voronoiDiagram

Returns vertices and cells of the Voronoi diagram of a delaunayTriangulation.

Category: Mathematics > Computational Geometry

Syntax

[V, R] = voronoiDiagram(DT)

Description

The function is the object-oriented way to get the Voronoi diagram. Cell R{k} belongs to the point k of DT.Points. Points on the convex hull have unbounded cells, which is why the index 1 (the point at infinity) appears in their lists.

Input arguments

DT

A delaunayTriangulation object.

Output arguments

V

Matrix of Voronoi vertices. The first row is [Inf Inf] and stands for the point at infinity.

R

Cell array, one entry per input point, listing the row indices into V that bound its cell. A cell containing 1 is unbounded.

Example

Cells of a square with a center point

P = [0 0; 1 0; 1 1; 0 1; 0.5 0.5];
DT = delaunayTriangulation(P);
[V, R] = voronoiDiagram(DT);
disp(size(V))
disp(numel(R))

     5     2
     5

See also

voronoin voronoi delaunayTriangulation convexHull