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Some New Results on Geometric Transversals 关于几何截线的一些新结果
IF 0.8 3区 数学
Discrete & Computational Geometry Pub Date : 2023-11-16 DOI: 10.1007/s00454-023-00573-2
Otfried Cheong, Xavier Goaoc, Andreas F. Holmsen
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引用次数: 1
The Visible-Volume Function of a Set of Cameras is Continuous, Piecewise Rational, Locally Lipschitz, and Semi-Algebraic in All Dimensions 一组相机的可见体积函数是连续的、分段有理的、局部Lipschitz的和全维半代数的
IF 0.8 3区 数学
Discrete & Computational Geometry Pub Date : 2023-08-12 DOI: 10.1007/s00454-023-00541-w
Jörg Rambau
{"title":"The Visible-Volume Function of a Set of Cameras is Continuous, Piecewise Rational, Locally Lipschitz, and Semi-Algebraic in All Dimensions","authors":"Jörg Rambau","doi":"10.1007/s00454-023-00541-w","DOIUrl":"https://doi.org/10.1007/s00454-023-00541-w","url":null,"abstract":"","PeriodicalId":50574,"journal":{"name":"Discrete & Computational Geometry","volume":"70 1","pages":"1038 - 1058"},"PeriodicalIF":0.8,"publicationDate":"2023-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43661006","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Self-Affine Tiles Generated by a Finite Number of Matrices 有限个矩阵生成的自仿射块
IF 0.8 3区 数学
Discrete & Computational Geometry Pub Date : 2023-07-23 DOI: 10.1007/s00454-023-00529-6
Guotai Deng, Chuntai Liu, Sze-Man Ngai
{"title":"Self-Affine Tiles Generated by a Finite Number of Matrices","authors":"Guotai Deng, Chuntai Liu, Sze-Man Ngai","doi":"10.1007/s00454-023-00529-6","DOIUrl":"https://doi.org/10.1007/s00454-023-00529-6","url":null,"abstract":"","PeriodicalId":50574,"journal":{"name":"Discrete & Computational Geometry","volume":"70 1","pages":"620 - 644"},"PeriodicalIF":0.8,"publicationDate":"2023-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47706627","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Complete Characterization of Polyhedral Self-Affine Tiles 多面体自仿射瓷砖的完全表征
IF 0.8 3区 数学
Discrete & Computational Geometry Pub Date : 2023-07-19 DOI: 10.1007/s00454-023-00527-8
V. Protasov, T. Zaitseva
{"title":"Complete Characterization of Polyhedral Self-Affine Tiles","authors":"V. Protasov, T. Zaitseva","doi":"10.1007/s00454-023-00527-8","DOIUrl":"https://doi.org/10.1007/s00454-023-00527-8","url":null,"abstract":"","PeriodicalId":50574,"journal":{"name":"Discrete & Computational Geometry","volume":"70 1","pages":"931 - 950"},"PeriodicalIF":0.8,"publicationDate":"2023-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41753973","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Uniformly Acute Triangulations of PSLGs PSLG的一致锐角三角剖分
IF 0.8 3区 数学
Discrete & Computational Geometry Pub Date : 2023-07-08 DOI: 10.1007/s00454-023-00524-x
C. Bishop
{"title":"Uniformly Acute Triangulations of PSLGs","authors":"C. Bishop","doi":"10.1007/s00454-023-00524-x","DOIUrl":"https://doi.org/10.1007/s00454-023-00524-x","url":null,"abstract":"","PeriodicalId":50574,"journal":{"name":"Discrete & Computational Geometry","volume":"70 1","pages":"1090 - 1120"},"PeriodicalIF":0.8,"publicationDate":"2023-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45731652","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Delaunay and Regular Triangulations as Lexicographic Optimal Chains 作为字典最优链的Delaunay和正则三角剖分
IF 0.8 3区 数学
Discrete & Computational Geometry Pub Date : 2023-05-16 DOI: 10.1007/s00454-023-00485-1
D. Cohen-Steiner, A. Lieutier, J. Vuillamy
{"title":"Delaunay and Regular Triangulations as Lexicographic Optimal Chains","authors":"D. Cohen-Steiner, A. Lieutier, J. Vuillamy","doi":"10.1007/s00454-023-00485-1","DOIUrl":"https://doi.org/10.1007/s00454-023-00485-1","url":null,"abstract":"","PeriodicalId":50574,"journal":{"name":"Discrete & Computational Geometry","volume":"70 1","pages":"1 - 50"},"PeriodicalIF":0.8,"publicationDate":"2023-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45486294","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Reconstructing Planar Ellipses from Translation-Invariant Minkowski Tensors of Rank Two 用平移不变的二阶闵可夫斯基张量重构平面椭圆
IF 0.8 3区 数学
Discrete & Computational Geometry Pub Date : 2023-04-03 DOI: 10.1007/s00454-022-00470-0
Rikke Eriksen, Markus Kiderlen
