Three-Dimensional Voronoi Mesh

newsites

number ofsites

12

z

0.05

nextsite

A three-dimensional Voronoi diagram partitions 3D space into a set of polyhedra linked to sites. Points inside the polyhedron for a site

P=(

x

i

,

y

i

,

z

i

}

are closer to

P

than to any other site.

This Demonstration lets you look inside a 3D Voronoi diagram using two-dimensional cross sections perpendicular to the

z

axis.

The cross sections are sets of polygons that change with each value of

z

as you drag the slider. The "next site" button takes a cross section at

z

i

for the next site and shows the site as the point

(

x

i

,

y

i

}

.

External Links

Voronoi Diagrams

Permanent Citation

Erik Mahieu

"Three-Dimensional Voronoi Mesh"
http://demonstrations.wolfram.com/ThreeDimensionalVoronoiMesh/
Wolfram Demonstrations Project
Published: September 20, 2016