6 papers · 1 filter
Differentiable Approximations for Distance Queries
Ahmed Abdelkader, David M. Mount
The widespread use of gradient-based optimization has motivated the adaptation of various classical algorithms into differentiable solvers compatible with learning pipelines. In th…
Convex Approximation and the Hilbert Geometry
Ahmed Abdelkader, David M. Mount
The efficient representation of convex bodies in multi-dimensional spaces is a fundamental problem in computational geometry. Several key developments were recently brought about u…
Smooth Distance Approximation
Ahmed Abdelkader, David M. Mount
Traditional problems in computational geometry involve aspects that are both discrete and continuous. One such example is nearest-neighbor searching, where the input is discrete, b…
Approximate Nearest Neighbor Searching with Non-Euclidean and Weighted Distances
Ahmed Abdelkader, Sunil Arya, Guilherme D. da Fonseca +1
We present a new approach to approximate nearest-neighbor queries in fixed dimension under a variety of non-Euclidean distances. We are given a set of points in $\mathbb{R}…
Approximate Nearest-Neighbor Search for Line Segments
Ahmed Abdelkader, David M. Mount
Approximate nearest-neighbor search is a fundamental algorithmic problem that continues to inspire study due its essential role in numerous contexts. In contrast to most prior work…
Sampling Conditions for Conforming Voronoi Meshing by the VoroCrust Algorithm
Ahmed Abdelkader, Chandrajit L. Bajaj, Mohamed S. Ebeida +4
We study the problem of decomposing a volume bounded by a smooth surface into a collection of Voronoi cells. Unlike the dual problem of conforming Delaunay meshing, a principled so…