Constrained Delaunay triangulation

In computational geometry, a constrained Delaunay triangulation is a generalization of the Delaunay triangulation that forces certain required segments into the triangulation.[1][2] Because a Delaunay triangulation is almost always unique, often a constrained Delaunay triangulation contains edges that do not satisfy the Delaunay condition. Thus a constrained Delaunay triangulation often is not a Delaunay triangulation itself.

In topographic surveying, one constructs a triangulation from points shot in the field. If an edge of the triangulation crosses a river, the resulting surface does not accurately model the path of the river. So one draws breaklines along rivers, edges of roads, mountain ridges, and the like. The breaklines are used as constraints when constructing the triangulation.