n = 18;

t = linspace(-1,1,n+1)'; y = t.^2 + t + 0.05*sin(20*t);

clf, plot(t,y,'.')

By default interp1 gives us an interpolating function that is linear between each pair of consecutive nodes.

x = linspace(-1,1,400)';

hold on, plot(x,interp1(t,y,x))

title('Piecewise linear interpolant') % ignore this line

We may instead request a smoother interpolant that is piecewise cubic.

cla

plot(t,y,'.')

plot(x,interp1(t,y,x,'spline'))

title('Piecewise cubic interpolant') % ignore this line