Past exam of the mathematics course of the University of Cambridge / 2005 / iii / Paper 66 / 4 / i

The tensor-product surface basis is $b_{jk}(u,v)={\varphi }_j(u){\psi }_k(v)$. If both univariate bases consist of nonnegative functions, thenIf both factors are strictly positive at the chosen parameters, their product is strictly positive there as well. Its support is the Cartesian product of the two factor supports. With partition of unity, this nonnegativity additionally places the parametric surface point in the convex hull of the active control points.