CS 3414 Problem Statement 2

One approach to drawing a smooth curve that passes through a specified set of points is to use a parametric representation of the curve. The idea is to represent the curve by two functions x(t) and y(t), one for the x-coordinate and one for the y-coordinate. A good choice for these functions is cubic splines.

The core of a drawing program would have to be a routine that computes these splines, given the specified points. To make things more challenging, there are several other issues that one might have to think about. For example, here are a few:

• To do complicated drawings (e.g., cursive letters), it must be possible to specify nonsmooth corners and points of discontinuity. Many splines would be needed, in general.
• If it is desired that the curve appear to move as control points are moved then it will be important to compute and evaluate the interpolants as quickly as possible.
• How flexible will the program be? Will users be allowed to add new control points in the middle of a curve? Will they be allowed to break an existing spline by introducing a a discontinuity in function value or derivative? Will they be allowed to smoothly link curves together?