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

If each univariate basis sums to one, distribute the finite sums, or use local finiteness when the basis is infinite: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.