{"title":"Reconstructing Planar Ellipses from Translation-Invariant Minkowski Tensors of Rank Two","authors":"Rikke Eriksen, Markus Kiderlen","doi":"10.1007/s00454-022-00470-0","DOIUrl":"https://doi.org/10.1007/s00454-022-00470-0","url":null,"abstract":"","PeriodicalId":50574,"journal":{"name":"Discrete & Computational Geometry","volume":"69 1","pages":"1095-1120"},"PeriodicalIF":0.8,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45389334","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Morphing Triangle Contact Representations of Triangulations 三角形的变形三角形接触表示
IF 0.8 3区 数学
Discrete & Computational Geometry Pub Date : 2023-03-15 DOI: 10.1007/s00454-022-00475-9
Patrizio Angelini, S. Chaplick, Sabine Cornelsen, Giordano Da Lozzo, Vincenzo Roselli
{"title":"Morphing Triangle Contact Representations of Triangulations","authors":"Patrizio Angelini, S. Chaplick, Sabine Cornelsen, Giordano Da Lozzo, Vincenzo Roselli","doi":"10.1007/s00454-022-00475-9","DOIUrl":"https://doi.org/10.1007/s00454-022-00475-9","url":null,"abstract":"","PeriodicalId":50574,"journal":{"name":"Discrete & Computational Geometry","volume":"70 1","pages":"991 - 1024"},"PeriodicalIF":0.8,"publicationDate":"2023-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48006648","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Tropical Carathéodory with Matroids. 带拟类的热带油葵。
IF 0.8 3区 数学
Discrete & Computational Geometry Pub Date : 2023-01-01 DOI: 10.1007/s00454-022-00446-0
Georg Loho, Raman Sanyal
{"title":"Tropical Carathéodory with Matroids.","authors":"Georg Loho,&nbsp;Raman Sanyal","doi":"10.1007/s00454-022-00446-0","DOIUrl":"https://doi.org/10.1007/s00454-022-00446-0","url":null,"abstract":"<p><p>Bárány's colorful generalization of Carathéodory's Theorem combines geometrical and combinatorial constraints. Kalai-Meshulam (2005) and Holmsen (2016) generalized Bárány's theorem by replacing color classes with matroid constraints. In this note, we obtain corresponding results in tropical convexity, generalizing the Tropical Colorful Carathéodory Theorem of Gaubert-Meunier (2010). Our proof is inspired by geometric arguments and is reminiscent of matroid intersection. Moreover, we show that the topological approach fails in this setting. We also discuss tropical colorful linear programming and show that it is NP-complete. We end with thoughts and questions on generalizations to polymatroids, anti-matroids as well as examples and matroid simplicial depth.</p>","PeriodicalId":50574,"journal":{"name":"Discrete & Computational Geometry","volume":"69 1","pages":"139-155"},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9805987/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10494381","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Combinatorial Properties and Recognition of Unit Square Visibility Graphs. 单位平方可见性图的组合性质与识别。
IF 0.8 3区 数学
Discrete & Computational Geometry Pub Date : 2023-01-01 Epub Date: 2023-03-22 DOI: 10.1007/s00454-022-00414-8
Katrin Casel, Henning Fernau, Alexander Grigoriev, Markus L Schmid, Sue Whitesides
{"title":"Combinatorial Properties and Recognition of Unit Square Visibility Graphs.","authors":"Katrin Casel,&nbsp;Henning Fernau,&nbsp;Alexander Grigoriev,&nbsp;Markus L Schmid,&nbsp;Sue Whitesides","doi":"10.1007/s00454-022-00414-8","DOIUrl":"10.1007/s00454-022-00414-8","url":null,"abstract":"<p><p>Unit square visibility graphs (USV) are described by axis-parallel visibility between unit squares placed in the plane. If the squares are required to be placed on integer grid coordinates, then USV become unit square grid visibility graphs (USGV), an alternative characterisation of the well-known rectilinear graphs. We extend known combinatorial results for USGV and we show that, in the weak case (i.e., visibilities do not necessarily translate into edges of the represented combinatorial graph), the area minimisation variant of their recognition problem is <math><mrow><mspace></mspace><mrow><mi>N</mi><mi>P</mi></mrow><mspace></mspace></mrow></math>-hard. We also provide combinatorial insights with respect to USV, and as our main result, we prove their recognition problem to be <math><mrow><mspace></mspace><mrow><mi>N</mi><mi>P</mi></mrow><mspace></mspace></mrow></math>-hard, which settles an open question.</p>","PeriodicalId":50574,"journal":{"name":"Discrete & Computational Geometry","volume":"69 4","pages":"937-980"},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10169907/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10301082","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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