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International Journal of Computational Geometry and Applications最新文献

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On Dihedral Angle Sums of Prisms and Hexahedra 关于棱镜与六面体的二面角和
International Journal of Computational Geometry and Applications Pub Date : 2023-11-07 DOI: 10.1142/s0218195923500036
Sergey Korotov, Jon Eivind Vatne
{"title":"On Dihedral Angle Sums of Prisms and Hexahedra","authors":"Sergey Korotov, Jon Eivind Vatne","doi":"10.1142/s0218195923500036","DOIUrl":"https://doi.org/10.1142/s0218195923500036","url":null,"abstract":"Various angle characteristics are used (e.g. in finite element methods or computer graphics) when evaluating the quality of computational meshes which may consist, in the three-dimensional case, of tetrahedra, prisms, hexahedra and pyramids. Thus, it is of interest to derive (preferably tight) bounds for dihedral angle sums, i.e. sums of angles between faces, of such mesh elements. For tetrahedra this task was solved by Gaddum in 1952. For pyramids, this was resolved by Korotov, Lund and Vatne in 2022. In this paper, we compute tight bounds for the remaining two cases, hexahedra and prisms.","PeriodicalId":285210,"journal":{"name":"International Journal of Computational Geometry and Applications","volume":"107 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135545464","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Some Results on Semi-Symmetric Spaces 关于半对称空间的一些结果
International Journal of Computational Geometry and Applications Pub Date : 2023-11-02 DOI: 10.1142/s0218195923500024
Abderrazzak Benroummane
{"title":"Some Results on Semi-Symmetric Spaces","authors":"Abderrazzak Benroummane","doi":"10.1142/s0218195923500024","DOIUrl":"https://doi.org/10.1142/s0218195923500024","url":null,"abstract":"We give some properties of semi-symmetric pseudo-Riemannian manifolds as an indecomposable irreducible Ricci pseudo-Riemannian manifold (i.e. the minimal polynomial of its Ricci operator is irreducible) is semi symmetric if and only if it is locally symmetric. We also show that any semi-symmetric pseudo-Riemannian manifold will be foliated. Moreover, if the metric is Lorentzian, the Ricci operator has only real eigenvalues and more precisely, on each leaf, it is diagonalizable with at most a single non zero eigenvalue or isotropic.","PeriodicalId":285210,"journal":{"name":"International Journal of Computational Geometry and Applications","volume":"29 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135973335","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Bottleneck Convex Subsets: Finding k Large Convex Sets in a Point Set 瓶颈凸子集:在一个点集中求k个大凸集
International Journal of Computational Geometry and Applications Pub Date : 2023-02-01 DOI: 10.1142/s0218195922410035
Stephane Durocher, J. Mark Keil, Saeed Mehrabi, Debajyoti Mondal
{"title":"Bottleneck Convex Subsets: Finding k Large Convex Sets in a Point Set","authors":"Stephane Durocher, J. Mark Keil, Saeed Mehrabi, Debajyoti Mondal","doi":"10.1142/s0218195922410035","DOIUrl":"https://doi.org/10.1142/s0218195922410035","url":null,"abstract":"Chvátal and Klincsek (1980) gave an [Formula: see text]-time algorithm for the problem of finding a maximum-cardinality convex subset of an arbitrary given set [Formula: see text] of [Formula: see text] points in the plane. This paper examines a generalization of the problem, the Bottleneck Convex Subsets problem: given a set [Formula: see text] of [Formula: see text] points in the plane and a positive integer [Formula: see text], select [Formula: see text] pairwise disjoint convex subsets of [Formula: see text] such that the cardinality of the smallest subset is maximized. Equivalently, a solution maximizes the cardinality of [Formula: see text] mutually disjoint convex subsets of [Formula: see text] of equal cardinality. We give an algorithm that solves the problem exactly, with running time polynomial in [Formula: see text] when [Formula: see text] is fixed. We then show the problem to be NP-hard when [Formula: see text] is an arbitrary input parameter, even for points in general position. Finally, we give a fixed-parameter tractable algorithm parameterized in terms of the number of points strictly interior to the convex hull.","PeriodicalId":285210,"journal":{"name":"International Journal of Computational Geometry and Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136019487","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Navigating Weighted Regions with Scattered Skinny Tetrahedra 用分散的瘦四面体导航加权区域
International Journal of Computational Geometry and Applications Pub Date : 2015-12-09 DOI: 10.1142/S0218195917600020
Siu-Wing Cheng, Man-Kwun Chiu, Jiongxin Jin, A. Vigneron
