K. Buchin, W. Evans, Fabrizio Frati, I. Kostitsyna, M. Löffler, Tim Ophelders, A. Wolff
{"title":"通过3D变形平面图形绘图","authors":"K. Buchin, W. Evans, Fabrizio Frati, I. Kostitsyna, M. Löffler, Tim Ophelders, A. Wolff","doi":"10.48550/arXiv.2210.05384","DOIUrl":null,"url":null,"abstract":". In this paper, we investigate crossing-free 3D morphs between planar straight-line drawings. We show that, for any two (not necessarily topologically equivalent) planar straight-line drawings of an n -vertex planar graph, there exists a piecewise-linear crossing-free 3D morph with O ( n 2 ) steps that transforms one drawing into the other. We also give some evidence why it is difficult to obtain a linear lower bound (which exists in 2D) for the number of steps of a crossing-free 3D morph.","PeriodicalId":266155,"journal":{"name":"Conference on Current Trends in Theory and Practice of Informatics","volume":"57 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Morphing Planar Graph Drawings Through 3D\",\"authors\":\"K. Buchin, W. Evans, Fabrizio Frati, I. Kostitsyna, M. Löffler, Tim Ophelders, A. Wolff\",\"doi\":\"10.48550/arXiv.2210.05384\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". In this paper, we investigate crossing-free 3D morphs between planar straight-line drawings. We show that, for any two (not necessarily topologically equivalent) planar straight-line drawings of an n -vertex planar graph, there exists a piecewise-linear crossing-free 3D morph with O ( n 2 ) steps that transforms one drawing into the other. We also give some evidence why it is difficult to obtain a linear lower bound (which exists in 2D) for the number of steps of a crossing-free 3D morph.\",\"PeriodicalId\":266155,\"journal\":{\"name\":\"Conference on Current Trends in Theory and Practice of Informatics\",\"volume\":\"57 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-10-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Conference on Current Trends in Theory and Practice of Informatics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.48550/arXiv.2210.05384\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Conference on Current Trends in Theory and Practice of Informatics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.48550/arXiv.2210.05384","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
. In this paper, we investigate crossing-free 3D morphs between planar straight-line drawings. We show that, for any two (not necessarily topologically equivalent) planar straight-line drawings of an n -vertex planar graph, there exists a piecewise-linear crossing-free 3D morph with O ( n 2 ) steps that transforms one drawing into the other. We also give some evidence why it is difficult to obtain a linear lower bound (which exists in 2D) for the number of steps of a crossing-free 3D morph.
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