Splines

Splines consist of a set of points along a line (on-line points) and a small set of control points (knots) which direct the line through the said on-line points.

They are used in graphics to represent smooth curves and surfaces. Computationally, a polynomial function generates a curve through the on-line points while setting the control points, wheras graphic design applications let users set the control points themselves.

Splines allow the creation of complex smooth shapes without the need for manipulating many short line segments or polygons at the cost of a little extra computation time.

One of the simplest ways of approximating a curve is Bezier curves, which were made popular by the French mathematician Pierre Bezier and are based on a mathematical formulation by another French mathematician, Paul de Casteljau.