% 'DXYMatrix': calculate the matrix of thin-plate shell derivatives % % function DMXY = DXYMatrix(dsites,ctrs) % % INPUT: % dsites: M x s matrix of interpolation site coordinates (s=space dimension) % ctrs: N x s matrix of centre coordinates (initial data) % % OUTPUT: % DMXY: Mx(N+1+s)xs matrix corresponding to M interpolation sites and % N centres, with s=space dimension, DMXY(:,:,k) gives the derivatives % along dimension k (=x, y,z) after multiplication by the N+1+s tps sources. function DMXY = tps_eval_dxy(dsites,ctrs) %% matrix declarations [M,s] = size(dsites); [N,s] = size(ctrs); Dsites=zeros(M,N,s); DM = zeros(M,N); DMXY = zeros(M,N+1+s,s); %% Accumulate sum of squares of coordinate differences % The ndgrid command produces two MxN matrices: % Dsites, consisting of N identical columns (each containing % the d-th coordinate of the M interpolation sites) % Ctrs, consisting of M identical rows (each containing % the d-th coordinate of the N centers) for d=1:s [Dsites(:,:,d),Ctrs] = ndgrid(dsites(:,d),ctrs(:,d));%d coordinates of interpolation points (Dsites) and initial points (Ctrs) DM = DM + (Dsites(:,:,d)-Ctrs).^2;% add d component squared end %% calculate mtrix of tps derivatives DM(DM~=0) = log(DM)+1; %=2 log(r)+1 derivative of the tps r^2 log(r) for d=1:s DMXY(:,1:N,d)=Dsites(:,:,d).*DM; DMXY(:,N+1+d,d)=1;% effect of mean gradient end