4
votes
1answer
375 views

Any reference to an algorithm for finding the largest empty circle on a sphere (with great-circle distance)?

Given a set $S$ of 2D points in the plane there are known algorithms for finding the largest empty circle ($LEC$) of the set of points. The $LEC$ problem is stated in this way: find a $LEC$ whose ...
2
votes
1answer
178 views

Regularity of Delaunay triangulation of a hypercube

First using a three dimensional unit cube as an example for the term "regularity", we can have two possible triangulations: (A) (B) We say the lower triangulation is more "regular" than upper ...
6
votes
2answers
292 views

Intersection of 2 visibility polygons

Let $P$ be a simple, closed and bounded polygon and $p_1,p_2 \in \mathrm{int}(P)$ be two points in its interior. Is it true that the intersection of the visibility polygons of $p_1$ and $p_2$ is ...
3
votes
1answer
177 views

What properties does generalized Delaunay triangulation have?

Suppose that instead of the usual circle, we pick some other convex set D and make the Delaunay triangulation of a finite planar point set with respect to this set, i.e. connect two points if there is ...
1
vote
0answers
141 views

Compute generalized pentagram map

Hi, (This is my first question on MathOverflow! :-) Imagine you have a set of points $S = \{p_1, \ldots, p_n\}$ in $\mathbb{R}^d$, of which $t$ are "bad". I want to compute a "safe convex hull", ...
2
votes
2answers
457 views

Decomposing a polygon with holes

It is known that given a polygon $P$ with holes it is NP-hard to find a decomposition of $P$ into convex polygons, s.t. their number is minimized (even if Steiner points are allowed). I am wondering ...
8
votes
3answers
716 views

Complexity of matching red and blue points in the plane.

I'm just asking because I'm curious. I was seeking references on the following problem, that a friend exposed to me last holidays : Problem Given $n$ red points and $n$ blue points in the plane in ...
1
vote
1answer
441 views

Graph drawing: unrooted undirected tree graphs with specified edge lengths.

Has Joseph Felsenstein's equal daylight layout been analyzed by the graph drawing community? The following description is taken from his drawtree documentation: "This iteratively improves an ...
16
votes
2answers
2k views

Missing document request

I received a request for another long-lost document: I am wondering if there is any way I might obtain a copy of The geometry of circles: Voronoi diagrams, Moebius transformations, ...