{"title":"An algorithm for the Euclidean cell decomposition of a non-compact strictly convex projective surface","authors":"Stephan Tillmann, Sampson Wong","doi":"10.20382/jocg.v7i1a12","DOIUrl":null,"url":null,"abstract":"Cooper and Long generalised Epstein and Penner's Euclidean cell decomposition of cusped hyperbolic $n$–manifolds of finite volume to non-compact strictly convex projective $n$–manifolds of finite volume. We show that Weeks' algorithm to compute this decomposition for a hyperbolic surface generalises to strictly convex projective surfaces.","PeriodicalId":54969,"journal":{"name":"International Journal of Computational Geometry & Applications","volume":"95 1","pages":"237-255"},"PeriodicalIF":0.0000,"publicationDate":"2016-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Computational Geometry & Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.20382/jocg.v7i1a12","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: 2
Abstract
Cooper and Long generalised Epstein and Penner's Euclidean cell decomposition of cusped hyperbolic $n$–manifolds of finite volume to non-compact strictly convex projective $n$–manifolds of finite volume. We show that Weeks' algorithm to compute this decomposition for a hyperbolic surface generalises to strictly convex projective surfaces.
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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