Visibility Extension via Reflective Edges to an Exact Quantity

Abstract

We consider extending the visibility polygon (V P ) of a given point q (V P (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 V P (q) are NPcomplete. 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.