{"title":"动态面向c的多边形交集搜索","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":null,"pages":null},"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":"{\"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\":null,\"pages\":null},\"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}","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
摘要
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。
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(log2n + t) time with O(n log n) space and O(n log2n) 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.