Control point (mathematics)

In CAGD, based on Bezier's representation of a polynomial curve called a Bézier curve, it has become customary to refer to the $d$-vectors $p_{i}\$ in a parametric representation $\sum _{i}p_{i}\phi _{i}\$ of a curve or surface in $d$-space as control points, while the scalar-valued functions $\phi _{i}$, defined over the relevant parameter domain, are the corresponding weight or blending functions. Some would reasonably insist, in order to give intuitive geometric meaning to the word `control', that the blending functions form a nonnegative partition of unity, i.e., the $\phi _{i}$ are nonnegative and sum to 1.