source: trunk/src/tps_coeff.m @ 246

Last change on this file since 246 was 246, checked in by sommeria, 10 years ago

thin plate shell (patch) introduced

File size: 1.6 KB
Line 
1%'tps_uvmat': calculate thin plate shell coefficients
2%------------------------------------------------------------------------
3%fasshauer@iit.edu MATH 590 ? Chapter 19 32
4% X,Y initial coordiantes
5% XI vector, YI column vector for the grid of interpolation points
6function [U_smooth,U_tps]=tps_coeff(X,Y,U,rho)
7%------------------------------------------------------------------------
8%rho smoothing parameter
9% ep = 1;
10X=reshape(X,[],1);
11Y=reshape(Y,[],1);
12N=numel(X);
13rhs = reshape(U,[],1);
14rhs = [rhs; zeros(3,1)];
15ctrs = [X Y];% coordinates of measurement sites, radial base functions are located at the measurement sites
16%ctrs = dsites;%radial base functions are located at the measurement sites
17EM = tps_eval(ctrs,ctrs);
18% DM_data = DistanceMatrix(ctrs,ctrs);%2D matrix of distances between spline centres (=initial points) ctrs
19% IM_sites = tps(1,DM_data);%values of thin plate at site points
20% PM=[ones(N,1) ctrs];
21% EM = [IM_sites PM];
22%IM = IM_sites + rho*eye(size(IM_sites));%  rho=1/(2*omega) , omega given by fasshauer;
23
24%IM=[IM PM; [PM' zeros(3,3)]];
25RhoMat=rho*eye(N,N);%  rho=1/(2*omega) , omega given by fasshauer;
26RhoMat=[RhoMat zeros(N,3)];
27PM=[ones(N,1) ctrs];
28
29IM=[EM+RhoMat; [PM' zeros(3,3)]];
30%fprintf('Condition number estimate: %e\n',condest(IM))
31%DM_eval = DistanceMatrix(epoints,ctrs);%2D matrix of distances between extrapolation points epoints and spline centres (=site points) ctrs
32%EM = tps(ep,DM_eval);%values of thin plate
33%PM = [ones(size(epoints,1),1) epoints];
34%EM = [EM PM];
35U_tps=(IM\rhs);
36% PM = [ones(size(dsites,1),1) dsites];
37
38U_smooth=EM *U_tps;
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