{"title":"三维凸多面体的结合","authors":"B. Aronov, M. Sharir, Boaz Tagansky","doi":"10.1109/SFCS.1993.366835","DOIUrl":null,"url":null,"abstract":"We show that the number of vertices, edges, and faces of the union of k convex polyhedra in 3-space, having a total of n faces, is O(k/sup 3/+knlog/sup 2/ k). This bound is almost tight in the worst case. We also describe a rather simple randomized incremental algorithm for computing the boundary of the union in O(k/sup 3/+knlog/sup 3/ k) expected time.<<ETX>>","PeriodicalId":253303,"journal":{"name":"Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science","volume":"50 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1993-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"72","resultStr":"{\"title\":\"The union of convex polyhedra in three dimensions\",\"authors\":\"B. Aronov, M. Sharir, Boaz Tagansky\",\"doi\":\"10.1109/SFCS.1993.366835\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that the number of vertices, edges, and faces of the union of k convex polyhedra in 3-space, having a total of n faces, is O(k/sup 3/+knlog/sup 2/ k). This bound is almost tight in the worst case. We also describe a rather simple randomized incremental algorithm for computing the boundary of the union in O(k/sup 3/+knlog/sup 3/ k) expected time.<<ETX>>\",\"PeriodicalId\":253303,\"journal\":{\"name\":\"Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science\",\"volume\":\"50 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1993-11-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"72\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SFCS.1993.366835\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SFCS.1993.366835","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We show that the number of vertices, edges, and faces of the union of k convex polyhedra in 3-space, having a total of n faces, is O(k/sup 3/+knlog/sup 2/ k). This bound is almost tight in the worst case. We also describe a rather simple randomized incremental algorithm for computing the boundary of the union in O(k/sup 3/+knlog/sup 3/ k) expected time.<>
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
