function spline_example(npts)

clf

% Run this example with npts = 5 to show a case when the shape
% preserving cubic spline works better than the regular cubic spline
% and with npts = 6 to show a case where the regular cubic spline
% works better than the shape preserving cubic spline. Also show what
% happens with npts = 7 and 8 and point out that the shape preserving
% cubic spline is not a good way to go if the function being fitted
% is known to have second derivative (or higher) continuity.

% First create data points for a simple sine curve
x = linspace(0,2*pi,npts);
y = sin(x);

plot(x,y,'kx')
legend('Original points')
axis([0 2*pi -1.5 1.5])
hold on
pause

% First fit these data points using the spline command

xtrue = linspace(0,2*pi,101);
ytrue = sin(xtrue);
xfit = xtrue;
yfit = spline(x,y,xfit);

plot(xtrue,ytrue,'k-',xfit,yfit,'r-')
legend('Original points','Original curve','Cubic spline fit')
pause

% Now fit the same data using the interp1 command with
% a shape preserving cubic spline

xfit2 = xtrue;
yfit2 = interp1(x,y,xfit2,'pchip');
plot(xfit2,yfit2,'b-')
legend('Original points','Original curve','Cubic spline fit','Shape preserving fit')