MeshCellHighlight allows you to specify highlighting for parts of a VoronoiMesh:

Individual cells can be highlighted using their cell index:

Or by the cell itself:

MeshCellLabel can be used to label parts of a VoronoiMesh:

Individual cells can be labeled using their cell index:

Or by the cell itself:

MeshCellMarker can be used to assign values to parts of a VoronoiMesh:

Use MeshCellLabel to show the markers:

MeshCellShapeFunction allows you to specify functions for parts of a VoronoiMesh:

Individual cells can be drawn using their cell index:

Or by the cell itself:

MeshCellStyle allows you to specify styling for parts of a VoronoiMesh:

Individual cells can be highlighted using their cell index:

Or by the cell itself:

Use a theme with grid lines and a legend:

Use a theme to draw a wireframe:

Create an interactive Voronoi mesh with draggable points. Use Click on the Voronoi mesh to add and remove draggable points:

Voronoi meshes for simple point configurations including a grid:

A circle of points:

Create an interactive map of the closest large city in Italy. Start by getting names and coordinate data for large cities in Italy:

Nearest function for labeling region cells:

Generate a Voronoi mesh from city coordinates:

Create a tooltip map from the Voronoi mesh:

Mouse over the map to get the name of the closest large city:

Given a 2D lattice basis:

Generate lattice points:

Generate and visualize the Voronoi cells, also known as Brillouin zones:

Create a polygonal mosaic from an image:

Find the edges of the image:

Create a Voronoi mesh from the edge positions:

Recursively apply VoronoiMesh to the mean vertex positions of the precursive Voronoi cells to create a more uniform mesh:

Color each polygon with the image color coinciding with its mean vertex positions:

Create a jigsaw puzzle from a random Voronoi mesh:

Extract lines from the mesh:

Define a function that converts a line to an interlocking edge:

Replace lines of sufficient length with an interlocking edge:

Visualize the result:

Visualize a piecewise constant interpolation of a function over a set of random point samples:

Voronoi mesh from , sample coordinates:

Function to rescale values to :

Piecewise constant contour plot of sample data:

A similar plot can also be achieved with ListContourPlot:

Plan a path for a point robot through a random set of point obstacles by following Voronoi edges:

Generate Voronoi edges around the obstacles:

Create an undirected Graph from the Voronoi edges with their lengths as edge weights:

Use Nearest function to find the closest Voronoi vertices to the start and end points:

Drag starting or ending points to explore different paths (red):