**General B-Splines**-
- Nonuniform B-splines (NUBS) generalize this construction
- A B-spline, , is a piecewise polynomial:
- each of its segments is of degree
- it is defined for all
*t* - its segmentation is give by
*knots* - it is zero for and
- it may have a discontinuity in its
*d*-*k*+1 derivative at ,

if has multiplicity*k* - it is nonnegative for
- for ,

and all other are zero on this interval - Bézier blending functions are the special case where

all knots have multiplicity*d*+1

**Example (Quadratic):**-
**Evaluation**-
- There is an efficient, recursive evaluation scheme for any curve point
- It generalizes the triangle scheme (de Casteljau) for Bézier curves
- Example (for cubics and ):

CS488/688: Introduction to Interactive Computer Graphics

University of Waterloo

Computer Graphics Lab