Coaxing a planar curve to comply

A long-standing problem in computer graphics is to find a planar curve that is shaped the way you want it to be shaped. A selection of various methods for achieving this goal is presented. The focus is on mathematical conditions that we can use to control curves while still allowing the curves some freedom. We start with methods invented by Newton (1643–1727) and Lagrange (1736–1813) and proceed to recent methods that are the subject of current research. We illustrate almost all the methods discussed with diagrams. Three methods of control that are of special interest are interpolation methods, global minimization methods (such as least squares), and (Bézier) control points. We concentrate on the first of these, interpolation methods.