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Polygon visibility decompositions wi...

Boland, Ralph Patrick.

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Polygon visibility decompositions with applications.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Polygon visibility decompositions with applications./
作者:	Boland, Ralph Patrick.
面頁冊數:	198 p.
附註:	Adviser: Jorge Urrutia.
Contained By:	Dissertation Abstracts International63-05B
標題:	Computer Science -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=NQ67943
ISBN:	0612679438

Polygon visibility decompositions with applications.
Boland, Ralph Patrick.

Polygon visibility decompositions with applications. - 198 p.

Adviser: Jorge Urrutia.

Thesis (Ph.D.)--University of Ottawa (Canada), 2002.

It is noteworthy that the solutions to problems that we provide are usually more efficient and always simpler than alternative solutions

ISBN: 0612679438Subjects--Topical Terms:

890869
Computer Science

Polygon visibility decompositions with applications.
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245 1 0 $a Polygon visibility decompositions with applications.
300 $a 198 p.
500 $a Adviser: Jorge Urrutia.
500 $a Source: Dissertation Abstracts International, Volume: 63-05, Section: B, page: 2452.
502 $a Thesis (Ph.D.)--University of Ottawa (Canada), 2002.
520 $a It is noteworthy that the solutions to problems that we provide are usually more efficient and always simpler than alternative solutions
520 $a We also develop several new polygon visibility decomposition classes. We then use these decomposition classes to solve a number of problems on polygons including the circular ray shooting problem and the largest axis-aligned rectangle problem
520 $a Many problems in Computational Geometry involve a simple polygon <italic>P</italic> and a family of geometric objects, say ς, contained in <italic>P</italic>. For example, if ς is the family of chords of <italic>P</italic> then we may want to find the longest chord in <italic> P</italic>. Alternatively, given a chord of <italic>P</italic>, we may wish to determine the areas of the two subpolygons of <italic>P</italic> determined by the chord. Let Π be a polygonal decomposition of a polygon <italic> P</italic>. We call Π a visibility decomposition with respect to ς if, for any object <italic>g</italic> ∈ ς, we can cover <italic> g</italic> with <italic>o</italic>(|<italic>P</italic>|) of the subpolygons of Π. We investigate the application of visibility decompositions of polygons to solving problems of the forms described.
520 $a Any visibility decomposition Π of a polygon <italic>P</italic> that we construct will have the property that, for some class of polygons &weierp; where the polygons in &weierp; have useful properties, Π &sube; &weierp;. Furthermore, the properties of &weierp; will be key to solving any problems we solve on <italic>P</italic> using Π.
520 $a Some of the visibility decomposition classes we investigate are already known in the literature, for example weakly edge visible polygon decompositions. We make improvements relating to these decomposition classes and in some cases we also find new applications for them
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