4.3.5 Examples of Cutting Heuristics

Many cutting heuristics are possible. The presented super-pixel renderings cut each pixel cluster into four equal pieces.

Another possibility is to consider the consraint region, and to cut each pixel cluster into two equal pieces, cutting across the longer side of the region.

After cutting is performed, the domain may be constricted to tightly bound the constrained region.

The regions exluded by such constriction are already determined exactly. The following figure illustrates

being rendered over the region , with each column representing a different cutting heuristics. As each heuristic requires a different number of interval evaluations per stage, one should not compare the different techniques based on the following figure.

The following diagram illustrates the gains possible using the different cutting heuristics.

The diagram illustrates the area contained within the constrained regions while rendering

over the region using linear interval arithmetic with various cutting heuristics. Data from a rendering using constant interval arithmetic is also included, for reference.

Jeff Tupper

March 1996