Dynamic C-oriented polygonal intersection searching

Q4 Mathematics 信息与控制 Pub Date : 1984-12-01 DOI:10.1016/S0019-9958(84)80011-X
Ralf Hartmut Güting
{"title":"Dynamic C-oriented polygonal intersection searching","authors":"Ralf Hartmut Güting","doi":"10.1016/S0019-9958(84)80011-X","DOIUrl":null,"url":null,"abstract":"<div><p>A set of polygons is called <em>c</em>-oriented if the edges of all polygons are oriented in a constant number of previously defined directions. The intersection searching problem is studied for such objects, namely: Given a set of <em>c</em>-oriented polygons <em>P</em> and a <em>c</em>-oriented query polygon <em>q</em>, find all polygons in <em>P</em> that intersect <em>q</em>. It is shown that this problem can be solved in <em>O</em>(log<sup>2</sup> <em>n</em> + <em>t</em>) time with <em>O</em>(<em>n</em> log <em>n</em>) space and <em>O</em>(<em>n</em> log<sup>2</sup> <em>n</em>) preprocessing, where <em>n</em> is the cardinality of <em>P</em> and <em>t</em> the number of answers to a query. Furthermore, the solution is extended to the cases in which <em>P</em> is a semidynamic or dynamic set of polygons. Whereas planar intersection searching can be carried out more efficiently for orthogonal objects (e.g., rectangles) it is expensive for arbitrary polygons. This suggests that the <em>c</em>-oriented solution be used in appropriate areas of application, for instance, in VLSI-design.</p></div>","PeriodicalId":38164,"journal":{"name":"信息与控制","volume":"63 3","pages":"Pages 143-163"},"PeriodicalIF":0.0000,"publicationDate":"1984-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0019-9958(84)80011-X","citationCount":"22","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"信息与控制","FirstCategoryId":"1093","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S001999588480011X","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 22

Abstract

A set of polygons is called c-oriented if the edges of all polygons are oriented in a constant number of previously defined directions. The intersection searching problem is studied for such objects, namely: Given a set of c-oriented polygons P and a c-oriented query polygon q, find all polygons in P that intersect q. It is shown that this problem can be solved in O(log2 n + t) time with O(n log n) space and O(n log2 n) preprocessing, where n is the cardinality of P and t the number of answers to a query. Furthermore, the solution is extended to the cases in which P is a semidynamic or dynamic set of polygons. Whereas planar intersection searching can be carried out more efficiently for orthogonal objects (e.g., rectangles) it is expensive for arbitrary polygons. This suggests that the c-oriented solution be used in appropriate areas of application, for instance, in VLSI-design.

查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
动态面向c的多边形交集搜索
如果一组多边形的所有边都以恒定数量的先前定义的方向定向,则称为面向c的多边形。研究了这类对象的相交搜索问题,即:给定一组面向c的多边形P和一个面向c的查询多边形q,找出P中与q相交的所有多边形。通过O(n log n)空间和O(n log2 n)预处理,可以在O(log2 n + t)时间内求解该问题,其中n为P的基数,t为查询的答案个数。进一步,将解推广到P是半动态或动态多边形集的情况。平面相交搜索对于正交对象(如矩形)可以更有效地进行,而对于任意多边形则是昂贵的。这表明,面向c的解决方案应用于适当的应用领域,例如,在vlsi设计中。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
信息与控制
信息与控制 Mathematics-Control and Optimization
CiteScore
1.50
自引率
0.00%
发文量
4623
期刊介绍:
期刊最新文献
Systolic trellis automata: Stability, decidability and complexity On relativized exponential and probabilistic complexity classes A note on succinct representations of graphs Function definitions in term rewriting and applicative programming Simulation of large networks on smaller networks
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1