Block Method for Convex Polygon Triangulation
In this paper, the block method for convex polygon triangulation is presented. The method is based on the usage of the previously generated triangulations for polygon with smaller number of vertices. In the beginning, we establish some relations between the triangulations of the polygons having the consecutive number of vertices. Using these relations, we decompose the triangulation problem into subproblems which are themselves smaller instances of the starting problem. The recursion with memoization is used to avoid repeating the calculation of results for previously processed inputs. The corresponding algorithm is developed and implemented.
convex polygon triangulation recursion memoization catalan numbers divide & conquer algorithms