%  Demo with different types of spline interpolation
f = inline('2.^x')
x = linspace(-.2, 4.2);
y = f(x);
X = [0 1 2 4]
Y = f(X)
plot(X,Y,'o',x,y), axis([-0.2 4.2 -1 20]); grid on
pause

%  linear interpolation
p = interp1(X,Y,x);
plot(X,Y,'o',x,y,x,p), axis([-0.2 4.2 -1 20]), grid on
title('Linear Splines')
pause

% Hermite Spline
S = log(2)*Y
a = pwch(X,Y,S);
p = ppval(a,x);

plot(X,Y,'o',x,y,x,p); grid on, axis([-0.2 4.2 -1 20])
title('Hermite Spline')
pause

plot(x,p-y), grid on, axis([-0.2 4.2 -0.1 0.03])
title('Error in Hermite Spline')
pause

% Not a knot spline

a = spline(X,Y);
p = ppval(a,x);

plot(X,Y,'o',x,y,x,p), axis([-0.2 4.2 -1 20]); grid on
title('Not-a-Knot Spline')
pause

plot(x,p-y), axis([-0.2 4.2 -0.1 0.4]); grid on
title('Error Not-a-Knot Spline')
pause; 

%  Clamped spline

Y1 = [log(2) Y 16*log(2)] 
a = spline(X,Y1);
p = ppval(a,x);

plot(X,Y,'o',x,y,x,p), axis([-0.2 4.2 -1 20]); grid on
title('Clamped Spline')
pause

plot(x,p-y), axis([-0.2 4.2 -0.15 0.05]); grid on
title('Error Clamped Spline')
pause; 

%  Shape preserving
a = pchip(X,Y);
p = ppval(a,x);

plot(X,Y,'o',x,y,x,p), axis([-0.2 4.2 -1 20]); grid on
title('Shape Preserving Spline')
pause

plot(x,p-y), axis([-0.2 4.2 -0.1 0.8]); grid on
title('Error Shape Preserving Spline')