= Solution
A <tensor-product surface basis> combines two independent univariate bases:
$$
\boxed{S(u,v)=\sum_{i=0}^{m}\sum_{j=0}^{n}P_{ij}B_i(u)C_j(v).}
$$
The coefficients $P_{ij}$ are three-dimensional <control points>. Fixing one parameter gives a curve in the other univariate basis; the coefficients of that curve are the corresponding weighted combinations of rows or columns of controls.
The <control net> must have a rectangular two-index topology, with row/column neighbors and quadrilateral mesh cells. “Rectangular” describes the index grid, not the geometry of the points: its faces need not be flat or rectangular in space. A surface requiring a triangular domain or arbitrary extraordinary mesh connectivity is not directly described by one such tensor-product patch.
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