Delaunay & Voronoi

The Delaunay triangulation and Voronoi tessellation are mathematical "duals," with numerous applications in engineering, mathematics, topology and computer science, formally defined by Georgy Voronoi in 1908, and expanded by Boris Delaunay in 1934.

The profound connection between the two lies in the circumcircle. A triangulation is strictly "Delaunay" if the circumcircle of every triangle contains no other points in its interior (the empty circumcircle property). Furthermore, the vertices of the Voronoi diagram are exactly the circumcenters of the Delaunay triangles. By drawing lines between the circumcenters of adjacent triangles, this visualization seamlessly generates the Voronoi edges, illustrating how these two structures are two sides of the same coin.

To use simply upload your image and then toggle between Points, Voronoi, triangles and circumcircles using keyboard shortcuts P, V, T, C then pres S to save.

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