function [ approx ] = interpol( a, points, origin, K )
    approx = 0;
    for i = 1 : K
        center = points(:,i);
        r = norm (origin - center);
        approx = approx + a(i) * phigauss(r);
    end
end

function [ output_args ] = phigauss( r )
    b = 0.653;
    output_args = exp (-1*(b*r)^2);
end



load('dataset0.mat')

K = Nt;
points = [ xt'; yt' ];

%calculate phi matrix
phiVector = zeros(Nt,Nt);
for i = 1 : Nt
   origin = points(:,i);
   for j = 1 : Nt
      center = points(:,j);
      r = norm (origin - center);
      phiVector(i,j) = phigauss(r);
   end
end

%calcualte a
phiVector = triu(phiVector);
a = phiVector^-1 * ft;

%calculate approximation
%{
approx = zeros(Nt,1);
for i = 1 : Nt
   origin = points(:,i);
   approx(i) = interpol(a, points, origin, K);
end
%}

emean = 0;
pointsV = [ xv'; yv' ];
approx = zeros(Nv,1);
for i = 1 : Nv
   origin = pointsV(:,i);
   approx(i) = interpol(a, points, origin, K);
   emean = emean + norm(fv(i) - approx(i));
end

emean = emean / Nv;
%error



%plot
%{
tri = delaunay(xt,yt);
trisurf(tri,xt,yt,approx)
shading interp
%}
tri = delaunay(xv,yv);
trisurf(tri,xv,yv,approx)
shading interp