Fast Cardinal and Catmull-Rom Spline Interpolation

Optimal generation of cardinal splines of arbitrary dimensions, comprising Catmull-Rom (centripetal) types.

Syntax

y = cspl(x)

y = cspl(x,n)

y = cspl(x,n,k)

Description

y = cspl(x,n,k) Returns a cardinal spline 'y' from its nodes 'x' and resolution 'n'. The parameter 'k' can optionally specify the tension of the curve, which is set to zero by default (centripetal). As per:

[1] Catmull, E. & Rom, R. 'A class of local interpolating splines'. CAGD, R. E. Barnhill and R. F. Reisenfeld, Eds. Academic Press. New York, 1974, pp. 317–326.

[2] Twigg, C. 'Catmull-Rom Splines' CMU School of Computer Science. Online Resource, 2003.

The function operates column-wise along the dimensions of 'x' and it is optimised for speed.

See also: bspl

Examples

% Generate random nodes
x = rand(4,2);

% Interpolate different splines
a = cspl(x);
b = cspl(x,[],0.25);
c = cspl(x,100,0.5);

% Plot curves
figure, hold on
plot(a(:,1), a(:,2))
plot(b(:,1), b(:,2))
plot(c(:,1), c(:,2))
plot(x(:,1), x(:,2), 'o')
legend 'Centripetal (0)' 'Cardinal (0.25)' ...
       'Cardinal (0.50)' 'Random Nodes'


% Interpolate in N-dimensions
figure
plot(cspl(rand(4),100),'.');
legend 'dim 1' 'dim 2' 'dim 3' 'dim 4'