{"title":"A Geometric Approach for Computing the Kernel of a Polyhedron","authors":"T. Sorgente, S. Biasotti, M. Spagnuolo","doi":"10.2312/STAG.20211470","DOIUrl":null,"url":null,"abstract":"We present a geometric algorithm to compute the geometric kernel of a generic polyhedron. The geometric kernel (or simply kernel) is definedas the set of points from which the whole polyhedron is visible. Whilst the computation of the kernel for a polygon has already been largely addressed in the literature, less has been done for polyhedra. Currently, the principal implementation of the kernel estimation is based on the solution of a linear programming problem. We compare against it on several examples, showing that our method is more efficient in analysing the elements of a generic tessellation. Details on the technical implementation and discussions on pros and cons of the method are also provided.","PeriodicalId":172563,"journal":{"name":"Smart Tools and Applications in Graphics","volume":"27 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Smart Tools and Applications in Graphics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2312/STAG.20211470","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3
Abstract
We present a geometric algorithm to compute the geometric kernel of a generic polyhedron. The geometric kernel (or simply kernel) is definedas the set of points from which the whole polyhedron is visible. Whilst the computation of the kernel for a polygon has already been largely addressed in the literature, less has been done for polyhedra. Currently, the principal implementation of the kernel estimation is based on the solution of a linear programming problem. We compare against it on several examples, showing that our method is more efficient in analysing the elements of a generic tessellation. Details on the technical implementation and discussions on pros and cons of the method are also provided.