When such a triangulation exists it is a special case of the Delaunay triangulation, and consists of the union of the Gabriel graph and convex hull.
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Thus, a circle having that edge as diameter must be empty of vertices, so the Pitteway triangulation consists of the Gabriel graph together with the convex hull of the point set.
triangulation | Delaunay triangulation | Triangulation station | Triangulation (geometry) | Triangulation | Polygon triangulation | Delaunay Triangulation | Causal dynamical triangulation |