Voronoitessellaatio

Voronoitessellaatio, also known as a Voronoi diagram or Voronoi partitioning, is a geometric construction that divides a plane into a set of regions. Given a set of points, called sites or seeds, a Voronoi tessellation assigns every point in the plane to the site closest to it. This results in a partitioning of the plane into convex polygons, where each polygon contains exactly one site, and all points within a polygon are closer to its corresponding site than to any other site.

The edges of the Voronoi polygons are the perpendicular bisectors of the lines connecting pairs of sites. Vertices of the diagram occur where three or more Voronoi edges meet, representing points equidistant from three or more sites. The number and arrangement of these vertices and edges depend on the configuration of the input sites.

Voronoi tessellations have numerous applications across various fields. In geography, they can be used to define areas of influence for facilities like stores or post offices. In biology, they model cell growth patterns or the distribution of biological entities. In computer science, they are employed in algorithms for nearest neighbor searches, mesh generation, and pattern recognition. The mathematical properties of Voronoi tessellations make them a fundamental tool in computational geometry.