= Subpartition of unity for B-splines
{title2=$0\le\sum_iN_{i,k}(t)\le1$}
A finite collection of the standard partition-normalized <B-splines> is nonnegative and has sum at most one on the entire real line. Extend the knot sequence in both directions. The full order-one collection sums to one, and summing the <Cox-de Boor recurrence> preserves that sum because the two coefficients of each lower-order function add to one. The finite collection is a subset. On the basic knot interval the finite sum equals one, also following from <Marsden's identity>.
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