Write a computer program computing the Voronoi diagram of asset of points in the plane. Can you do it in time O(n2logn)? Prove that condition (2) of Definition 10.3 is equivalent to condition: (2′)...

Write a computer program computing the Voronoi diagram of asset of points in the plane. Can you do it in time O(n2logn)?

Prove that condition (2) of Definition 10.3 is equivalent to condition: (2′) For any two distinct simplices σ1,σ2, Intσ1∩Int σ2=/0.10.7.Complete the proof of (1) in Lemma 10.2 (useinduction).  10.8.Prove that as phere does not have any triangulation in which every vertex belong stosix triangles. Conclude that as pherecan not betri angulated by regular hexagons. Look at ago lf ball!