Delaunay triangulations, theory vs practice.

International audienceThirty years ago, at the early ages of computational geometry, the game of computational geometers was to design fancy algorithms with optimal theoretical complexities. The result was usually an algorithmic journal article, but not an implementation. In the same period, some people were actually cod- ing geometric algorithms, but without regard for the asymptotic complexities, and without proof of cor- rectness of the result. They were not using the algo- rithms designed by theoreticians for two reasons [14]: - these algorithms were too intricate and - they rely on the arithmetic of real numbers, which differs from the floating-point arithmetic of comput- ers. These drawbacks of old computational geometry al- gorithms have been addressed in various ways to ob- tain algorithms that reconcile robustness, practical ef- ficiency, and theoretical guarantees. The aim of this talk is to illustrate some steps of this transition from theoretical stuff to efficient algo- rithms actually used in industrial applications. I will do this using my favorite problem: the construction of the Delaunay triangulation of a set of points and the dynamic maintenance of such a triangulation under point insertions and deletions