## 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.