Create and plot a piecewise linear spline.

spline = spmak(augknt(1:7,2),[1,0,1,-1,0,0,1]);
figure
fnplt(spline)

Find the roots of the spline. The spline has each of the three kinds of zeros: touch zero, cross zero, and zero over an interval.

x = fnzeros(spline)

x = 2×3

    2.0000    3.5000    5.0000
    2.0000    3.5000    6.0000

Plot the roots of the spline using right-pointing triangles at the left endpoints and left-pointing triangles at the right endpoints.

nz = size(x,2);
hold on
plot(x(1,:),zeros(1,nz),'r>',x(2,:),zeros(1,nz),'r<','MarkerSize',10)
hold off

Create a spline with many local extrema. Locate the local extrema of the spline by finding the roots of its first derivative.

spline = spmak(1:31,rand(1,25)-0.5); 
x = fnzeros(fnder(spline));

Plot the spline and its local extrema.

figure
fnplt(spline)
hold on
x = unique(x(:));
y = fnval(spline,x);
plot(x,y,'ro')
xlim([-Inf Inf])
hold off

Create and plot a discontinuous piecewise linear spline.

 spline = spmak([0 0 1 1 2 2],[-1 1 -1 1]);
 figure
 fnplt(spline);

Find the roots of the spline. The roots include the jump through zero at x = 1.

x = fnzeros(spline)

x = 2×3

    0.5000    1.0000    1.5000
    0.5000    1.0000    1.5000