M. Dobbins

activity

20152019

collaborators

6 papers

math.MG2019

The Inverse Kakeya Problem

Sergio Cabello, Otfried Cheong, Michael Gene Dobbins

We prove that the largest convex shape that can be placed inside a given convex shape $Q \subset R^{d}$ in any desired orientation is the largest inscribed ball of $Q$ . Th…

cs.CG2019

A Universality Theorem for Nested Polytopes

Michael G. Dobbins, Andreas Holmsen, Tillmann Miltzow

In a nutshell, we show that polynomials and nested polytopes are topological, algebraic and algorithmically equivalent. Given two polytops $A \subseteq B$ and a number $k$ , the Nest…

cs.CG2018

Smoothed Analysis of the Art Gallery Problem

Michael Gene Dobbins, Andreas Holmsen, Tillmann Miltzow

In the Art Gallery Problem we are given a polygon $P \subset [0, L]^{2}$ on $n$ vertices and a number $k$ . We want to find a guard set $G$ of size $k$ , such that each point in $P$ is s…

math.MG2018

Barycenters of points in polytope skeleta

Michael Gene Dobbins, Florian Frick

The first author showed that for a given point $p$ in an $nk$ -polytope $P$ there are $n$ points in the $k$ -faces of $P$ , whose barycenter is $p$ . We show that we can increase the d…

math.MG2017

Shadows of a Closed Curve

Michael Gene Dobbins, Heuna Kim, Luis Montejano +1

A shadow of a geometric object $A$ in a given direction $v$ is the orthogonal projection of $A$ on the hyperplane orthogonal to $v$ . We show that any topological embedding of a cir…

cs.CG2015

The Shadows of a Cycle Cannot All Be Paths

Prosenjit Bose, Jean-Lou De Carufel, Michael G. Dobbins +2

A "shadow" of a subset $S$ of Euclidean space is an orthogonal projection of $S$ into one of the coordinate hyperplanes. In this paper we show that it is not possible for all three…