9.1. The Draughtman's Tool   

Smooth curves and surfaces must be generated in many computer graphics applications. Computer graphics involves modelling the real world which most of the shapes of the objects are smooth and complex. Presenting curves and surfaces in mathematical description is very important because one can hardly duplicate the same curve or surface exactly.

Spline functions provide a direct and effective representation of curves, understandable both to the computer and the person trying to manipulate the curves. The spline was originally used in the construction of boats, and was a long, thin strip of metal or wood. This strip was warped into a smooth curve passing through specified points by attaching suitable numbers of weights called ducks. The splines assumed the shape of minimal strain and therefore was both mechanically and visually pleasing.

This meant that the layout remained in location for the next construction as the curves could not be recreated exactly. Any damage that occured would ruin the layout completely. Another method of storing and recreating the layout was required.

In the past several decades, researchers have spent considerable time figuring out how best to fit curves to a set of data points. A lot of methods have developed according to the spline function. There are cubic splines, B-splines, Beta- splines and v-splines, etc.