This flashcard is just one of a free flashcard set. See all flashcards!
51
Give two definitions of the Voronoi diagram of a point set!
Given: Set of sites 
Closest Points
The Voronoi cell
of a site 
is given by the set of all points which are closer to than to any other site 
:
Halfspace Intersection
Each pair of sites
divides the space into a halfspace points which are closer to than to 
Then, can be described as the intersection of all halfspaces formed with other sites:
From this definition, it is obvious that all Voronoi cells are convex.
Closest Points
The Voronoi cell
of a site is given by the set of all points which are closer to than to any other site :Halfspace Intersection
Each pair of sites
divides the space into a halfspace points which are closer to than to Then,
can be described as the intersection of all halfspaces formed with other sites:From this definition, it is obvious that all Voronoi cells are convex.
Flashcard info:
Author: janisborn
Main topic: Informatik
Topic: Computergrafik
School / Univ.: RWTH Aachen
City: Aachen
Published: 18.05.2022