# Control point (mathematics)

For Bézier curves, 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 partition of unity, i.e., that the $\phi_i$ are nonnegative and sum to one. This property implies that the curve lies within the convex hull of its control points.[2] This is the case for Bézier's representation of a polynomial curve as well as for the B-spline representation of a spline curve or tensor-product spline surface.