clear

%%
% We use n=3 and n=6 with equally spaced nodes for the function
% sin(exp(2x)) over [0,1].

%%  
f = @(x) sin(exp(2*x));

figure(1)
fplot(f, [0.0, 1.0]) 
hold on

t = linspace(0.0, 1.0, 4)';
plot(t, f(t), 'o');
p = polyinterp(t, f(t));
fplot(p, [0.0, 1.0])

xlabel('x')
ylabel('f(x)')
title('Interpolation on 4 nodes')
grid on
legend('f(x)', 'data points', 'p(x)', 'location', 'best')

%%
figure(2)
fplot(f, [0.0, 1.0])
hold on

t = linspace(0.0, 1.0, 7)';
plot(t, f(t), 'o');
p = polyinterp(t, f(t));
fplot(p, [0.0, 1.0]);

xlabel('x')
ylabel('f(x)')
title('Interpolation on 7 nodes')
grid on
legend('f(x)', 'data points', 'p(x)', 'location', 'best')

%%
% The curves always intersect at the interpolation nodes.