S. Cappell, J. Goodman, J. Pach, R. Pollack, M. Sharir, R. Wenger
{"title":"The combinatorial complexity of hyperplane transversals","authors":"S. Cappell, J. Goodman, J. Pach, R. Pollack, M. Sharir, R. Wenger","doi":"10.1145/98524.98542","DOIUrl":null,"url":null,"abstract":"We show that the maximum combinatorial complexity of the space of hyperplane transversals to a family of <italic>n</italic> separated and strictly convex sets in R<italic><supscrpt>d</supscrpt></italic> is &THgr;(<italic>n<supscrpt>⌊d/2⌋</supscrpt></italic>), which generalizes results of Edelsbrunner and Sharir in the plane. As a key step in the argument, we show that the space of hyperplanes tangent to <italic>&kgr;</italic> ≤ <italic>d</italic> separated and strictly convex sets in R<italic><supscrpt>d</supscrpt></italic> is a topological (<italic>d</italic> - <italic>&kgr;</italic>)-sphere.","PeriodicalId":113850,"journal":{"name":"SCG '90","volume":"16 1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1990-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SCG '90","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/98524.98542","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 5
Abstract
We show that the maximum combinatorial complexity of the space of hyperplane transversals to a family of n separated and strictly convex sets in Rd is &THgr;(n⌊d/2⌋), which generalizes results of Edelsbrunner and Sharir in the plane. As a key step in the argument, we show that the space of hyperplanes tangent to &kgr; ≤ d separated and strictly convex sets in Rd is a topological (d - &kgr;)-sphere.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
