A simple algorithm which graphs implicit equations has been presented. The algorithm progressively renders a graph: vast stretches are initially carved out; as the algorithm proceeds, intricate details of the graph are revealed. At all times, the rendering presents completely reliable information. This contrasts strongly with traditional sampling techniques, which evade the general problem and produce renderings which have no formal connection to the underlying graph. Computers bring unheralded speed and precision to mathematical tasks, such as graphing; this thesis demonstrates that such technology may produce accurate results, contrary to common practice.
| Jeff Tupper | March 1996 |