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Greatest personal satisfaction: Constrained Delaunay Triangulations, I: Combinatorial Properties. This report is an exercise in trying to make a difficult subject as transparent and easy to understand as humanly possible.

The circumscribing circle of any facet of a constrained Delaunay triangulation contains in its interior no data point if every constrained edge is a Delaunay edge.

Because any edge in a constrained Delaunay triangulation is either a Delaunay edge or a constrained edge, a conforming Delaunay triangulation is in fact a Delaunay triangulation.

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A major advantage of the method is that it does not require extra points to be added to the data set in order to ensure that the specified edges are present.

of a set of obstacle line segments in the plane is the Delaunay triangulation of the endpoint set of these obstacles with the restriction that the edge set of the triangulation contains all these obstacles.

Most recent: Aggressive Tetrahedral Mesh Improvement. construct meshes of triangles or tetrahedra (“elements”) that are suitable for applications like interpolation, rendering, terrain databases, geographic information systems, and most demandingly, the solution of partial differential equations by the finite element method.

Conforming triangulations will be described in Section Conforming Triangulations and meshes in Section Meshes.

A triangulation is a Delaunay triangulation is a constrained triangulation which is as much Delaunay as possible.

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