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International Journal of Computational Geometry and Applications最新文献

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A Case Study in Algorithm Engineering for Geometric Computing 几何计算算法工程案例研究
International Journal of Computational Geometry and Applications Pub Date : 1997-12-01 DOI: 10.1142/S0218195901000390
R. Tamassia, L. Vismara
{"title":"A Case Study in Algorithm Engineering for Geometric Computing","authors":"R. Tamassia, L. Vismara","doi":"10.1142/S0218195901000390","DOIUrl":"https://doi.org/10.1142/S0218195901000390","url":null,"abstract":"The goal of this paper is to prove the applicability of some advanced software design concepts to geometric computing through a vertical case study. The work is presented within the framework of the GeomLib project, aimed at developing an easy to use, reliable, open library of robust and efficient geometric algorithms. We present the criteria that have inspired the preliminary design of GeomLib and discuss the guidelines that we have followed in the initial implementation.","PeriodicalId":285210,"journal":{"name":"International Journal of Computational Geometry and Applications","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132742899","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: 17
The Three-Phase Method: A Unified Approach to Orthogonal Graph Drawing 三相法:一种统一的正交图绘制方法
International Journal of Computational Geometry and Applications Pub Date : 1997-09-18 DOI: 10.1142/S0218195900000310
T. Biedl, B. Madden, I. Tollis
{"title":"The Three-Phase Method: A Unified Approach to Orthogonal Graph Drawing","authors":"T. Biedl, B. Madden, I. Tollis","doi":"10.1142/S0218195900000310","DOIUrl":"https://doi.org/10.1142/S0218195900000310","url":null,"abstract":"In this paper, we study orthogonal graph drawings from a practical point of view. Most previously existing algorithms restricted the attention to graphs of maximum degree four. Here we study orthogonal drawing algorithms that work for any input graph, and discuss different models for such drawings. Then we introduce the three-phase method, a generic technique to create high-degree orthogonal drawings. This approach simplifies the description and implementation of orthogonal graph drawing, and can be applied to global as well as interactive and incremental settings.","PeriodicalId":285210,"journal":{"name":"International Journal of Computational Geometry and Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129001052","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: 54
On Geometric Path Query Problems 关于几何路径查询问题
International Journal of Computational Geometry and Applications Pub Date : 1997-08-06 DOI: 10.1142/S0218195901000675
D. Chen, O. Daescu, K. Klenk
{"title":"On Geometric Path Query Problems","authors":"D. Chen, O. Daescu, K. Klenk","doi":"10.1142/S0218195901000675","DOIUrl":"https://doi.org/10.1142/S0218195901000675","url":null,"abstract":"In this dissertation, we study several geometric path query problems. Our focus is primarily on the so-called \"two-point\" query problem: Given a scene of disjoint polygonal obstacles with totally n vertices in the plane, we construct efficient data structures that enable fast reporting of an \"optimal\" obstacle-avoiding path (or its length, cost, directions, etc.) between two arbitrary query points s and t that are given in an on-line fashion. We consider geometric paths under several optimality criteria: $rm Lsb{p}$ length, number of edges (called links), monotonicity with respect to a certain direction, and some combinations of length and links. Our methods are centered around the notion of gateways, a small number of easily identified points in the plane that control the paths we seek. We present solutions for the general cases based upon the computation of the minimum size visibility polygon for query points. We also give better solutions for several special cases based upon new geometric observations. Very few algorithms were previously known for two-point query problems and our results represent a significant addition to the field. In addition to our theoretical results, we also perform experimental studies on issues involved with the implementation of geometric algorithms. These studies are a necessary first step in the implementation of full path-planning systems.","PeriodicalId":285210,"journal":{"name":"International Journal of Computational Geometry and Applications","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121233162","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: 23
Optimal Algorithms to Detect Null-Homologous Cycles on 2-Manifolds 2-流形上零同源环检测的最优算法