{"title":"Navigating Weighted Regions with Scattered Skinny Tetrahedra","authors":"Siu-Wing Cheng, Man-Kwun Chiu, Jiongxin Jin, A. Vigneron","doi":"10.1142/S0218195917600020","DOIUrl":"https://doi.org/10.1142/S0218195917600020","url":null,"abstract":"We propose an algorithm for finding a ((1+varepsilon ))-approximate shortest path through a weighted 3D simplicial complex (mathcal T). The weights are integers from the range [1, W] and the vertices have integral coordinates. Let N be the largest vertex coordinate magnitude, and let n be the number of tetrahedra in (mathcal T). Let (rho ) be some arbitrary constant. Let (kappa ) be the size of the largest connected component of tetrahedra whose aspect ratios exceed (rho ). There exists a constant C dependent on (rho ) but independent of (mathcal T) such that if (kappa le frac{1}{C}log log n + O(1)), the running time of our algorithm is polynomial in n, (1/varepsilon ) and (log (NW)). If (kappa = O(1)), the running time reduces to (O(n varepsilon ^{-O(1)}(log (NW))^{O(1)})).","PeriodicalId":285210,"journal":{"name":"International Journal of Computational Geometry and Applications","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114326403","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
An Optimal Algorithm for Reconstructing Point Set Order Types from Radial Orderings 一种从径向排序重构点集排序类型的最优算法
International Journal of Computational Geometry and Applications Pub Date : 2014-12-15 DOI: 10.1142/S0218195917600044
O. Aichholzer, Vincent Kusters, Wolfgang Mulzer, Alexander Pilz, Manuel Wettstein
{"title":"An Optimal Algorithm for Reconstructing Point Set Order Types from Radial Orderings","authors":"O. Aichholzer, Vincent Kusters, Wolfgang Mulzer, Alexander Pilz, Manuel Wettstein","doi":"10.1142/S0218195917600044","DOIUrl":"https://doi.org/10.1142/S0218195917600044","url":null,"abstract":"Let $P$ be a set of $n$ labeled points in the plane. The radial system of $P$ describes, for each $pin P$, the order in which a ray that rotates around $p$ encounters the points in $P setminus {p}$. This notion is related to the order type of $P$, which describes the orientation (clockwise or counterclockwise) of every ordered triple in $P$. Given only the order type, the radial system is uniquely determined and can easily be obtained. The converse, however, is not true. Indeed, let $R$ be the radial system of $P$, and let $T(R)$ be the set of all order types with radial system $R$ (we define $T(R) = emptyset$ for the case that $R$ is not a valid radial system). Aichholzer et al. (Reconstructing Point Set Order Types from Radial Orderings, in ISAAC 2014) show that $T(R)$ may contain up to $n-1$ order types. They also provide polynomial-time algorithms to compute $T(R)$ when only $R$ is given. \u0000We describe a new algorithm for finding $T(R)$. The algorithm constructs the convex hulls of all possible point sets with the radial system $R$. After that, orientation queries on point triples can be answered in constant time. A representation of this set of convex hulls can be found in $O(n)$ queries to the radial system, using $O(n)$ additional processing time. This is optimal. Our results also generalize to abstract order types.","PeriodicalId":285210,"journal":{"name":"International Journal of Computational Geometry and Applications","volume":"155 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116633218","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 14
On the Most Likely Voronoi Diagram and Nearest Neighbor Searching 关于最可能Voronoi图和最近邻搜索
International Journal of Computational Geometry and Applications Pub Date : 2014-12-15 DOI: 10.1142/S0218195916600025
S. Suri, Kevin Verbeek
{"title":"On the Most Likely Voronoi Diagram and Nearest Neighbor Searching","authors":"S. Suri, Kevin Verbeek","doi":"10.1142/S0218195916600025","DOIUrl":"https://doi.org/10.1142/S0218195916600025","url":null,"abstract":"We consider the problem of nearest-neighbor searching among a set of stochastic sites, where a stochastic site is a tuple ((s_i, pi _i)) consisting of a point (s_i) in a (d)-dimensional space and a probability (pi _i) determining its existence. The problem is interesting and non-trivial even in (1)-dimension, where the Most Likely Voronoi Diagram (LVD) is shown to have worst-case complexity (Omega (n^2)). We then show that under more natural and less adversarial conditions, the size of the (1)-dimensional LVD is significantly smaller: (1) (Theta (k n)) if the input has only (k) distinct probability values, (2) (O(n log n)) on average, and (3) (O(n sqrt{n})) under smoothed analysis. We also present an alternative approach to the most likely nearest neighbor (LNN) search using Pareto sets, which gives a linear-space data structure and sub-linear query time in 1D for average and smoothed analysis models, as well as worst-case with a bounded number of distinct probabilities. Using the Pareto-set approach, we can also reduce the multi-dimensional LNN search to a sequence of nearest neighbor and spherical range queries.","PeriodicalId":285210,"journal":{"name":"International Journal of Computational Geometry and Applications","volume":"302 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115439808","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 22
Dynamic Point Labeling is Strongly PSPACE-Complete 动态点标记是强pspace完备的
International Journal of Computational Geometry and Applications Pub Date : 2014-12-01 DOI: 10.1142/S0218195914600127
K. Buchin, Dirk H. P. Gerrits
