= Solution
If each univariate basis sums to one, distribute the finite sums, or use local finiteness when the basis is infinite:
$$
\boxed{\sum_j\sum_kb_{jk}(u,v)=\left(\sum_j\phi_j(u)\right)\left(\sum_k\psi_k(v)\right)=1.}
$$
Thus the <tensor-product surface basis> is a <partition of unity>. In particular, translating every <control point> by a fixed vector translates the <parametric surface> by precisely that vector, and constant control data produce a constant <parametric surface>.
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