2
votes
2answers
132 views

Largest inscribed rectangle inside a convex polygon

It has been proved by Radziszewski in this paper K. Radziszewski. Sur une probleme extremal relatif aux gures inscrites et circonscrites aux gures convexes. Ann. Univ. Mariae Curie-Sklodowska, Sect. ...
4
votes
1answer
277 views

Biggest ball included in an intersection of balls

I would like to prove that for any family of balls $\{B(c_i,r_i)\}_i \subset \mathbb{R}^d$ such that $\{c_1, \dots, c_n\} \subset \bigcap_i B(c_i,r_i) $ and $\forall i, r_i \geq 1$, there exists a ...
1
vote
0answers
88 views

Boundary surfaces in a 3d Voronoi tessellation with obstacles

Let $x_1,\dots,x_n$ be a set of points in $\mathbb{R}^3$ and let $\mathcal{O}_1 ,\dots, \mathcal{O}_m$ denote a set of polyhedral obstacles. What is the name for the surfaces that describe the ...
15
votes
9answers
2k views

Determine if circle is covered by some set of other circles

Suppose you have a set of circles $\mathcal{C} = \{ C_1, \ldots, C_n \}$ each with a fixed radius $r$ but varying centre coordinates. Next, you are given a new circle $C_{n+1}$ with the same radius ...