Non-Uniform Splines
The knot sequence is the parameter spacing of knots.
So far we’ve been assuming a uniform knot sequence: u in [0,1] for each piece of the spline.
A non-uniform knot sequence relaxes this assumption.
Different knot spacings yield different basis matrices (so when doing non-uniform splines you typically don’t use matrices).
Tangents are scaled, this gives tension control
- curve can be regarded as a time trajectory - tangents are velocities
Each segment has a different basis functions!
Advantages
- Can reduce continuity by duplicating knots (& control points)
- Can add detail to a curve without changing knot spacing globally