% GriddataExample0305.m  L Braile 
% Modified from example in Matlab Help, Griddata
rand('seed',0)
% Find 100 random x,y locations between -2 to 2
x = rand(100,1)*4-2; y = rand(100,1)*4-2;
% Calculate function z(x,y) at x,y locations
z = x.*exp(-x.^2-y.^2); % function definition
ti = -2:.25:2; % set grid parameters
[XI,YI] = meshgrid(ti,ti); % make x,y grid
ZI = griddata(x,y,z,XI,YI,'cubic'); % grid (2-D interpolate)
figure
mesh(XI,YI,ZI), hold on % Make a mesh of gridded surface
plot3(x,y,z,'o'), hold off % Show original x,y,z data values
%
% Plot color image and overlay contours
figure
pcolor(XI,YI,ZI)
shading interp
colormap jet
colorbar
hold on
% plot the x-y locations of the original data
plot(x,y,'+k')
% Contour the gridded data
v = [-0.5:0.1:0.5];
[c,h] = contour(XI,YI,ZI,v,'w-');
clabel(c,h,'color','w','fontweight','bold','fontsize',15)
axis square
hold off
%
% use interp2 to regrid for increased resolution and smoothness
figure
[X2,Y2] = meshgrid(-2:0.05:2); % set finer grid interval
Z2 = interp2(XI,YI,ZI,X2,Y2,'cubic');
% replot color display and contour map for interpolated data
pcolor(X2,Y2,Z2)
shading interp
colorbar
hold on
% Contour the gridded data
v = [-0.5:0.1:0.5];
[c,h] = contour(X2,Y2,Z2,v,'w-');
clabel(c,h,'color','w','fontweight','bold','fontsize',15)
axis square
hold off
%
% Calculate and plot exact 2-D function for comparison
t3 = -2:.05:2; % set grid parameters
[X3,Y3] = meshgrid(t3,t3); % make x,y grid
Z3 = X3.*exp(-X3.^2-Y3.^2); % function definition
figure
pcolor(X3,Y3,Z3)
shading interp
colormap jet
colorbar
hold on
% Contour the gridded data
v = [-0.5:0.1:0.5];
[c,h] = contour(X3,Y3,Z3,v,'w-');
clabel(c,h,'color','w','fontweight','bold','fontsize',15)
axis square
hold off