Control point (mathematics)

In CAGD, based on Bezier's representation of a polynomial curve called curve title="Bézier curve"s, it has become customary the 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 <it>control points</it>, while the scalar-valued functions phi_i, defined over the relevant parameter domain, are the corresponding <it>weight</it> or <it>blending functions</it>. Some would reasonably insist that the blending functions form a <it>nonnegative partition of unity</it>, i.e., the phi_i are nonnegative and sum to 1.