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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.
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.