Arithmetic Issues in Geometric Computations

This paper rst recalls by some examples the damages that the numerical inaccuracy of the oating-point arithmetic can cause during geometric computations, and it intends to explain why damages for geometric computations diier from those met in numerical computations. Then it surveys the various approaches proposed to overcome inaccuracy diiculties; conservative approaches use classical geometric methods but withèxotic' arithmetics instead of the standard oating-point one; radical ones go farther and reject classical techniques, considering them not robust enough against inaccuracy.

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