1 | %'tps_eval': calculate the thin plate spline (tps) interpolation at a set of points |
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2 | % see tps_coeff.m for more information and test_tps.m for an example |
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3 | %------------------------------------------------------------------------ |
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4 | % function EM = tps_eval(dsites,ctrs) |
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5 | %------------------------------------------------------------------------ |
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6 | % OUTPUT: |
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7 | % EM: Mx(N+s) matrix representing the contributions at the M sites |
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8 | % from unit sources located at each of the N centers, + (s+1) columns |
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9 | % representing the contribution of the linear gradient part. |
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10 | % use : U_interp=EM*U_tps |
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11 | % |
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12 | % INPUT: |
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13 | % dsites: Mxs matrix representing the postions of the M 'observation' sites, with s the space dimension |
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14 | % ctrs: Nxs matrix representing the postions of the N centers, sources of the tps, |
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15 | % |
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16 | % RELATED FUNCTIONS: |
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17 | % tps_coeff, tps_eval_dxy |
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18 | % tps_coeff_field, set_subdomains, filter_tps, calc_field |
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19 | |
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20 | %======================================================================= |
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21 | % Copyright 2008-2022, LEGI UMR 5519 / CNRS UGA G-INP, Grenoble, France |
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22 | % http://www.legi.grenoble-inp.fr |
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23 | % Joel.Sommeria - Joel.Sommeria (A) legi.cnrs.fr |
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24 | % |
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25 | % This file is part of the toolbox UVMAT. |
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26 | % |
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27 | % UVMAT is free software; you can redistribute it and/or modify |
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28 | % it under the terms of the GNU General Public License as published |
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29 | % by the Free Software Foundation; either version 2 of the license, |
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30 | % or (at your option) any later version. |
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31 | % |
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32 | % UVMAT is distributed in the hope that it will be useful, |
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33 | % but WITHOUT ANY WARRANTY; without even the implied warranty of |
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34 | % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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35 | % GNU General Public License (see LICENSE.txt) for more details. |
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36 | %======================================================================= |
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37 | |
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38 | function EM = tps_eval(dsites,ctrs) |
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39 | [M,s] = size(dsites); [N,s] = size(ctrs); |
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40 | EM = zeros(M,N); |
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41 | |
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42 | % calculate distance matrix: accumulate sum of squares of coordinate differences |
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43 | % The ndgrid command produces two MxN matrices: |
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44 | % Dsite, consisting of N identical columns (each containing |
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45 | % the d-th coordinate of the M data sites) |
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46 | % Ctrs, consisting of M identical rows (each containing |
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47 | % the d-th coordinate of the N centers) |
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48 | for d=1:s |
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49 | [Dsites,Ctrs] = ndgrid(dsites(:,d),ctrs(:,d)); |
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50 | EM = EM + (Dsites-Ctrs).^2;%EM=square of distance matrices |
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51 | end |
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52 | |
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53 | % calculate tps |
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54 | np=find(EM~=0); |
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55 | EM(np) = EM(np).*log(EM(np))/2;%= tps formula r^2 log(r) (EM=r^2) |
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56 | |
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57 | % add linear gradient part: |
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58 | EM = [EM ones(M,1) dsites]; |
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