NURBS Curve

A nonuniform rational B-Spline curve defined by

$${\bf C}(t)={\sum_{i=0}^n N_{i,p}(t)w_i{\bf P}_i\over \sum_{i=0}^n N_{i,p}(t)w_i},$$

where $p$ is the order, $N_{i,p}$ are the B-Spline basis functions, ${\bf P}_i$ are control points, and the weight $w_i$ of ${\bf P}_i$ is the last ordinate of the homogeneous point ${\bf P}_i^w$. These curves are closed under perspective transformations and can represent Conic Sections exactly.

See also B-Spline, Bézier Curve, NURBS Surface

References

Piegl, L. and Tiller, W. The NURBS Book, 2nd ed New York: Springer-Verlag, 1997.