We study problems that arise in the context of covering certain geometric objects (so-called seeds, e.g., points or disks) by a set of other geometric objects (a so-called cover, e.g., a set of disks or homo-thetic triangles). We insist that the interiors of the seeds and the cover elements are pairwise disjoint, but they can touch. We call the contact… (More)
We show that any two outer-triangulations on the same closed surface can be transformed into each other by a sequence of diagonal ips, up to isotopy, if they have a suuciently large and equal number of vertices.
The problem of computing a representation of the stabbing lines of a set S of segments in the plane was solved by Edelsbrunner et al. We provide efficient algorithms for the following problems: computing the stabbing wedges for S, finding a stabbing wedge for a set of parallel segments with equal length, and computing other stabbers for S such as a… (More)
We study the relationship between some alternative deenitions of the concept of the width of a convex set on the sphere. Those relations allow to characterize whether a convex set on the sphere can pass through a spherical interval by rigid motions. Finally, we give an optimal algorithm to compute the width on the sphere.
We consider whether any two triangulations of a polygon or a point set on a non-planar surface with a given metric can be transformed into each other by a sequence of edge flips. The answer is negative in general with some remarkable exceptions, such as polygons on the cylinder, and on the flat torus, and certain configurations of points on the cylinder. 1.… (More)