How to Extend Visibility Polygons by Mirrors to Cover Invisible Segments

Vaezi, Arash; Ghodsi, Mohammad

doi:10.1007/978-3-319-53925-6_4

Cited by 3 publications

(3 citation statements)

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“…This is a natural and non-trivial extension of the classical art gallery setting. This setting has been considered before in few papers [2,3,4,5]. The problem considered in this paper is to find a minimum number of edges that can be converted to mirrors so that the visibility region of a given point gets expanded by an area of k. Depending on the reflection type (specular or diffuse) and number (single or multiple) one can consider four cases.…”

Section: Our Resultsmentioning

confidence: 99%

“…Rays may be permitted to bounce a limited number of times or travel through a limited number of edges. The viewpoint q may become a segment inside P [2].…”

Section: Our Resultsmentioning

confidence: 99%

“…We dealt with another version of the problem of extending visibility polygons in another paper [3] and we improved our results in [2]. In those papers, we had a given object (a point or a segment) as a target inside a simple polygon P. This target is not visible to the given viewer (a point).…”

Section: Our Resultsmentioning

confidence: 99%

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Visibility Extension via Reflective Edges to an Exact Quantity

Vaezi,

Ghodsi

2018

Preprint

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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.

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Section: Our Resultsmentioning

confidence: 99%

“…Rays may be permitted to bounce a limited number of times or travel through a limited number of edges. The viewpoint q may become a segment inside P [2].…”

Section: Our Resultsmentioning

confidence: 99%