The theory of Delaunay triangulation can be generalized to account for constrained edges also referred to as prespecified edges or break lines. This leads to the notion of
constrained Delaunay triangulation
(CDT). Constrained edges may represent rivers, roads, lake boundaries and mountain ridges in cartography, or linear features in finite element grids. CDT may also be used to construct triangulations with holes and triangulations with arbitrarily shaped (non-convex) boundaries, while preserving Delaunay properties on the interior of the triangulation away from holes and boundaries.