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Algorithms for Computing Diffuse Reflection Paths in Polygons

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WALCOM: Algorithms and Computation (WALCOM 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5431))

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Abstract

Let s be a point source of light inside a polygon P of n vertices. A polygonal path from s to some point t inside P is called a diffuse reflection path if the turning points of the path lie on polygonal edges of P. We present three different algorithms for computing diffuse reflection paths from s to t inside P. For constructing such a path, the first algorithm uses a greedy method, the second algorithm uses a transformation of a minimum link path, and the third algorithm uses the edge-edge visibility graph of P. The first two algorithms are for polygons without holes, and they run in O(n + k logn) time, where k denotes the number of reflections in the path. The third algorithm is for both polygons with or without holes, and it runs in O(n 2) time. The number of reflections in the path produced by this algorithm can be at most 3 times that of an optimal diffuse reflection path. The problem of computing a diffuse reflection path between two points inside a polygon has not been considered in the past.

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Author information

Authors and Affiliations

  1. School of Technology & Computer Science, Tata Institute of Fundamental Research, Mumbai, 400005, India

    Subir Kumar Ghosh

  2. Institute of Radiophysics and Electronics, University of Calcutta, Kolkata, 700009, India

    Partha Pratim Goswami

  3. School of Computer Science, Carleton University, Ottawa, Canada, KIS 5B6

    Anil Maheshwari

  4. Advanced Computing and Microelectronics Unit, Indian Statistical Institute, Kolkata, 700108, India

    Subhas Chandra Nandy

  5. Department of Computer Science and Engineering, Indian Institute of Technology, Kharagpur, 721302, India

    Sudebkumar Prasant Pal

  6. School of Mathematical Sciences, Ramakrishna Mission Vivekananda University, Belur, 711202, India

    Swami Sarvattomananda

Authors
  1. Subir Kumar Ghosh
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  2. Partha Pratim Goswami
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  3. Anil Maheshwari
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  4. Subhas Chandra Nandy
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  5. Sudebkumar Prasant Pal
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  6. Swami Sarvattomananda
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Editor information

Editors and Affiliations

  1. Indian Statistical Institute, 700 108, Kolkata, India

    Sandip Das

  2. Japan Advanced Institute of Science and Technology, 923-1292, Ishikawa, Japan

    Ryuhei Uehara

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© 2009 Springer-Verlag Berlin Heidelberg

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Ghosh, S.K., Goswami, P.P., Maheshwari, A., Nandy, S.C., Pal, S.P., Sarvattomananda, S. (2009). Algorithms for Computing Diffuse Reflection Paths in Polygons. In: Das, S., Uehara, R. (eds) WALCOM: Algorithms and Computation. WALCOM 2009. Lecture Notes in Computer Science, vol 5431. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00202-1_5

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  • DOI: https://doi.org/10.1007/978-3-642-00202-1_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00201-4

  • Online ISBN: 978-3-642-00202-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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