PDA

View Full Version : Cubic splines



Victor Ng-thow-hing
07-24-1995, 06:21 AM
There are various formulations for basis functions of cubic splines that
do different things. Catmull-Rom and Hermite both have the ability to
interpolate points. Several spline segments are often used to fit data
points. The most popular formulations like Bezier and B-spline can have
some built in constraints for C1 and c2 continuity, but these can be
circumvented by using tricks like multiple knots for B-splines.

For higher degree splines, there is always the danger of greater instability
with the curve shape (eg., unwanted oscillations), especially when fitting
data. NURBS (non-rational uniform B-splines) also get around many problems
and can represent a wide variety of shapes, such as cusps, and perfect
circles.

In conclusion, I think cubic splines are very stable and useful.

Vic.