# source:trunk/src/tps_eval_dxy.m@246

Last change on this file since 246 was 246, checked in by sommeria, 13 years ago

thin plate shell (patch) introduced

File size: 1.4 KB
Line
1% 'DXYMatrix': calculate the matrix of thin-plate shell derivatives
2%
3% function DMXY = DXYMatrix(dsites,ctrs)
4%
5% INPUT:
6%   dsites: M x s matrix of interpolation site coordinates (s=space dimension)
7%   ctrs: N x s matrix of centre coordinates (initial data)
8%
9% OUTPUT:
10%     DMXY: Mx(N+1+s)xs matrix corresponding to M interpolation sites and
11%            N centres, with s=space dimension, DMXY(:,:,k) gives the derivatives
12%            along dimension k (=x, y,z) after multiplication by the N+1+s tps sources.
13  function DMXY = tps_eval_dxy(dsites,ctrs)
14  %%  matrix declarations
15  [M,s] = size(dsites); [N,s] = size(ctrs);
16  Dsites=zeros(M,N,s);
17  DM = zeros(M,N);
18  DMXY = zeros(M,N+1+s,s);
19
20  %% Accumulate sum of squares of coordinate differences
21  % The ndgrid command produces two MxN matrices:
22  %   Dsites, consisting of N identical columns (each containing
23  %       the d-th coordinate of the M interpolation sites)
24  %  Ctrs, consisting of M identical rows (each containing
25  %       the d-th coordinate of the N centers)
26  for d=1:s
27     [Dsites(:,:,d),Ctrs] = ndgrid(dsites(:,d),ctrs(:,d));%d coordinates of interpolation points (Dsites) and initial points (Ctrs)
28     DM = DM + (Dsites(:,:,d)-Ctrs).^2;% add d component squared
29  end
30
31  %% calculate mtrix of tps derivatives
32  DM(DM~=0) = log(DM)+1; %=2 log(r)+1 derivative of the tps r^2 log(r)
33  for d=1:s
34    DMXY(:,1:N,d)=Dsites(:,:,d).*DM;
35    DMXY(:,N+1+d,d)=1;% effect of mean gradient
36  end
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