cscvn (Spline Toolbox)

Generate an interpolating parametric cubic spline curve.

Syntax

curve = cscvn(points)

Description

cscvn(points) returns a parametric variational, or natural cubic spline curve (in ppform) passing through the given sequence points(:,j), j = 1:end. The parameter value t(j) for the jth point is chosen by Eugene Lee's [1] centripetal scheme, i.e., as accumulated squareroot of chord length:

If the first and last point coincide (and there are no other repeated points), then a periodic cubic spline curve is constructed. However, double points result in corners.

Examples

The following provides the plot of a questionable curve through some points (marked as circles):

points=[0 1 1 0 -1 -1 0 0 ;
          0 0 1 2 1 0 -1 -2]; 
fnplt(cscvn(points)); hold on, 
plot(points(1,:),points(2,:),'o'), hold off

Here is a closed curve, good for 14 February, with one double point:

fnplt(cscvn([0 .8 .9 0 0 -.9 -.8 0; .5 1 0 -1 -1 0 1 .5])) 
 axis equal

Algorithm

The break sequence t is determined as

t=cumsum([0;((diff(points.').^2)*ones(d,1)).^(1/4)]).';

and csape (with either periodic or variational side conditions) is used to construct the smooth pieces between double points (if any).