Algorithms for Computing Diffuse Reflection Paths in Polygons

  • Authors:

  • Subir Kumar Ghosh;Partha Pratim Goswami;Anil Maheshwari;Subhas Chandra Nandy;Sudebkumar Prasant Pal;Swami Sarvattomananda

  • Affiliations:

  • School of Technology & Computer Science, Tata Institute of Fundamental Research, Mumbai, India 400005;Institute of Radiophysics and Electronics, University of Calcutta, Kolkata, India 700009;School of Computer Science, Carleton University, Ottawa, Canada KIS 5B6;Advanced Computing and Microelectronics Unit, Indian Statistical Institute, Kolkata, India 700108;Department of Computer Science and Engineering, Indian Institute of Technology, Kharagpur, India 721302;School of Mathematical Sciences, Ramakrishna Mission Vivekananda University, Belur, India 711202

  • Venue:
  • WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
  • Year:
  • 2009

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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.