📐 Delaunay Triangulation Generator

A Delaunay triangulation of a set of points is a triangulation in which no point lies inside the circumcircle of any triangle. This empty-circumcircle property makes it maximize the minimum angle across all triangles, so it avoids the long, skinny slivers that other triangulations produce. It is named after the Russian mathematician Boris Delaunay, who introduced it in 1934, and it is the go-to triangulation whenever well-shaped triangles matter.

The Delaunay triangulation is the dual of the Voronoi diagram. If you connect every pair of points whose Voronoi cells share an edge, you get exactly the Delaunay triangulation. In other words, each Delaunay edge crosses one Voronoi edge, and each triangle corresponds to a Voronoi vertex at its circumcenter. Toggle the Voronoi overlay to see both structures drawn together and watch how the cells and triangles line up.

Delaunay triangulations show up across science and engineering: terrain and mesh generation for maps and games, finite element analysis where well-conditioned triangles keep simulations stable, spatial interpolation of scattered data, and computer graphics and 3D reconstruction where point clouds are turned into surfaces. Their quality guarantees make them a default choice for turning scattered points into a usable mesh.