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# Lec16 - Proximity Planar triangulations Problem definitions...

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Problem definitions, 1 TRIANGULATION INSTANCE: Set S = { p 1 , p 2 , ..., p N } of N points in the plane. QUESTION: Join the points in S with nonintersecting straight line segments so that every region internal to the convex hull of S is a triangle. Proximity Planar triangulations A triangulation for a set S is not necessarily unique. As a planar graph, a triangulation on N vertices has 3 N - 6 edges.

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Problem definitions, 2 CONSTRAINED TRIANGULATION INSTANCE: Set S = { p 1 , p 2 , ..., p N } of N points in the plane, and set E = { { p i , p j }, … } of nonintersecting edges on S . QUESTION: Join the points in S with nonintersecting straight line segments so that every region internal to the convex hull of S is a triangle and every edge of E is in the triangulation. Proximity Planar triangulations
Problem definitions, 3 POLYGON TRIANGULATION INSTANCE: Polygon P = { p 1 , p 2 , ..., p N } of N points in the plane. QUESTION: Triangulate the interior of P . As a polygon, P has a set of edges by definition, hence POLYGON TRIANGULATION is a special case of CONSTRAINED TRIANGULATION.

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Lec16 - Proximity Planar triangulations Problem definitions...

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