Computing a visibility polygon using few variables

• Autor(a) principal: Barba, Luis
• Data de Publicação: 2014
• Outros Autores: Korman, Matias, Langerman, Stefan, Silveira, Rodrigo
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10773/21926
• topic: Computational geometry; Memory-constrained algorithms; Time-space-trade-off visibility; Simple polygon

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(nr¯) time, where r¯ 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(nr2s+nlog2r) (or O(nr2s+nlogr) randomized expected time), where s∈O(logr). This is the first algorithm in which an exponential space-time trade-off for a geometric problem is obtained.