Optimal placement of convex polygons to maximize point containment
Computational Geometry: Theory and Applications
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We present a diagram that captures containmen information for scalable rotated and ranslated versions of a convex polygon. For a given polygon P and a contact point q in a point set S , the diagram parameterizes possible translations, rotations, and scales of he polygon in order to represent containmen regions for each additional point v ∈ S . We present geometric and combinatorial properties for this diagram, and describe how it can be computed and used for solving several geometric problems.