The foundation of delaunay triangulation and constrained delaunay triangulation is the basis of three dimensional geographical information system which is one of hot issues of the contemporary era; moreover it is widely applied in finite element methods, terrain modeling and object reconstruction, euclidean minimum spanning tree and other applications. An algorithm for generating constrained delaunay triangulation in two dimensional planes is presented. The algorithm permits constrained edges and polygons (possibly with holes) to be specified in the triangulations, and describes some data structures related to constrained edges and polygons. In order to maintain the delaunay criterion largely，some new incremental points are added onto the constrained ones. After the data set is preprocessed, the foundation of constrained delaunay triangulation is showed as follows: firstly, the constrained edges and polygons generate initial triangulations，then the remained points completes the triangulation . Some pseudo-codes involved in the algorithm are provided. Finally, some conclusions and further studies are given.