  
function demo_designs(example)

if nargin == 0, example=1; end

I=[];
if nargin < 1, example=3; end
nv=2:6;
I=[];
switch example
    case 1
        f=@(x,y,z) exp(x)+0*y+0*z;
        I=1.476801374576529e+01;
    case 2
        f=@(x,y,z) exp(-x.^2-0.1*y.^2-2*z.^2);
        I=5.028153009823267;
     case 3
        f=@(x,y,z) (0.1*x+y.^2+0.5*z.^3).^3;
        I=1.969928193450972;
end

if isempty(I),  F=spherefun(f); I=sum2(F); format long; I, end

P=set11;
x=P(:,1); y=P(:,2); z=P(:,3); N=length(x);

w=(4*pi/N)*ones(N,1);

fnodes=feval(f,x,y,z);

In=w'*fnodes;
AE=abs(In-I); RE=AE/(I+(I == 0));
fprintf('\n \t AE: %1.2e RE: %1.2e \n \n',AE,RE);



% sphere(20);
% hold on;
% plot3(x,y,z,'o','MarkerEdgeColor','k',...
%                        'MarkerFaceColor','g',...
%                        'MarkerSize',10)
% hold off;




