Move the points[br]Press "Go"[br]Be amazed!

[b][size=150][url=https://en.wikipedia.org/wiki/Voronoi_diagram]Voronoi diagram[/url][/size][/b][br]We are given a finite set of points {[i]p[/i][sub]1[/sub], …, [i]p[/i][sub][i]n[/i][/sub]} in the [url=https://en.wikipedia.org/wiki/Euclidean_plane]Euclidean plane[/url]. Voronoi cell [i]R[/i][sub][i]k[/i][/sub] corresponding to point [i]p[/i][sub][i]k[/i][/sub] consists of every point in the Euclidean plane whose distance to [i]p[/i][sub][i]k[/i][/sub] is less than or equal to its distance to any other [i]p[/i][sub][i]k[/i][/sub]. Each such cell is obtained from the intersection of [url=https://en.wikipedia.org/wiki/Half-space_%28geometry%29]half-spaces[/url], and hence it is a [url=https://en.wikipedia.org/wiki/Convex_polygon]convex polygon[/url]. The [url=https://en.wikipedia.org/wiki/Line_segment]line segments[/url] of the Voronoi diagram are all the points in the plane that are equidistant to the two nearest sites, i. e. [url=https://en.wikipedia.org/wiki/Bisection]line segment bisector[/url]. The Voronoi vertices ([url=https://en.wikipedia.org/wiki/Node_%28graph_theory%29]nodes[/url]) are the points equidistant to three (or more) sites[br][i][color=#444444][br]Liebling, T., Pournin, L. [url=http://www.math.uiuc.edu/documenta/vol-ismp/60_liebling-thomas.pdf]"Voronoi diagrams and Delaunay triangulations: ubiquitous Siamese twins"[/url]. In: Optimization Stories. Documenta Mathematica. Extra Volume ISMP. s. 419–431. 2012.[/color][/i][br][br][br]