NDLI: Algorithms for computing diffuse reflection paths in polygons

Content Provider	Springer Nature Link
Author	Ghosh, Subir Kumar Goswami, Partha Pratim Maheshwari, Anil Nandy, Subhas Chandra Pal, Sudebkumar Prasant Sarvattomananda, Swami
Copyright Year	2012
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 edges of P. A diffuse reflection path is said to be optimal if it has the minimum number of reflections on the path. The problem of computing a diffuse reflection path from s to t inside P has not been considered explicitly in the past. We present three different algorithms for this problem which produce suboptimal paths. 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+klogn) time, where k denotes the number of reflections in the constructed path. The third algorithm is for polygons with or without holes, and it runs in O(n 2) time. The number of reflections in the path produced by this third algorithm can be at most three times that of an optimal diffuse reflection path. Though the combinatorial approach used in the third algorithm gives a better bound on the number of reflections on the path, the first and the second algorithms stand on the merit of their elegant geometric approaches based on local geometric information.
Starting Page	1229
Ending Page	1237
Page Count	9
File Format	PDF
ISSN	01782789
Journal	The Visual Computer
Volume Number	28
Issue Number	12
e-ISSN	14322315
Language	English
Publisher	Springer-Verlag
Publisher Date	2012-01-12
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Diffuse reflection Specular reflection Visibility polygon Visibility graph Shortest path Minimum link path Greedy path Computer Science Computer Graphics Artificial Intelligence (incl. Robotics) Image Processing and Computer Vision
Content Type	Text
Resource Type	Article
Subject	Computer Graphics and Computer-Aided Design Computer Vision and Pattern Recognition Software

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