 Control point

A control point is geometric data used to specify a curve or surface through a basis or refinement rule. In a linear representation $C(t)={\sum }_i{b}_i(t)P_i$, moving $P_i$ by $h$ changes the curve by $b_i(t)h$. The support of $b_i$ is therefore precisely its influence region. A control point need not lie on the curve: Bézier curves interpolate their endpoint controls, whereas generic interior B-spline controls are approximated.