% Example 11.4b (Physics 330)

clear; close all;

x=-3:.4:3; y=x;

% build the full 2-d grid for the crude x and y data
% and make a surface plot

[X,Y]=meshgrid(x,y);
Z=cos((X.^2+Y.^2)/2);
surf(X,Y,Z);
title('Crude Data')

%*********************************************************
% now make a finer 2-d grid, interpolate linearly to
% build a finer z(x,y) and surface plot it.

% Note that because the interpolation is linear the mesh is finer
% but the crude corners are still there
%*********************************************************

xf=-3:.1:3;
yf=xf;
[XF,YF]=meshgrid(xf,yf);
ZF=interp2(X,Y,Z,XF,YF,'linear');
figure
surf(XF,YF,ZF);
title('Linear Interpolation')

%*********************************************************
% Now use cubic interpolation to round the corners.  Note that there is
% still trouble near the edge because these points only have data on one
% side to work with, so interpolation doesn't work very well
%*********************************************************

ZF=interp2(X,Y,Z,XF,YF,'cubic');
figure
surf(XF,YF,ZF);
title('Cubic Interpolation')

%*********************************************************
% Now use spline interpolation to also round the corners and see how
% it is different from cubic.  You should notice that it looks better,
% especially near the edges.  Spline interpolation is often the
% best.
%*********************************************************

ZF=interp2(X,Y,Z,XF,YF,'spline');
figure
surf(XF,YF,ZF);
title('Spline Interpolation')