function y=tps(r)

% This is the thin-plate spline

if r < 0.000000000001

 y=0;

else

 y=r^2*log(r);

end

function y=fun(point)

% my target function

x=point(1);

z=point(2);

y=7-4*x^2+z^3;

function y=interpmat(points)

% this file computes the interpolation matrix

[n,m]=size(points);

for i=1:n

ipoint=points(i,:);

for j=1:n

jpoint=points(j,:);

mat(i,j)=tps(norm(ipoint-jpoint));

end

mat(i,n+1)=1;

mat(n+1,i)=1;

mat(i,n+2)=ipoint(1);

mat(n+2,i)=ipoint(1);

mat(i,n+3)=ipoint(2);

mat(n+3,i)=ipoint(2);

end

y=mat;

function y=righthandside(points)

% find the right hand side of the interpolation system

[n,m]=size(points);

for i=1:n

y(i)=fun(points(i,:));

end

y(n+1)=0;

y(n+2)=0;

y(n+3)=0;

function y=testinterp(n,m)

% this file test our interpolation routine

points=rand(n,2);

% compute interpolation matrix

mat=interpmat(points);

% create the right hand side

rhs=righthandside(points);

solution=inv(mat)*rhs';

% test solution

tpoints=rand(m,2)

maxerr=testsol(points,tpoints,solution);