We show that in the worst case, (ndd=2e;1 +n logn) sidedness queries are required to determine whether the convex hull of n points in IRd is simplicial, or to determine the number ...
Color red and blue the n vertices of a convex polytope P in R3 . Can we compute the convex hull of each color class in o(n log n)? What if we have χ > 2 colors? What if the co...
This paper looks at axioms for convexity, and shows how they can be applied to discrete spaces. Two structures for a discrete geometry are considered: oriented matroids, and cell c...
We propose a linear in time and easy-to-implement algorithm that robustly decomposes a digital curve into convex and concave parts. This algorithm is based on classical tools in d...