3-D Voronoi Diagram

Compute the Voronoi diagram for a set of 3-D points, and plot a single region associated with one point.

Create a sample of 25 points in 3-D.

rng("default")
X = -3 + 6.*rand([25 3]);

Create the Delaunay triangulation for the set of points.

dt = delaunayTriangulation(X);

Compute the topology of the Voronoi diagram.

[V,R] = voronoiDiagram(dt);

In 3-D a Voronoi region is a convex polyhedron. To plot a single region of a Voronoi diagram, first choose a point. For example, find the point closest to the origin.

tid = nearestNeighbor(dt,0,0,0);
XR10 = V(R{tid},:);

Compute the convex hull of this point by using the convhull function.

K = convhull(XR10);

Use the resulting matrix to plot the Voronoi region associated with this point.

trisurf(K,XR10(:,1),XR10(:,2),XR10(:,3), ...
    FaceColor=[0.7 0.9 0.9],FaceAlpha=0.8)
title("3-D Voronoi Region")

Alternatively, you can use the voronoin function to compute the topology of the Voronoi diagram.

[V,R] = voronoin(X);