NURBS Surface

A nonuniform rational B-Spline surface of degree $(p,q)$ is defined by

$${\bf S}(u,v)={\sum_{i=0}^m\sum_{j=0}^n N_{i,p}(u)N_{j,q}(v)w... ...,j}\over\sum_{i=0}^m\sum_{j=0}^n N_{i,p}(u)N_{j,q}(v)w_{i,j}},$$

where $N_{i,p}$ and $N_{j,q}$ are the B-Spline basis functions, ${\bf P}_{i,j}$ are control points, and the weight $w_{i,j}$ of ${\bf P}_{i,j}$ is the last ordinate of the homogeneous point ${\bf P}_{i,j}^w$.

See also B-Spline, Bézier Curve, NURBS Curve