Abstract
Given a simple polygon \(\mathcal P\) with n vertices, the visibility polygon (\(VP\)) of a point q (\(VP(q)\)), or a segment \(\overline{pq}\) \((VP(\overline{pq}))\) inside \(\mathcal P\) can be computed in linear time. We propose a linear time algorithm to extend \(VP\) of a viewer (point or segment), by converting some edges of \(\mathcal P\) into mirrors, such that a given non-visible segment \(\overline{uw}\) 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 algorithm finds every edge such that, when converted to a mirror, makes \(\overline{uw}\) visible to our viewer. We find out exactly which interval of \(\overline{uw}\) becomes visible, by every edge middling as mirror, all in linear time.
M. Ghodsi—This author’s research was partially supported by the IPM under grant No: CS1392-2-01.
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Vaezi, A., Ghodsi, M.: Extending visibility polygons by mirrors to cover specific targets. In: EuroCG 2013, pp. 13–16 (2013)
Aronov, B., Davis, A., Day, T., Pal, S.P., Prasad, D.: Visibility with one reflection. Discrete Comput. Geom. 19, 553–574 (1998)
Avis, D., Toussaint, G.T.: An optional algorithm for determining the visibility of a polygon from an edge. IEEE Trans. Comput. C–30, 910–1014 (1981)
de Berg, M., van Kreveld, M., Overmars, M., Schwarzkopf, O.: Computational Geometry Algorithms and Applications, 3rd edn., pp. 13–14. Department of Computer Science Utrecht University (2008)
Guibas, L.J., Hershberger, J., Leven, D., Sharir, M., Tarjan, R.E.: Linear-time algorithms for visibility and shortest path problems inside triangulated simple polygons. Algorithmica 2, 209–233 (1987)
Kouhestani, B., Asgaripour, M., Mahdavi, S.S., Nouri, A., Mohades, A.: Visibility polygons in the presence of a mirror edge. In: Proceedings of the 26th European Workshop on Computational Geometry, vol. 26, pp. 209–212 (2010)
Lee, D.T.: Visibility of a simple polygon. Comput. Vis. Graph. Image Process. 22, 207–221 (1983)
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Vaezi, A., Ghodsi, M. (2017). How to Extend Visibility Polygons by Mirrors to Cover Invisible Segments. In: Poon, SH., Rahman, M., Yen, HC. (eds) WALCOM: Algorithms and Computation. WALCOM 2017. Lecture Notes in Computer Science(), vol 10167. Springer, Cham. https://doi.org/10.1007/978-3-319-53925-6_4
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DOI: https://doi.org/10.1007/978-3-319-53925-6_4
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