23 citations · 67 across the 33 of their papers we have counts for
5 papers · 1 filter
The Topology of the set of line Transversals
Otfried Cheong, Xavier Goaoc, Andreas F. Holmsen
We prove that for any set of pairwise disjoint open convex sets in , the connected components of the set of lines intersecting every member of are co…
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 in any desired orientation is the largest inscribed ball of . Th…
Shortcuts for the Circle
Sang Won Bae, Mark de Berg, Otfried Cheong +2
Let be the unit circle in . We can view as a plane graph whose vertices are all the points on , and the distance between any two points on is the lengt…
Geometric Permutations of Non-Overlapping Unit Balls Revisited
Jae-Soon Ha, Otfried Cheong, Xavier Goaoc +1
Given four congruent balls in that have disjoint interior and admit a line that intersects them in the order , we show that the distance between the cent…
Lines pinning lines
Boris Aronov, Otfried Cheong, Xavier Goaoc +1
A line g is a transversal to a family F of convex polytopes in 3-dimensional space if it intersects every member of F. If, in addition, g is an isolated point of the space of line…