Reliable and Efficient Computations with Algebraic Curves

operations on polygons and arrangement computations. In principle, it generalizes nicely from line segments to algebraic curves.

However, what is simple in the case of line segments, namely the analysis of a single curve and a pair of curves, becomes a nontrivial task for algebraic curves. I report on new algorithms for analyzing single curves and pair of curves and their implementation in CGAL.

The new algorithms allow us to compute the exact arrangement of hundreds of low degree algebraic curves; a computation that was assumed to be impossible only a few years ago.