Existence of a Convex Polyhedron with Respect to the Given Radii

06/19/2019
by   Supanut Chaidee, et al.
0

Given a set of radii measured from a fixed point, the existence of a convex configuration with respect to the set of distinct radii in the two-dimensional case is proved when radii are distinct or repeated at most four points. However, we proved that there always exists a convex configuration in the three-dimensional case. In the application, we can imply the existence of the non-empty spherical Laguerre Voronoi diagram.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
09/06/2023

Most likely balls in Banach spaces: existence and non-existence

We establish a general criterion for the existence of convex sets of fix...
research
03/27/2020

Barycentric cuts through a convex body

Let K be a convex body in ℝ^n (i.e., a compact convex set with nonempty ...
research
10/21/2022

Blocking Delaunay Triangulations from the Exterior

Given two distinct point sets P and Q in the plane, we say that Q blocks...
research
07/24/2023

On Maximizing the Distance to a Given Point over an Intersection of Balls II

In this paper the problem of maximizing the distance to a given fixed po...
research
01/22/2021

Homotopy Methods for Eigenvector-Dependent Nonlinear Eigenvalue Problems

Eigenvector-dependent nonlinear eigenvalue problems are considered which...
research
07/21/2014

Certifying the Existence of Epipolar Matrices

Given a set of point correspondences in two images, the existence of a f...
research
11/04/2019

Fast Reliability Ranking of Matchstick Minimal Networks

In this article, we take a closer look at the reliability of large minim...

Please sign up or login with your details

Forgot password? Click here to reset