For B-spline what does $\sum_{i=0,n}N_{i,k}(t)=1$ mean?

Question

For B-spline what does $\sum_{i=0,n}N_{i,k}(t)=1$ mean?

I don't understand what this means cause $N_{i,k}(t)$ are basis functions so what does it mean for them to all sum up to 1?

Answer 1

That means that all the B-Spline basis functions sum to 1 at every $t$.

Without that constraint, any scaling of valid basis functions would give a new, valid set of basis functions that could represent a spline, but with different coefficients.