emptycircumcircle
emptycircumcircle is a term used in computational geometry to describe the empty circumcircle property of a triangulation of a finite set P of points in the plane. The property states that for every triangle in the triangulation, the circumcircle determined by its three vertices contains no other point of P in its interior. When this condition holds for all triangles, the triangulation is called a Delaunay triangulation.
The empty circumcircle property is central to Delaunay triangulations. Among all triangulations of a given point
Algorithmically, many triangulation methods are designed to enforce the empty circumcircle property. Incremental construction such as
In higher dimensions, the analogous condition uses circumspheres instead of circumcircles, yielding Delaunay tessellations. Degenerate cases
Applications of structures with the empty circumcircle property include mesh generation for finite element methods, computer