% '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 [DMX,DMY] = tps_eval_dxy(dsites,ctrs) %% matrix declarations [M,s] = size(dsites); [N,s] = size(ctrs); Dsites=zeros(M,N); DM = zeros(M,N); % DMXY = zeros(M,N+1+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) [Dsites,Ctrs] = ndgrid(dsites(:,1),ctrs(:,1));%d coordinates of interpolation points (Dsites) and initial points (Ctrs) DX=Dsites-Ctrs; [Dsites,Ctrs] = ndgrid(dsites(:,2),ctrs(:,2));%d coordinates of interpolation points (Dsites) and initial points (Ctrs) DY=Dsites-Ctrs; DM = DX.*DX + DY.*DY;% add d component squared %% calculate matrix of tps derivatives DM(DM~=0) = log(DM(DM~=0))+1; %=2 log(r)+1 derivative of the tps r^2 log(r) DMX=[DX.*DM zeros(M,1) ones(M,1) zeros(M,1)];% effect of mean gradient DMY=[DY.*DM zeros(M,1) ones(M,1) zeros(M,1)];% effect of mean gradient