4.7.1 Sampling 4.7.2 Line Tracing Interval arithmetic may form the basis for rendering algorithms other than those given here.
Sophisticated methods are certainly possible.
Care should be taken to preserve the strength of the underlying interval arithmetic, so that algorithm guarantees may be given. The output of the algorithm is a collection of line segments, which approximate G . Using a linear interval arithmetic in place of a constant interval arithmetic allows a similar algorithm to be constructed, which returns a collection of polygons which include G . With domain and continuity tracking in conjunction with automated derivative analysis, some of the assumptions may be lifted, as they may be verified as the algorithm proceeds. Many algorithms which use interval arithmetic, do so peripherally, and would benefit from a re-engineering which allows the concepts of interval arithmetic to permeate the entire algorithm.