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  "body": "\n## Summary\n\nA Delaunay triangulation of a finite point set in the plane is a special [[triangulation|V0B6C6TMWD]] of it.\nThe circumcircle of each of its triangles has no point of the set inside.\nAmong all triangulations of the set, it maximizes the smallest angle, so it avoids thin triangles.\nIt is the geometric dual of the [[Voronoi diagram|QDNEBBVZ84]], and it is widely used for meshes.\n\n## Explanations\n\n### L1 human\n\nTake a triangulation of a set of points and look at the circle through the three corners of each triangle.\nThe triangulation is Delaunay when no other point of the set sits strictly inside any of these circles.\nFor four points at the corners of a square, all four lie on one circle, and both diagonals give a Delaunay triangulation.\nIf you push one corner slightly outward, only one diagonal remains Delaunay.\n",
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