A linear worst-case lower bound on the number of holes inside regions visible due to multiple diffuse reflections |
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Authors: | Siddhartha Brahma Sudebkumar Prasant Pal Dilip Sarkar |
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Affiliation: | (1) Department of Computer Science and Engineering, Indian Institute of Technology, Kharagpur, 721302, India;(2) Department of Computer Science, University of Miami, Coral Gables, Miami, FL 33124, USA |
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Abstract: | It is known that the region V(s) of a simple polygon P, directly visible (illuminable) from an internal point s, is simply connected. Aronov et al. [2] established that the region V1(s) of a simple polygon visible from an internal point s due to at most one diffuse reflection on the boundary of the polygon P, is also simply connected. In this paper we establish that the region V2(s), visible from s due to at most two diffuse reflections may be multiply connected; we demonstrate the construction of an n-sided simple polygon with a point s inside it so that the region of P visible from s after at most two diffuse reflections is multiply connected. We also show that V3(s), the region of P visible from s after at most three diffuse reflections, can have (n) holes.A part of this work was done when this author was visiting the University of Miami, Coral Gables, Florida, USA. |
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Keywords: | 52C45 68U05 |
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