arXiv - CS - Computational Geometry最新文献_第7页

Parallel Metric-based Anisotropic Mesh Adaptation using Speculative Execution on Shared Memory 利用共享内存上的指定执行实现基于公制的并行各向异性网格适配

arXiv - CS - Computational Geometry Pub Date : 2024-04-27 DOI: arxiv-2404.18030

Christos Tsolakis, Nikos Chrisochoides

引用次数: 0

Sibson's formula for higher order Voronoi diagrams 高阶沃罗诺图的西布森公式

arXiv - CS - Computational Geometry Pub Date : 2024-04-26 DOI: arxiv-2404.17422

Mercè Claverol, Andrea de las Heras-Parrilla, Clemens Huemer, Dolores Lara

引用次数: 0

Filling holes in LoD2 building models 填补 LoD2 建筑模型中的漏洞

arXiv - CS - Computational Geometry Pub Date : 2024-04-24 DOI: arxiv-2404.15892

Weixiao Gao, Ravi Peters, Hugo Ledoux, Jantien Stoter

{"title":"Filling holes in LoD2 building models","authors":"Weixiao Gao, Ravi Peters, Hugo Ledoux, Jantien Stoter","doi":"arxiv-2404.15892","DOIUrl":"https://doi.org/arxiv-2404.15892","url":null,"abstract":"This paper presents a new algorithm for filling holes in Level of Detail 2\u0000(LoD2) building mesh models, addressing the challenges posed by geometric\u0000inaccuracies and topological errors. Unlike traditional methods that often\u0000alter the original geometric structure or impose stringent input requirements,\u0000our approach preserves the integrity of the original model while effectively\u0000managing a range of topological errors. The algorithm operates in three\u0000distinct phases: (1) pre-processing, which addresses topological errors and\u0000identifies pseudo-holes; (2) detecting and extracting complete border rings of\u0000holes; and (3) remeshing, aimed at reconstructing the complete geometric\u0000surface. Our method demonstrates superior performance compared to related work\u0000in filling holes in building mesh models, achieving both uniform local geometry\u0000around the holes and structural completeness. Comparative experiments with\u0000established methods demonstrate our algorithm's effectiveness in delivering\u0000more complete and geometrically consistent hole-filling results, albeit with a\u0000slight trade-off in efficiency. The paper also identifies challenges in\u0000handling certain complex scenarios and outlines future directions for research,\u0000including the pursuit of a comprehensive repair goal for LoD2 models to achieve\u0000watertight 2-manifold models with correctly oriented normals. Our source code\u0000is available at\u0000https://github.com/tudelft3d/Automatic-Repair-of-LoD2-Building-Models.git","PeriodicalId":501570,"journal":{"name":"arXiv - CS - Computational Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140802618","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

Neural Slicer for Multi-Axis 3D Printing 用于多轴三维打印的神经切片机

arXiv - CS - Computational Geometry Pub Date : 2024-04-23 DOI: arxiv-2404.15061

Tao Liu, Tianyu Zhang, Yongxue Chen, Yuming Huang, Charlie C. L. Wang

引用次数: 0

Eliminating Crossings in Ordered Graphs 消除有序图中的交叉点

arXiv - CS - Computational Geometry Pub Date : 2024-04-15 DOI: arxiv-2404.09771

Akanksha Agrawal, Sergio Cabello, Michael Kaufmann, Saket Saurabh, Roohani Sharma, Yushi Uno, Alexander Wolff

