Decomposing a simple polygon into simpler components is one of the basic tasks in computational geometry and its applications. The most important simple polygon decomposition is triangulation. Different techniques for triangulating a simple polygon were designed. The first part of the paper is an overview of triangulation algorithms based on diagonal insertion. In the second part, we present algorithms based on Delaunay triangulation. The basic ideas and approach for each algorithm are presented. Finally, some representative algorithms are compared by efficiency.
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