Spline curves

Demonstrating the use of CSCVN.

Copyright 1987-2003 C. de Boor and The MathWorks, Inc. $Revision: 1.16 $

Overview

Selecting the points

The spline toolbox will draw a smooth curve through a list of points, in the order in which they are received. You could use the Spline Toolbox command GETCURVE if you wanted the input such a list of points interactively. Here, we select random points, storing them in the array XY, one point per c o l u m n .

npts = 10;
xy = [randn(1,npts); randn(1,npts)];
plot(xy(1,:),xy(2,:),'ro','LineWidth',2);
text(xy(1,:), xy(2,:),[repmat('  ',npts,1), num2str([1:npts]')])
set(gca,'XTick',[],'YTick',[])

Connecting the points

The curve is constructed by

>> cv = cscvn(xy);

and plotted by

>> fnplt(cv,'r',2)
hold on
fnplt(cscvn(xy),'r',2)
hold off

3-D spline curves

Notice that it's just as easy to create spline curves in three dimensions. This time, we'll do something less random. First, we generate the points:

npts = 13;
t = linspace(0,8*pi,npts); z = linspace(-1,1,npts); omz = sqrt(1-z.^2);
xyz = [cos(t).*omz; sin(t).*omz; z]; 
plot3(xyz(1,:),xyz(2,:),xyz(3,:),'ro','LineWidth',2);
text(xyz(1,:),xyz(2,:),xyz(3,:),[repmat('  ',npts,1), num2str([1:npts]')])
set(gca,'XTick',[],'YTick',[],'ZTick',[])
box on

Connecting the points

Here is the 3D spline curve through these points provided by CSCVN. By appending the first point to the end of the list, we get a smooth c l o s e d curve.

hold on
fnplt(cscvn(xyz(:,[1:end 1])),'r',2)
hold off
% axis vis3d