19 citations · 59 across the 23 of their papers we have counts for
4 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…
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…
Line transversals to disjoint balls
Ciprian Borcea, Xavier Goaoc, Sylvain Petitjean
We prove that the set of directions of lines intersecting three disjoint balls in in a given order is a strictly convex subset of . We then generalize this result to …