{"title":"Dynamic Point Labeling is Strongly PSPACE-Complete","authors":"K. Buchin, Dirk H. P. Gerrits","doi":"10.1142/S0218195914600127","DOIUrl":"https://doi.org/10.1142/S0218195914600127","url":null,"abstract":"An important but strongly NP-hard problem in automated cartography is how to best place textual labels for point features on a static map. We examine the complexity of various generalizations of this problem for dynamic and/or interactive maps. Specifically, we show that it is strongly PSPACE/complete to decide whether there is a smooth dynamic labeling (function from time to static labelings) when the points move, when points are added and removed, or when the user pans, rotates, and/or zooms their view of the points.","PeriodicalId":285210,"journal":{"name":"International Journal of Computational Geometry and Applications","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124975914","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 14
Geodesic-Preserving Polygon Simplification 保持测地线的多边形简化
International Journal of Computational Geometry and Applications Pub Date : 2013-09-16 DOI: 10.1142/S0218195914600097
O. Aichholzer, T. Hackl, Matias Korman, Alexander Pilz, B. Vogtenhuber
{"title":"Geodesic-Preserving Polygon Simplification","authors":"O. Aichholzer, T. Hackl, Matias Korman, Alexander Pilz, B. Vogtenhuber","doi":"10.1142/S0218195914600097","DOIUrl":"https://doi.org/10.1142/S0218195914600097","url":null,"abstract":"Polygons are a paramount data structure in computational geometry. While the complexity of many algorithms on simple polygons or polygons with holes depends on the size of the input polygon, the intrinsic complexity of the problems these algorithms solve is often related to the reflex vertices of the polygon. In this paper, we give an easy-to-describe linear-time method to replace an input polygon (mathcal{P}) by a polygon (mathcal{P}') such that (1) (mathcal{P}') contains (mathcal{P}), (2) (mathcal{P}') has its reflex vertices at the same positions as (mathcal{P}), and (3) the number of vertices of (mathcal{P}') is linear in the number of reflex vertices. Since the solutions of numerous problems on polygons (including shortest paths, geodesic hulls, separating point sets, and Voronoi diagrams) are equivalent for both (mathcal{P}) and (mathcal{P}'), our algorithm can be used as a preprocessing step for several algorithms and makes their running time dependent on the number of reflex vertices rather than on the size of (mathcal{P}).","PeriodicalId":285210,"journal":{"name":"International Journal of Computational Geometry and Applications","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127498266","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Testing Mutual duality of Planar graphs 平面图互对偶性的检验
International Journal of Computational Geometry and Applications Pub Date : 2013-03-07 DOI: 10.1142/S0218195914600103
Patrizio Angelini, Thomas Bläsius, Ignaz Rutter
{"title":"Testing Mutual duality of Planar graphs","authors":"Patrizio Angelini, Thomas Bläsius, Ignaz Rutter","doi":"10.1142/S0218195914600103","DOIUrl":"https://doi.org/10.1142/S0218195914600103","url":null,"abstract":"We introduce and study the problem Mutual Planar Duality, which asks for planar graphs G 1 and G 2 whether G 1 can be embedded such that its dual is isomorphic to G 2. We show NP-completeness for general graphs and give a linear-time algorithm for biconnected graphs.","PeriodicalId":285210,"journal":{"name":"International Journal of Computational Geometry and Applications","volume":"127 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117043808","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
On the Farthest Line-Segment Voronoi Diagram 关于最远线段Voronoi图
International Journal of Computational Geometry and Applications Pub Date : 2012-12-19 DOI: 10.1142/S0218195913600121
Evanthia Papadopoulou, S. Dey
{"title":"On the Farthest Line-Segment Voronoi Diagram","authors":"Evanthia Papadopoulou, S. Dey","doi":"10.1142/S0218195913600121","DOIUrl":"https://doi.org/10.1142/S0218195913600121","url":null,"abstract":"The farthest line-segment Voronoi diagram shows properties surprisingly different from the farthest point Voronoi diagram: Voronoi regions may be disconnected and they are not characterized by convex-hull properties. In this paper we introduce the farthest line-segment hull and its Gaussian map, a closed polygonal curve that characterizes the regions of the farthest line-segment Voronoi diagram similarly to the way an ordinary convex hull characterizes the regions of the farthest-point Voronoi diagram. We also derive tighter bounds on the (linear) size of the farthest line-segment Voronoi diagram. With the purpose of unifying construction algorithms for farthest-point and farthest line-segment Voronoi diagrams, we adapt standard techniques for the construction of a convex hull to compute the farthest line-segment hull in O(n logn) or output-sensitive O(n logh) time, where n is the number of segments and h is the size of the hull (number of Voronoi faces). As a result, the farthest line-segment Voronoi diagram can be constructed in output sensitive O(n logh) time.","PeriodicalId":285210,"journal":{"name":"International Journal of Computational Geometry and Applications","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130437402","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 22
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