% the code below illustrates phong/gouraud shading and mach banding

clf; colormap('default')
echo on

[x,y,z] = sphere(8); h = surf(x,y,z); 
vn=x; vn(:,:,2)=y; vn(:,:,3)=z;set(h,'VertexNormals',vn)
set(h,'EdgeColor','none','FaceColor',[1 0 0]); axis equal;
light('Position',[1 -1 1]); lighting flat

fprintf('here is the actual shape (polygon mesh)\n')

pause(5)

lighting phong

fprintf('here is phong shading; observe:\n')
fprintf('+ interior shading looks pretty convincing,		\n')
fprintf('  but outside shape not a smooth curve			\n')
fprintf('+ the highlight is perhaps a bit "washed out",		\n')
fprintf('  suggesting that matlab does color clipping by pinning\n')

pause(5)

lighting gouraud

fprintf('here is gouraud shading; observe:			  \n')
fprintf('+ the polygonal shape of the highlight			  \n')
fprintf('+ mach banding, e.g. the "starry" aspect of the highlight\n')

pause(5)

clf; colormap('default')
a = 30; x = [1:a a-1:-1:2]; x = [x x x];
x = x(ones(1,length(x)),:);
y = x';
z = max(x,y);
surf(z); axis equal; shading flat

fprintf('consider this smooth shape of intensities\n')

pause(5)

imagesc(z); colormap(gray); 

fprintf('do not the "grid edges" look especially bright,\n')
fprintf('although the intensity varies linearly?\n')
fprintf('and what is with the "diagonal black grid"?\n')
fprintf('all of this is (related to) mach banding')