Computing a visibility polygon using few variables
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European Commisision's projectMFHQTERRAINS - Mathematical Foundations of High-Quality Terrain Models (EC-FP7-251235)
We present several algorithms for computing the visibility polygon of a simple polygon P of n vertices (out of which r are reflex) from a viewpoint inside P, when P resides in read-only memory and only few working variables can be used. The first algorithm uses a constant number of variables, and outputs the vertices of the visibility polygon in O (n (r) over bar) time, where (r) over bar denotes the number of reflex vertices of P that are part of the output. Whenever we are allowed to use O(s) variables, the running time decreases to O (nr/2(s) + n log(2) r) (or O (nr/2(s) + n log r) randomized expected time), where s is an element of O (log r). This is the first algorithm in which an exponential space-time trade-off for a geometric problem is obtained. (C) 2014 Elsevier B.V. All rights reserved.
CitationBarba, L. [et al.]. Computing a visibility polygon using few variables. "Computational geometry: theory and applications", 01 Octubre 2014, vol. 47, núm. 9, p. 918-926.
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