Even originally used to describe a long thin slat in shipbuilding, the term spline is nowadays used in connection with CAD systems.
In mathematics, a spline is a smooth curve, which runs through (or near) a series of points. These points (also called control points) influence the shape of the resulting spline curve.
If a spline curve can be described in all sections using a linear function, the spline is also called polygon or linear spline.
Similarly, square or cubic splines can be found.
In CAD systems mostly Non-Uniform Rational B-Splines (NURBS) are used for the representation of a curve. Based on spline curces spline surfaces can be created.
For them the term free-form surfaces is very often used. Free form surfaces are needed in particular in automotive engineering.