{"title":"Approximating Curves via Alpha Shapes","authors":"Takis Sakkalis , Ch Charitos","doi":"10.1006/gmip.1999.0496","DOIUrl":null,"url":null,"abstract":"<div><p>We present a method of approximating a nonsingular curve <em>C</em> in the plane or in space with the use of <em>alpha shapes</em>. The procedure is based on sampling the curve <em>C</em> with a finite set <em>S</em> and then construct the alpha shape,\n<span><math><mi>S</mi></math></span><sub>α</sub>, of <em>S</em>. Then,\n<span><math><mi>S</mi></math></span><sub>α</sub> is shown to be a piecewise linear curve that is <em>ambiently</em> homeomorphic to, and within a prescribed tolerance from, <em>C</em>.</p></div>","PeriodicalId":100591,"journal":{"name":"Graphical Models and Image Processing","volume":"61 3","pages":"Pages 165-176"},"PeriodicalIF":0.0000,"publicationDate":"1999-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1006/gmip.1999.0496","citationCount":"16","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Graphical Models and Image Processing","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1077316999904963","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 16
Abstract
We present a method of approximating a nonsingular curve C in the plane or in space with the use of alpha shapes. The procedure is based on sampling the curve C with a finite set S and then construct the alpha shape,
α, of S. Then,
α is shown to be a piecewise linear curve that is ambiently homeomorphic to, and within a prescribed tolerance from, C.
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