Explain the reason why it is convenient to represent the bicubic spline in the form [operatorname{spline}(K, T)=sum_{i=1}^{p}

Question:

Explain the reason why it is convenient to represent the bicubic spline in the form

\[\operatorname{spline}(K, T)=\sum_{i=1}^{p} \sum_{j=1}^{q} c_{i j} M_{i}(K) N_{j}(T)\]

where $M_{i}(K), i=1, \ldots, p, N_{j}(T)$, and $j=1, \ldots, q$ are normalized $B$-splines instead of

\[\operatorname{spline}(K, T)=\sum_{i=0}^{3} \sum_{j=0}^{3} a_{i j} K^{i} T^{j}\]

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