source: trunk/src/tps_eval_dxy.m @ 932

Last change on this file since 932 was 924, checked in by g7moreau, 5 years ago
  • Update Copyright Copyright 2008-2016, LEGI UMR 5519 / CNRS UGA G-INP, Grenoble, France
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1%'tps_eval_dxy': calculate the derivatives of thin plate spline (tps) interpolation at a set of points (limited to the 2D case)
2%------------------------------------------------------------------------
3% function [DMX,DMY] = tps_eval_dxy(dsites,ctrs)
4%------------------------------------------------------------------------
5% OUTPUT:
6%  DMX: Mx(N+3) matrix representing the contributions to the X
7%  derivatives at the M sites from unit sources located at each of the N
8%  centers, + 3 columns representing the contribution of the linear gradient part.
9%  DMY: idem for Y derivatives
10%
11% INPUT:
12%  dsites: M x s matrix of interpolation site coordinates (s=space dimension=2 here)
13%  ctrs: N x s matrix of centre coordinates (initial data)
14%
15% RELATED FUNCTIONS:
16%  tps_coeff, tps_eval
17%  tps_coeff_field, set_subdomains, filter_tps, calc_field
18
19%=======================================================================
20% Copyright 2008-2016, LEGI UMR 5519 / CNRS UGA G-INP, Grenoble, France
21%   http://www.legi.grenoble-inp.fr
22%   Joel.Sommeria - Joel.Sommeria (A) legi.cnrs.fr
23%
24%     This file is part of the toolbox UVMAT.
25%
26%     UVMAT is free software; you can redistribute it and/or modify
27%     it under the terms of the GNU General Public License as published
28%     by the Free Software Foundation; either version 2 of the license,
29%     or (at your option) any later version.
30%
31%     UVMAT is distributed in the hope that it will be useful,
32%     but WITHOUT ANY WARRANTY; without even the implied warranty of
33%     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
34%     GNU General Public License (see LICENSE.txt) for more details.
35%=======================================================================
36
37function [DMX,DMY] = tps_eval_dxy(dsites,ctrs)
38  %%  matrix declarations
39  [M,s] = size(dsites); [N,s] = size(ctrs);
40  Dsites=zeros(M,N);
41  DM = zeros(M,N);
42 % DMXY = zeros(M,N+1+s);
43 
44  %% Accumulate sum of squares of coordinate differences
45  % The ndgrid command produces two MxN matrices:
46  %   Dsites, consisting of N identical columns (each containing
47  %       the d-th coordinate of the M interpolation sites)
48  %  Ctrs, consisting of M identical rows (each containing
49  %       the d-th coordinate of the N centers)
50 
51[Dsites,Ctrs] = ndgrid(dsites(:,1),ctrs(:,1));%d coordinates of interpolation points (Dsites) and initial points (Ctrs)
52DX=Dsites-Ctrs;% set of x wise distances between sites and centres
53[Dsites,Ctrs] = ndgrid(dsites(:,2),ctrs(:,2));%d coordinates of interpolation points (Dsites) and initial points (Ctrs)
54DY=Dsites-Ctrs;% set of y wise distances between sites and centres
55DM = DX.*DX + DY.*DY;% add d component squared
56
57 %% calculate matrix of tps derivatives
58DM(DM~=0) = log(DM(DM~=0))+1; %=2 log(r)+1 derivative of the tps r^2 log(r)
59
60DMX=[DX.*DM zeros(M,1)  ones(M,1) zeros(M,1)];% effect of mean gradient
61DMY=[DY.*DM zeros(M,1)  zeros(M,1) ones(M,1)];% effect of mean gradient
62
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