spcrv (Spline Toolbox)

Generate a spline curve

Syntax

spcrv(c)
curve = spcrv(c,k,maxpnt)

Description

spcrv(c,k) provides a dense sequence f(tt) of points on the uniform B-spline curve f of order k with B-spline coefficients c. Explicitly, this is the curve

with B(.|a,...,z) the B-spline with knots a,...,z, and n the number of coefficients in c, i.e., [d,n]:=size(c).

The default value for k is 4. The default value for the maximum number of points tt to be generated is 100.

The parameter interval that the point sequence tt fills out uniformly is the interval [k/2 .. (n-k/2)].

The output consists of the array f(tt).

Examples

The following would show a questionable broken line and its smoothed version:

points = [0 0 1 1 0 -1 -1 0 0 ;
        0 0 0 1 2 1 0 -1 -2]; 
plot(points(1,:),points(2,:),':') 
values = spcrv(points,3); 
hold on, plot(values(1,:),values(2,:)), hold off

Algorithm

Repeated midpoint knot insertion is used until there are at least maxpnt points. There are situations where use of fnplt would be more efficient.