International Journal of Computational Geometry and Applications Pub Date : 1997-06-01 DOI: 10.1142/S0218195997000119
T. Dey
{"title":"Optimal Algorithms to Detect Null-Homologous Cycles on 2-Manifolds","authors":"T. Dey","doi":"10.1142/S0218195997000119","DOIUrl":"https://doi.org/10.1142/S0218195997000119","url":null,"abstract":"Given a cycle of length k on a triangulated 2-manifold, we determine if it is null-homologous (bounds a surface) in O(n+k) optimal time and space where n is the size of the triangulation. Further, with a preprocessing step of O(n) time we answer the same query for any cycle of length k in O(g+k) time, g the genus of the 2-manifold. This is optimal for k < g.","PeriodicalId":285210,"journal":{"name":"International Journal of Computational Geometry and Applications","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134379427","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: 3
The Floodlight Problem 泛光灯问题
International Journal of Computational Geometry and Applications Pub Date : 1997-02-01 DOI: 10.1142/S0218195997000090
P. Bose, L. Guibas, A. Lubiw, M. Overmars, D. Souvaine, J. Urrutia
{"title":"The Floodlight Problem","authors":"P. Bose, L. Guibas, A. Lubiw, M. Overmars, D. Souvaine, J. Urrutia","doi":"10.1142/S0218195997000090","DOIUrl":"https://doi.org/10.1142/S0218195997000090","url":null,"abstract":"Given three angles summing to 2π, given n points in the plane and a tripartition k1 + k2 + k3 = n, we can tripartition the plane into three wedges of the given angles so that the i-th wedge contains ki of the points. This new result on dissecting point sets is used to prove that lights of specified angles not exceeding π can be placed at n fixed points in the plane to illuminate the entire plane if and only if the angles sum to at least 2π. We give O(nlog n) algorithms for both these problems.","PeriodicalId":285210,"journal":{"name":"International Journal of Computational Geometry and Applications","volume":"119 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126904713","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: 53
k-Pairs Non-Crossing Shortest Paths in a Simple Polygon 简单多边形中的k对非交叉最短路径
International Journal of Computational Geometry and Applications Pub Date : 1996-12-16 DOI: 10.1142/S0218195999000315
Evanthia Papadopoulou
{"title":"k-Pairs Non-Crossing Shortest Paths in a Simple Polygon","authors":"Evanthia Papadopoulou","doi":"10.1142/S0218195999000315","DOIUrl":"https://doi.org/10.1142/S0218195999000315","url":null,"abstract":"This paper presents an O(n+k) time algorithm to compute the set of k non-crossing shortest paths between k source-destination pairs of points on the boundary of a simple polygon of n vertices. Paths are allowed to overlap but are not allowed to cross in the plane. A byproduct of this result is an O(n) time algorithm to compute a balanced geodesic triangulation which is easy to implement. The algorithm extends to a simple polygon with one hole where source destination pairs may appear on both the inner and outer boundary of the polygon. In the latter case, the goal is to compute a collection of non-crossing paths of minimum total cost.","PeriodicalId":285210,"journal":{"name":"International Journal of Computational Geometry and Applications","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127985859","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: 30
Drawing Directed Acyclic Graphs: An Experimental Study 绘制有向无环图的实验研究
International Journal of Computational Geometry and Applications Pub Date : 1996-09-18 DOI: 10.1142/S0218195900000358
G. Battista, Ashim Garg, G. Liotta, A. Parise, R. Tamassia, Emanuele Tassinari, F. Vargiu, L. Vismara
{"title":"Drawing Directed Acyclic Graphs: An Experimental Study","authors":"G. Battista, Ashim Garg, G. Liotta, A. Parise, R. Tamassia, Emanuele Tassinari, F. Vargiu, L. Vismara","doi":"10.1142/S0218195900000358","DOIUrl":"https://doi.org/10.1142/S0218195900000358","url":null,"abstract":"In this paper we consider the class of directed acyclic graphs (DAGs), and present the results of an experimental study on four drawing algorithms specifically developed for DAGs. Our study is conducted on two large test suites of DAGs and yields more than 30 charts comparing the performance of the drawing algorithms with respect to several quality measures, including area, crossings, bends, and aspect ratio. The algorithms exhibit various trade-offs with respect to the quality measures, and none of them clearly outperforms the others.","PeriodicalId":285210,"journal":{"name":"International Journal of Computational Geometry and Applications","volume":"1631 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132127473","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: 38
