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.
In [66], an implicit curve approximation algorithm is given; it is argued, therein, that the given algorithm is more reliable than those based on sampling. This is clear, although the algorithm given assumes the following:
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.
An adoption of linear interval arithmetic in place of constant interval arithmetic increases the efficiency of a method, and may be enacted using a minimal expenditure of effort. Portions which performed derivative analysis may be removed, as such analysis is done automatically, within the linear interval arithmetic library. The desired results may be obtained from the linear interval arithmetic library. A generalized interval arithmetic library may use demotions to shield an application from the interval arithmetic being used.
Jeff Tupper | March 1996 |