{"title":"Eliminating Crossings in Ordered Graphs","authors":"Akanksha Agrawal, Sergio Cabello, Michael Kaufmann, Saket Saurabh, Roohani Sharma, Yushi Uno, Alexander Wolff","doi":"arxiv-2404.09771","DOIUrl":"https://doi.org/arxiv-2404.09771","url":null,"abstract":"Drawing a graph in the plane with as few crossings as possible is one of the\u0000central problems in graph drawing and computational geometry. Another option is\u0000to remove the smallest number of vertices or edges such that the remaining\u0000graph can be drawn without crossings. We study both problems in a\u0000book-embedding setting for ordered graphs, that is, graphs with a fixed vertex\u0000order. In this setting, the vertices lie on a straight line, called the spine,\u0000in the given order, and each edge must be drawn on one of several pages of a\u0000book such that every edge has at most a fixed number of crossings. In book\u0000embeddings, there is another way to reduce or avoid crossings; namely by using\u0000more pages. The minimum number of pages needed to draw an ordered graph without\u0000any crossings is its (fixed-vertex-order) page number. We show that the page number of an ordered graph with $n$ vertices and $m$\u0000edges can be computed in $2^m cdot n^{O(1)}$ time. An $O(log\u0000n)$-approximation of this number can be computed efficiently. We can decide in\u0000$2^{O(d sqrt{k} log (d+k))} cdot n^{O(1)}$ time whether it suffices to\u0000delete $k$ edges of an ordered graph to obtain a $d$-planar layout (where every\u0000edge crosses at most $d$ other edges) on one page. As an additional parameter,\u0000we consider the size $h$ of a hitting set, that is, a set of points on the\u0000spine such that every edge, seen as an open interval, contains at least one of\u0000the points. For $h=1$, we can efficiently compute the minimum number of edges\u0000whose deletion yields fixed-vertex-order page number $p$. For $h>1$, we give an\u0000XP algorithm with respect to $h+p$. Finally, we consider spine+$t$-track\u0000drawings, where some but not all vertices lie on the spine. The vertex order on\u0000the spine is given; we must map every vertex that does not lie on the spine to\u0000one of $t$ tracks, each of which is a straight line on a separate page,\u0000parallel to the spine.","PeriodicalId":501570,"journal":{"name":"arXiv - CS - Computational Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140587030","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

Hardness of Packing, Covering and Partitioning Simple Polygons with Unit Squares 简单多边形与单位正方形的包、盖和分割的硬度

arXiv - CS - Computational Geometry Pub Date : 2024-04-15 DOI: arxiv-2404.09835

Jack Stade, Mikkel Abrahamsen

{"title":"Hardness of Packing, Covering and Partitioning Simple Polygons with Unit Squares","authors":"Jack Stade, Mikkel Abrahamsen","doi":"arxiv-2404.09835","DOIUrl":"https://doi.org/arxiv-2404.09835","url":null,"abstract":"We show that packing axis-aligned unit squares into a simple polygon $P$ is\u0000NP-hard, even when $P$ is an orthogonal and orthogonally convex polygon with\u0000half-integer coordinates. It has been known since the early 80s that packing\u0000unit squares into a polygon with holes is NP-hard~[Fowler, Paterson, Tanimoto,\u0000Inf. Process. Lett., 1981], but the version without holes was conjectured to be\u0000polynomial-time solvable more than two decades ago~[Baur and Fekete,\u0000Algorithmica, 2001]. Our reduction relies on a new way of reducing from textsc{Planar-3SAT}.\u0000Interestingly, our geometric realization of a planar formula is non-planar.\u0000Vertices become rows and edges become columns, with crossings being allowed.\u0000The planarity ensures that all endpoints of rows and columns are incident to\u0000the outer face of the resulting drawing. We can then construct a polygon\u0000following the outer face that realizes all the logic of the formula\u0000geometrically, without the need of any holes. This new reduction technique proves to be general enough to also show\u0000hardness of two natural covering and partitioning problems, even when the input\u0000polygon is simple. We say that a polygon $Q$ is emph{small} if $Q$ is\u0000contained in a unit square. We prove that it is NP-hard to find a minimum\u0000number of small polygons whose union is $P$ (covering) and to find a minimum\u0000number of pairwise interior-disjoint small polygons whose union is $P$\u0000(partitioning), when $P$ is an orthogonal simple polygon with half-integer\u0000coordinates. This is the first partitioning problem known to be NP-hard for\u0000polygons without holes, with the usual objective of minimizing the number of\u0000pieces.","PeriodicalId":501570,"journal":{"name":"arXiv - CS - Computational Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140587031","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

SimpliCity: Reconstructing Buildings with Simple Regularized 3D Models SimpliCity：用简单的正则化 3D 模型重建建筑物

arXiv - CS - Computational Geometry Pub Date : 2024-04-11 DOI: arxiv-2404.08104

Jean-Philippe Bauchet, Raphael Sulzer, Florent Lafarge, Yuliya Tarabalka

引用次数: 0

Approximating shortest paths in weighted square and hexagonal meshes 近似加权正方形和六边形网格中的最短路径

