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sus11005 committed Nov 21, 2014
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Expand Up @@ -2,5 +2,8 @@ PolygonTriangulation
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Class Project of Introduction to Computational Geometry - Fall 2014
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In computational geometry, polygon triangulation is the decomposition of a polygonal area (simple polygon) P into a set of triangles, i.e., finding the set of triangles with pairwise non-intersecting interiors whose union is P. The problem of triangulating a simple polygon is an old and important computational problem. It can be simply stated as finding all the diagonals from one vertex to another in a given polygon that will partition the polygon into a set of triangles. A simple polygon is a polygon that has no self-intersections, n edges and n vertices. Polygon triangulation is used in many areas, and the search for optimal algorithms to compute it has a long history. Many algorithms assume that the polygon is already triangulated, and several would not be possible without the triangulation. Given a triangulation, other partitions such as convex or star polygons can easily be found in linear time. Some algorithms that rely entirely upon partitioned polygons are character recognition, shading and shortest path.

The algorithm of Seidel will be implemented in Java programming language. There will be a user interface where a user can draw a simple polygon. If the polygon is crossed by itself or it has hole(s), the program will warning the user and erase the content of the current window to draw another polygon. Otherwise the tool will triangulate the polygon and the user will see the step by step animation how the polygon is triangulated. In this procedure user will understand the steps of the algorithm in more detail and how the algorithm works visually. It will give the user in-depth knowledge of the algorithm without reading the text.

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