Computer graphics, linear interpolation, and nonstandard intervals

This document is an assessment of the value of optimal linear interpolation enclosures and of nonstandard intervals, especially with respect to applications in computer graphics, and of the extent a future IEEE interval standard should support these. It turns out that essentially all present applications of nonstandard intervals to practical problems can be matched by similarly efficient approaches based on standard intervals only. On the other hand, a number of applications were inspired by the use of nonstandard arithmetic. This suggests the requirement of a minimal support for nonstandard intervals, allowing implementations of nonstandard interval arithmetic to be compatible with the standard, while a full support by making one of the conflicting variants required seems not appropriate.