= Non-uniform rational B-spline
{title2=$F(u,v)$}
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= NURBS
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A <non-uniform rational B-spline> surface is
$$
F(u,v)=\frac{\sum_{i,j}w_{ij}N_{i,p}(u)M_{j,q}(v)P_{ij}}{\sum_{i,j}w_{ij}N_{i,p}(u)M_{j,q}(v)}.
$$
Here the $N_{i,p}$ and $M_{j,q}$ are <B-spline> basis functions for possibly nonuniform <spline knot sequences>, and the $w_{ij}$ are weights. Positive weights make each evaluated point a <convex combination> of the active <control points>, supplying <bounding volumes> for geometric searches. The denominator must remain nonzero for the parametrization to be defined.
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