrs] = ndgrid(dsites(:,2),ctrs(:,2));%d coordinates of interpolation points (Dsites) and initial points (Ctrs) |
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54 | DY=Dsites-Ctrs;% set of y wise distances between sites and centres |
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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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61 | DMY=[DY.*DM zeros(M,1) zeros(M,1) ones(M,1)];% effect of mean gradient |
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62 | |
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