Theorems of Algebraic Numbers: Thom's Lemma and the Routh-Hurwitz Theorem are presented, which state that theorems can be applied to both classical and ideal geometry.Expand

We present efficient parallel algorithms for several basic problems in computational geometry: convex hulls, Voronoi diagrams, detecting line segment intersections, triangulating simple polygons,… Expand

The potato-peeling problem asks for the largest convex polygon contained inside a given simple polygon. We give anO(n7) time algorithm to this problem, answering a question of Goodman. We also give… Expand

A new technique is introduced that computes the Voronoi diagram ofX inO(n logn) time, which improves on several previous algorithms for special cases of the problem.Expand

A new framework for dynamic labeling is developed that achieves the desiderata and allows for fast interactive display by moving all of the selection and placement decisions into the preprocessing phase and a solution to a simple version of the problem is given.Expand

A new C/C++ library for robust numeric and geometric computation based on the principles of Exact Geometric Computation (EGC) is described, and for the first time, any programmer can write robust and efficient algorithms.Expand