Triangulations are important objects in computational geometry and has a lot of application, such as computer graphics, finite element analysis, mesh generation, and so on. In this paper, we present an algorithm that generate a variety of edge-constrained triangulations. Enumerating all the triangulations of a given point set is one of strategies to obtain the best triangulation for designated criterias. However, when an input point set is large, it takes a huge amount of computation time. Hence, we present an algorithm that generate a lot of triangulations.

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