{"title":"随机多面体的剪影","authors":"M. Glisse, S. Lazard, J. Michel, M. Pouget","doi":"10.20382/jocg.v7i1a5","DOIUrl":null,"url":null,"abstract":"We consider random polytopes defined as the convex hull of a Poisson point process on a sphere in $\\R^3$ such that its average number of points is $n$. We show that the expectation over all such random polytopes of the maximum size of their silhouettes viewed from infinity is $\\Theta(\\sqrt{n})$.","PeriodicalId":54969,"journal":{"name":"International Journal of Computational Geometry & Applications","volume":"1 1","pages":"86-99"},"PeriodicalIF":0.0000,"publicationDate":"2016-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Silhouette of a random polytope\",\"authors\":\"M. Glisse, S. Lazard, J. Michel, M. Pouget\",\"doi\":\"10.20382/jocg.v7i1a5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider random polytopes defined as the convex hull of a Poisson point process on a sphere in $\\\\R^3$ such that its average number of points is $n$. We show that the expectation over all such random polytopes of the maximum size of their silhouettes viewed from infinity is $\\\\Theta(\\\\sqrt{n})$.\",\"PeriodicalId\":54969,\"journal\":{\"name\":\"International Journal of Computational Geometry & Applications\",\"volume\":\"1 1\",\"pages\":\"86-99\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2016-03-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Computational Geometry & Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.20382/jocg.v7i1a5\",\"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":"International Journal of Computational Geometry & Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.20382/jocg.v7i1a5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
We consider random polytopes defined as the convex hull of a Poisson point process on a sphere in $\R^3$ such that its average number of points is $n$. We show that the expectation over all such random polytopes of the maximum size of their silhouettes viewed from infinity is $\Theta(\sqrt{n})$.
期刊介绍：
The International Journal of Computational Geometry & Applications (IJCGA) is a quarterly journal devoted to the field of computational geometry within the framework of design and analysis of algorithms.
Emphasis is placed on the computational aspects of geometric problems that arise in various fields of science and engineering including computer-aided geometry design (CAGD), computer graphics, constructive solid geometry (CSG), operations research, pattern recognition, robotics, solid modelling, VLSI routing/layout, and others. Research contributions ranging from theoretical results in algorithm design — sequential or parallel, probabilistic or randomized algorithms — to applications in the above-mentioned areas are welcome. Research findings or experiences in the implementations of geometric algorithms, such as numerical stability, and papers with a geometric flavour related to algorithms or the application areas of computational geometry are also welcome.
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