The Robustness Issue

This article rst recalls with some examples the damages that numerical inaccuracy of oating point arithmetic can cause during geometric computations, in methods from Computational Geometry, Computer Graphics or CADCAM. Then it surveys the various approaches proposed to overcome inaccuracy diiculties. It seems that the only way to achieve robustness for existing methods from Computational Geometry is exact computation, it is the "Exact Computation Paradigm" of C.K. Yap and T. Dub e. In Computer Graphics or CADCAM, people prefer to abandon methods and data structures not robust enough against inaccuracy, namely Boundary Representations and related methods, this may be called the "Approximate Computation Paradigm".