A constrained Delaunay triangulation is a Delaunay triangulation of a set of points and straight-line segments. A constrained Delaunay triangulation is a basic tool for describing a topographic surface in several applications. In this paper, the definition of constrained Delaunay triangulation is introduced and its basic properties are discussed. Existing algorithms for constrained Delaunay triangulation are briefly analyzed. A new on-line algorithm for constrained Delaunay triangulation that is based on the stepwise refinement of an existing triangulation by the incremental insertion of points and constraint segments is proposed.