Rational B-spline manifold

For given $d$-dimensional B-spline basis functions $B_{(i^1,p^1,k^1)} \otimes \cdots \otimes B_{(i^d,p^d,k^d)}$, given points $\bm{a}_{i^1 \dots i^d} \in V$ and real numbers $w_{i^1 \dots i^d} > 0$, rational B-spline manifold is defined by the following equality:

\[\bm{p}(t^1,\dots,t^d; \bm{a}_{i^1 \dots i^d}, w_{i^1 \dots i^d}) =\sum_{i^1,\dots,i^d} \frac{(B_{(i^1,p^1,k^1)} \otimes \cdots \otimes B_{(i^d,p^d,k^d)})(t^1,\dots,t^d) w_{i^1 \dots i^d}} {\sum\limits_{j^1,\dots,j^d}(B_{(j^1,p^1,k^1)} \otimes \cdots \otimes B_{(j^d,p^d,k^d)})(t^1,\dots,t^d) w_{j^1 \dots j^d}} \bm{a}_{i^1 \dots i^d}\]

Where $\bm{a}_{i^1,\dots,i^d}$ are called control points, and $w_{i^1 \dots i^d}$ are called weights.