= Solution
The <tensor-product surface basis> is $b_{jk}(u,v)=\phi_j(u)\psi_k(v)$. If both univariate bases consist of <nonnegative functions>, then
$$
\boxed{b_{jk}(u,v)\ge0.}
$$
If 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>.
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