Diamonds are Not a Minimum Weight Triangulation's Best Friend 钻石不是最小重量三角测量的好朋友
International Journal of Computational Geometry and Applications Pub Date : 1996-08-12 DOI: 10.1142/S0218195902000979
P. Bose, L. Devroye, W. Evans
{"title":"Diamonds are Not a Minimum Weight Triangulation's Best Friend","authors":"P. Bose, L. Devroye, W. Evans","doi":"10.1142/S0218195902000979","DOIUrl":"https://doi.org/10.1142/S0218195902000979","url":null,"abstract":"Two recent methods have increased hopes of finding a polynomial time solution to the problem of computing the minimum weight triangulation of a set S of n points in the plane. Both involve computing what was believed to be a connected or nearly connected subgraph of the minimum weight triangulation, and then completing the triangulation optimally. The first method uses the light graph of S as its initial subgraph. The second method uses the LMT-skeleton of S. Both methods rely, for their polynomial time bound, on the initial subgraphs having only a constant number of components. Experiments performed by the authors of these methods seemed to confirm that randomly chosen point sets displayed this desired property. We show that there exist point sets where the number of components is linear in n. In fact, the expected number of components in either graph on a randomly chosen point set is linear in n, and the probability of the number of components exceeding some constant times n tends to one.","PeriodicalId":285210,"journal":{"name":"International Journal of Computational Geometry and Applications","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116770664","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: 17
Computing Largest Circles Separating Two Sets of Segments 计算分离两组分段的最大圆
International Journal of Computational Geometry and Applications Pub Date : 1996-08-12 DOI: 10.1142/S0218195900000036
J. Boissonnat, J. Czyzowicz, O. Devillers, J. Urrutia, M. Yvinec
{"title":"Computing Largest Circles Separating Two Sets of Segments","authors":"J. Boissonnat, J. Czyzowicz, O. Devillers, J. Urrutia, M. Yvinec","doi":"10.1142/S0218195900000036","DOIUrl":"https://doi.org/10.1142/S0218195900000036","url":null,"abstract":"A circle $C$ separates two planar sets if it encloses one of the sets and its open interior disk does not meet the other set. A separating circle is a largest one if it cannot be locally increased while still separating the two given sets. An $Theta(n log n)$ optimal algorithm is proposed to find all largest circles separating two given sets of line segments when line segments are allow ed to meet only at their endpoints. This settles an open problem from a previous papercite{bcdy-csp-95}. In the general case, when line segments may intersect $Omega(n^2)$ times, our algorithm can be adapted to work in $O(n alpha(n) log n)$ time and $O(n alpha(n))$ space, where $alpha(n)$ represents the extremely slowly growing inverse of Ackermann function.","PeriodicalId":285210,"journal":{"name":"International Journal of Computational Geometry and Applications","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131001626","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
Finite representations of real parametric curves and surfaces 实参数曲线和曲面的有限表示
International Journal of Computational Geometry and Applications Pub Date : 1995-09-01 DOI: 10.1142/S0218195995000180
C. Bajaj, A. Royappa
{"title":"Finite representations of real parametric curves and surfaces","authors":"C. Bajaj, A. Royappa","doi":"10.1142/S0218195995000180","DOIUrl":"https://doi.org/10.1142/S0218195995000180","url":null,"abstract":"Algebraic curves and surfaces are commonly used in geometric modeling. Parametric curves and surfaces are those that can be represented using rational parametric equations, and are particularly important. In geometric modeling applications, the parametric equations are restricted to some bounded portion of the domain, yielding a segment of a curve or a patch of a surface. However, the algebraic curve or surface is an image of the entire infinite parameter domain. Attempting to map the entire curve or surface using very large regions of the parameter domain is not a solution because some finite points may be images of infinite parameter values.","PeriodicalId":285210,"journal":{"name":"International Journal of Computational Geometry and Applications","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1995-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116680195","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: 29
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