arXiv - CS - Computational Geometry Pub Date : 2024-04-11 DOI: arxiv-2404.07562

Prosenjit Bose, Guillermo Esteban, David Orden, Rodrigo I. Silveira

{"title":"Approximating shortest paths in weighted square and hexagonal meshes","authors":"Prosenjit Bose, Guillermo Esteban, David Orden, Rodrigo I. Silveira","doi":"arxiv-2404.07562","DOIUrl":"https://doi.org/arxiv-2404.07562","url":null,"abstract":"Continuous 2-dimensional space is often discretized by considering a mesh of\u0000weighted cells. In this work we study how well a weighted mesh approximates the\u0000space, with respect to shortest paths. We consider a shortest path $\u0000mathit{SP_w}(s,t) $ from $ s $ to $ t $ in the continuous 2-dimensional space,\u0000a shortest vertex path $ mathit{SVP_w}(s,t) $ (or any-angle path), which is a\u0000shortest path where the vertices of the path are vertices of the mesh, and a\u0000shortest grid path $ mathit{SGP_w}(s,t) $, which is a shortest path in a graph\u0000associated to the weighted mesh. We provide upper and lower bounds on the\u0000ratios $ frac{lVert mathit{SGP_w}(s,t)rVert}{lVert\u0000mathit{SP_w}(s,t)rVert} $, $ frac{lVert mathit{SVP_w}(s,t)rVert}{lVert\u0000mathit{SP_w}(s,t)rVert} $, $ frac{lVert mathit{SGP_w}(s,t)rVert}{lVert\u0000mathit{SVP_w}(s,t)rVert} $ in square and hexagonal meshes, extending previous\u0000results for triangular grids. These ratios determine the effectiveness of\u0000existing algorithms that compute shortest paths on the graphs obtained from the\u0000grids. Our main results are that the ratio $ frac{lVert\u0000mathit{SGP_w}(s,t)rVert}{lVert mathit{SP_w}(s,t)rVert} $ is at most $\u0000frac{2}{sqrt{2+sqrt{2}}} approx 1.08 $ and $ frac{2}{sqrt{2+sqrt{3}}}\u0000approx 1.04 $ in a square and a hexagonal mesh, respectively.","PeriodicalId":501570,"journal":{"name":"arXiv - CS - Computational Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140587281","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

Walking Your Frog Fast in 4 LoC 在 4 LoC 中快速遛青蛙

arXiv - CS - Computational Geometry Pub Date : 2024-04-08 DOI: arxiv-2404.05708

Nis Meinert

引用次数: 0

Approximation Schemes for Geometric Knapsack for Packing Spheres and Fat Objects 用于包装球体和胖物体的几何包的近似方案

arXiv - CS - Computational Geometry Pub Date : 2024-04-05 DOI: arxiv-2404.03981

Pritam Acharya, Sujoy Bhore, Aaryan Gupta, Arindam Khan, Bratin Mondal, Andreas Wiese

{"title":"Approximation Schemes for Geometric Knapsack for Packing Spheres and Fat Objects","authors":"Pritam Acharya, Sujoy Bhore, Aaryan Gupta, Arindam Khan, Bratin Mondal, Andreas Wiese","doi":"arxiv-2404.03981","DOIUrl":"https://doi.org/arxiv-2404.03981","url":null,"abstract":"We study the geometric knapsack problem in which we are given a set of\u0000$d$-dimensional objects (each with associated profits) and the goal is to find\u0000the maximum profit subset that can be packed non-overlappingly into a given\u0000$d$-dimensional (unit hypercube) knapsack. Even if $d=2$ and all input objects\u0000are disks, this problem is known to be NP-hard [Demaine, Fekete, Lang, 2010].\u0000In this paper, we give polynomial-time $(1+varepsilon)$-approximation\u0000algorithms for the following types of input objects in any constant dimension\u0000$d$: - disks and hyperspheres, - a class of fat convex polygons that generalizes regular $k$-gons for $kge\u00005$ (formally, polygons with a constant number of edges, whose lengths are in a\u0000bounded range, and in which each angle is strictly larger than $pi/2$) - arbitrary fat convex objects that are sufficiently small compared to the\u0000knapsack. We remark that in our textsf{PTAS} for disks and hyperspheres, we output the\u0000computed set of objects, but for a $O_varepsilon(1)$ of them we determine\u0000their coordinates only up to an exponentially small error. However, it is not\u0000clear whether there always exists a $(1+varepsilon)$-approximate solution that\u0000uses only rational coordinates for the disks' centers. We leave this as an open\u0000problem which is related to well-studied geometric questions in the realm of\u0000circle packing.","PeriodicalId":501570,"journal":{"name":"arXiv - CS - Computational Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140587025","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