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We consider extending the visibility polygon of a given point q inside a simple polygon by converting one or some of the edges to mirrors. It is known that the visibility polygon of a point inside a polygon in the presence of a mirror can be computed in linear time. We propose a linear time algorithm that checks whether a given segment inside a simple polygon is visible by a given point q via a mirror-edge, and finds all such edges. And we prove that finding edges to add exactly k unit squares to the visibility polygon of a query point q in most cases is NP-complete and its minimization is NP-hard. These cases contain single and muliple, either with secular or difuse reflections. Moreover,... 

This document deals with the following results in details:Given a simple polygon P with $n$ vertices, the visibility polygon (VP) of a point q, or a segment pq inside P can be computed in linear time. It is known that the visibility polygon of a point inside a polygon in the presence of a mirror can be computed in linear time. We propose a linear time algorithm to extend the VP of a viewer (point or segment) by converting some edges of P into mirrors (reflecting-edges with specular type of reflection), such that a given non-visible segment uw can also be seen from the viewer.Various definitions for the visibility of a segment, such as weak, strong, or complete visibility, are considered. Our...