Visibility Extension via Reflective Edges to an Exact Quantity
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We consider extending the visibility polygon of a given point q, inside a simple polygon P by converting some edges of P to mirrors. We will show that several variations of the problem of finding mirror-edges to add precisely k units of area to VP(q) are NP-complete. The optimal cases are NP-hard. We are unaware of any result on adding an exact number to a polygon, or covering an area with an exact surface. We deal with both single and multiple reflecting mirrors for both specular or diffuse types of reflections.
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