Specifying Curves

Take an hammer and some nails, fix the nails and try to make a piece of wood go through all the nails. You'll get a B spline...
Spline [n.] : A flexible strip (wood or rubber) used in drawing curved lines.

Control Points a set of points that influence the curve's shape Knots control points that lie on the curve Interpolating spline curve passes through the control points knots Approximating spline control points merely influence shape Convex Hull convex polygon boundary that encloses a set of control points

If some data points are used to construct a curve the curve can either pass through the points, in which case the curve is interpolating, or the points can just be used to control the general shape of the curve and the curve doesn't actually pass through the points, in which case the curve is approximating.