Note:

[V, R] = voronoiDiagram(DT)
[V, R] = voronoiDiagram(DT)
returns the
vertices V
and regions R
of
the Voronoi diagram of the points DT.X
. The region R{i}
is
a cell array of indices into V
that represents
the Voronoi vertices bounding the region. The Voronoi region associated
with the i
'th point, DT.X(i)
is R{i}
.
For 2D, vertices in R{i}
are listed in adjacent
order, i.e. connecting them will generate a closed polygon (Voronoi
diagram). For 3D the vertices in R{i}
are listed
in ascending order.
The Voronoi regions associated with points that lie on the convex
hull of DT.X
are unbounded. Bounding edges of
these regions radiate to infinity. The vertex at infinity is represented
by the first vertex in V
.
DT  Delaunay triangulation. 
V  numv byndim matrix representing
the coordinates of the Voronoi vertices, where numv is
the number of vertices and ndim is the dimension
of the space where the points reside. 
R  Vector cell array of length(DR.X) , representing
the Voronoi cell associated with each point. 
The Voronoi diagram of a discrete set
of points X
decomposes the space around each point X(i)
into
a region of influence R{i}
. Locations within the
region are closer to point i
than any other point.
The region of influence is called the Voronoi region. The collection
of all the Voronoi regions is the Voronoi diagram.
The convex hull of a set of points X
is
the smallest convex polygon (or polyhedron in higher dimensions) containing
all of the points of X
.
Compute the Voronoi Diagram of a set of points:
X = [ 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 = DelaunayTri(X) [V,R] = voronoiDiagram(dt)