{"title":"带边界流形上的单三角带和环","authors":"Pablo Diaz-Gutierrez, D. Eppstein, M. Gopi","doi":"10.1109/SIBGRAPI.2006.41","DOIUrl":null,"url":null,"abstract":"The single triangle-strip loop generation algorithm on a triangulated two-manifold presented by Gopi and Eppstein (2004) is based on the guaranteed existence of a perfect matching in its dual graph. However, such a perfect matching is not guaranteed in the dual graph of triangulated manifolds with boundaries. In this paper, we present algorithms that suitably modify the results of the dual graph matching to generate a single strip loop on manifolds with boundaries. Further, the algorithm presented by Gopi and Eppstein (2004) can produce only strip loops, but not linear strips. We present an algorithm that does topological surgery to construct linear strips, with user-specified start and end triangles, on manifolds with or without boundaries. The main contributions of this paper include graph algorithms to handle unmatched triangles, reduction of the number of Steiner vertices introduced to create strip loops, and finally a novel method to generate single linear strips with arbitrary start and end positions","PeriodicalId":253871,"journal":{"name":"2006 19th Brazilian Symposium on Computer Graphics and Image Processing","volume":"63 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2006-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Single Triangle Strip and Loop on Manifolds with Boundaries\",\"authors\":\"Pablo Diaz-Gutierrez, D. Eppstein, M. Gopi\",\"doi\":\"10.1109/SIBGRAPI.2006.41\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The single triangle-strip loop generation algorithm on a triangulated two-manifold presented by Gopi and Eppstein (2004) is based on the guaranteed existence of a perfect matching in its dual graph. However, such a perfect matching is not guaranteed in the dual graph of triangulated manifolds with boundaries. In this paper, we present algorithms that suitably modify the results of the dual graph matching to generate a single strip loop on manifolds with boundaries. Further, the algorithm presented by Gopi and Eppstein (2004) can produce only strip loops, but not linear strips. We present an algorithm that does topological surgery to construct linear strips, with user-specified start and end triangles, on manifolds with or without boundaries. The main contributions of this paper include graph algorithms to handle unmatched triangles, reduction of the number of Steiner vertices introduced to create strip loops, and finally a novel method to generate single linear strips with arbitrary start and end positions\",\"PeriodicalId\":253871,\"journal\":{\"name\":\"2006 19th Brazilian Symposium on Computer Graphics and Image Processing\",\"volume\":\"63 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2006-12-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2006 19th Brazilian Symposium on Computer Graphics and Image Processing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SIBGRAPI.2006.41\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2006 19th Brazilian Symposium on Computer Graphics and Image Processing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SIBGRAPI.2006.41","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Single Triangle Strip and Loop on Manifolds with Boundaries
The single triangle-strip loop generation algorithm on a triangulated two-manifold presented by Gopi and Eppstein (2004) is based on the guaranteed existence of a perfect matching in its dual graph. However, such a perfect matching is not guaranteed in the dual graph of triangulated manifolds with boundaries. In this paper, we present algorithms that suitably modify the results of the dual graph matching to generate a single strip loop on manifolds with boundaries. Further, the algorithm presented by Gopi and Eppstein (2004) can produce only strip loops, but not linear strips. We present an algorithm that does topological surgery to construct linear strips, with user-specified start and end triangles, on manifolds with or without boundaries. The main contributions of this paper include graph algorithms to handle unmatched triangles, reduction of the number of Steiner vertices introduced to create strip loops, and finally a novel method to generate single linear strips with arbitrary start and end positions