COMPGEOM
2005
ACM
14 years 2 months ago
2005
ACM
We present a new multi-dimensional data structure, which we call the skip quadtree (for point data in R2) or the skip octree (for point data in Rd, with constant d > 2). Our da...
COMPGEOM
2005
ACM
14 years 2 months ago
2005
ACM
We present a multi-dimensional generalization of the Szemer´edi-Trotter Theorem, and give a sharp bound on the number of incidences of points and not-too-degenerate hyperplanes i...
COMPGEOM
2005
ACM
14 years 2 months ago
2005
ACM
COMPGEOM
2005
ACM
14 years 2 months ago
2005
ACM
We illustrate the Link Solver software for computing 1-link shortest paths in weighted regions. The Link Solver implements a prune-and-search method that can be used to approximat...
COMPGEOM
2005
ACM
14 years 2 months ago
2005
ACM
The persistence diagram of a real-valued function on a topological space is a multiset of points in the extended plane. We prove that under mild assumptions on the function, the p...
COMPGEOM
2005
ACM
14 years 2 months ago
2005
ACM
In this paper, we bound the difference between the total mean curvatures of two closed surfaces in R3 in terms of their total absolute curvatures and the Fr´echet distance betwee...
COMPGEOM
2005
ACM
14 years 2 months ago
2005
ACM
Let S be an ordered set of disjoint unit spheres in R3 . We show that if every subset of at most six spheres from S admits a line transversal respecting the ordering, then the ent...
COMPGEOM
2005
ACM
14 years 2 months ago
2005
ACM
COMPGEOM
2005
ACM
14 years 2 months ago
2005
ACM
An open question in Exact Geometric Computation is whether there are transcendental computations that can be made “geometrically exact”. Perhaps the simplest such problem in c...
COMPGEOM
2005
ACM
14 years 2 months ago
2005
ACM
We initiate the study of exact geometric algorithms that require limited storage and make only a small number of passes over the input. Fundamental problems such as lowdimensional...