Voronoi diagram of Delaunay triangulation
returns the Voronoi vertices
V and the Voronoi regions
r of the points in a Delaunay triangulation. Each region in
r represents the points surrounding a triangulation vertex
that are closer to that vertex than any other vertex in the triangulation. The
collection of Voronoi regions make up a Voronoi diagram.
2-D Delaunay Triangulation
Compute the Voronoi vertices and regions of a 2-D Delaunay triangulation.
Create a Delaunay triangulation from a set of 2-D points.
P = [ 0.5 0 0 0.5 -0.5 -0.5 -0.2 -0.1 -0.1 0.1 0.1 -0.1 0.1 0.1 ]; DT = delaunayTriangulation(P);
Compute the Voronoi vertices and regions.
[V,r] = voronoiDiagram(DT);
Display the connectivity of the Voronoi region associated with the 3rd point in the triangulation.
ans = 1×4 1 6 10 3
Display the coordinates of the Voronoi vertices bounding the 3rd region. The
Inf values indicate that the region contains points on the convex hull.
ans = 4×2 Inf Inf 0.7000 -1.6500 -0.0500 -0.5250 -1.7500 0.7500
DT — Delaunay triangulation
Delaunay triangulation, specified as a scalar
V — Voronoi vertices
Voronoi vertices, returned as a 2-column matrix (2-D) or a 3-column matrix
(3-D). Each row of
V contains the coordinates of a
The Voronoi regions associated with points that lie on the convex hull of
the triangulation vertices are unbounded. Bounding edges of these regions
radiate to infinity. The first vertex in
V represents the
vertex at infinity and is designated with
r — Voronoi regions
Voronoi regions, returned as a cell array whose elements contain the
connectivity of the Voronoi vertices in
V. The points in
each row of
r form the bounding region associated with
the corresponding row in the
Introduced in R2013a