Restricted-orientation convexity is the study of geometric objects whose intersection with lines from some fixed set is empty or connected. We have studied the properties of restri...
We show that any point in the convex hull of each of (d + 1) sets of (d + 1) points in Rd is contained in at least (d + 2)2 /4 simplices with one vertex from each set.
We propose a novel subdivision of the plane that consists of both convex polygons and pseudotriangles. This pseudo-convex decomposition is significantly sparser than either conve...
Oswin Aichholzer, Clemens Huemer, S. Kappes, Betti...
Let B be a set of n arbitrary possibly intersecting convex obstacles in Rd. It is shown that any two points which can be connected by a path avoiding the obstacles can also be c...
We present a convex formulation of dictionary learning for sparse signal decomposition. Convexity is obtained by replacing the usual explicit upper bound on the dictionary size by...