A modification of Graham's algorithm for determining the convex hull of a finite planar set.
Computing parametric rational generating functions with a primal Barvinok algorithm.
Construction of minimal bracketing covers for rectangles.
Discrete geometry and numeration
On the number of intersections of two polygons
We study the maximum possible number of intersections of the boundaries of a simple -gon with a simple -gon in the plane for . To determine the number is quite easy and known when or is even but still remains open for and both odd. We improve (for ) the easy upper bound to and obtain exact bounds for
Tesselation of a triangle by repeated barycentric subdivision.
Windings of planar random walks and averaged Dehn function
We prove sharp estimates on the expected number of windings of a simple random walk on the square or triangular lattice. This gives new lower bounds on the averaged Dehn function, which measures the expected area needed to fill a random curve with a disc.