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On illumination in the plane by line segments

โœ Scribed by A. Bezdek; K. Bezdek; T. Bisztriczky

Publisher
Springer
Year
1992
Tongue
English
Weight
504 KB
Volume
41
Category
Article
ISSN
0046-5755

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โœฆ Synopsis

We show that S c E 2 contains a line segment illuminator if any two points of S are illuminated by a line segment of S in a given direction or if any eight points of S are illuminated by a connected set of line segments of S and a certain connectedness condition is fulfilled. We also show that if any three points of S ~ E 2 are illuminated by a translate in S of a line segment T, then S contains a line segment illuminator, which is also a translate of T. As a further result; we have that if any three points of a polygon P are illuminated by some line segment of P then the so-called link center of P illuminates P. Finally, we prove that if any three points of an osymmetric polygon P are illuminated by a line segment of P through the point 0 then P contains an o-symmetric convex illuminator which is either a line segment or a parallelogram.

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