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4th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2007)最新文献

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Variants of Jump Flooding Algorithm for Computing Discrete Voronoi Diagrams 计算离散Voronoi图的跳跃泛洪算法的变体
4th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2007) Pub Date : 2007-07-09 DOI: 10.1109/ISVD.2007.41
Guodong Rong, T. Tan
{"title":"Variants of Jump Flooding Algorithm for Computing Discrete Voronoi Diagrams","authors":"Guodong Rong, T. Tan","doi":"10.1109/ISVD.2007.41","DOIUrl":"https://doi.org/10.1109/ISVD.2007.41","url":null,"abstract":"Jump flooding algorithm (JFA) is an interesting way to utilize the graphics processing unit to efficiently compute Voronoi diagrams and distance transforms in 2D discrete space. This paper presents three novel variants of JFA. They focus on different aspects of JFA: the first variant can further reduce the errors of JFA; the second variant can greatly increase the speed of JFA; and the third variant enables JFA to compute Voronoi diagrams in 3D space in a slice-by-slice manner, without a high end graphics processing unit. These variants are orthogonal to each other. In other words, it is possible to combine any two or all of them together.","PeriodicalId":148710,"journal":{"name":"4th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2007)","volume":"101 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131418960","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: 52
Direct Diffusion Method for the Construction of Generalized Voronoi Diagrams 构造广义Voronoi图的直接扩散法
4th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2007) Pub Date : 2007-07-09 DOI: 10.1109/ISVD.2007.17
T. Nishida, Shingo Ono, K. Sugihara
{"title":"Direct Diffusion Method for the Construction of Generalized Voronoi Diagrams","authors":"T. Nishida, Shingo Ono, K. Sugihara","doi":"10.1109/ISVD.2007.17","DOIUrl":"https://doi.org/10.1109/ISVD.2007.17","url":null,"abstract":"We propose a new method to construct discrete Voronoi diagrams, which we call the direct diffusion method. Once we implement it as software, we can easily modify it for various types of digital Voronoi diagrams by changing only the the distance function from a point to a generator represented by a general shape. Our method can construct discrete Voronoi diagrams even if the generator points are not at the centers of pixels. Furthermore, our method can construct the Voronoi diagrams without approximating general shapes by sets of pixels.","PeriodicalId":148710,"journal":{"name":"4th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2007)","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128333614","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: 5
Two-dimensional line space Voronoi Diagram 二维线空间Voronoi图
4th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2007) Pub Date : 2007-07-09 DOI: 10.1109/ISVD.2007.39
Stéphane Rivière, Dominique Schmitt
{"title":"Two-dimensional line space Voronoi Diagram","authors":"Stéphane Rivière, Dominique Schmitt","doi":"10.1109/ISVD.2007.39","DOIUrl":"https://doi.org/10.1109/ISVD.2007.39","url":null,"abstract":"Given a set of points called sites, the Voronoi diagram is a partition of the plane into sets of points having the same closest site. Several generalizations of the Voronoi diagram have been studied, mainly Voronoi diagrams for different distances (other than the Euclidean one), and Voronoi diagrams for sites that are not necessarily points (line segments for example). In this paper we present a new generalization of the Voronoi diagram in the plane, in which we shift our interest from points to lines, that is, we compute the partition of the set of lines in the plane into sets of lines having the same closest site (where sites are points in the plane). We first define formally this diagram and give first properties. Then we use a duality relationship between points and lines to visualize this data structure and give more properties. We show that the size of this line space Voronoi diagram for n sites is in Theta(n2) and give an optimal algorithm for its explicit computation. We then show a remarkable relationship between this diagram and the dual arrangement of the sites and give a new result on an arrangement of lines: we show that the size of the zone of a line augmented with its incident faces is still in O(n). We finally apply this result to show that the size of the zone of a line in the line space Voronoi diagram is in O(n).","PeriodicalId":148710,"journal":{"name":"4th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2007)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130320000","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: 8
Computing the 3D Voronoi Diagram Robustly: An Easy Explanation 计算三维Voronoi图稳健:一个简单的解释
4th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2007) Pub Date : 2007-07-09 DOI: 10.1109/ISVD.2007.10
H. Ledoux
{"title":"Computing the 3D Voronoi Diagram Robustly: An Easy Explanation","authors":"H. Ledoux","doi":"10.1109/ISVD.2007.10","DOIUrl":"https://doi.org/10.1109/ISVD.2007.10","url":null,"abstract":"Many algorithms exist for computing the 3D Voronoi diagram, but in most cases they assume that the input is in general position. Because of the many degeneracies that arise in 3D geometric computing, their implementation is still problematic in practice. In this paper, I describe a simple 3D Voronoi diagram (and Delaunay tetrahedralization) algorithm, and I explain, by giving as many details and insights as possible, how to ensure that it outputs a correct structure, regardless of the spatial distribution of the points in the input.","PeriodicalId":148710,"journal":{"name":"4th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2007)","volume":"163 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123135339","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: 36
The Voronoi diagram of circles made easy Voronoi的圆图变得简单了
4th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2007) Pub Date : 2007-07-09 DOI: 10.1109/ISVD.2007.37
F. Anton, D. Mioc, C. Gold
{"title":"The Voronoi diagram of circles made easy","authors":"F. Anton, D. Mioc, C. Gold","doi":"10.1109/ISVD.2007.37","DOIUrl":"https://doi.org/10.1109/ISVD.2007.37","url":null,"abstract":"Proximity queries among circles could be effectively answered if the Delaunay graph for sets of circles could be computed in an efficient and exact way. In this paper, we first show a necessary and sufficient condition of connectivity of the Voronoi diagram of circles. Then, we show how the Delaunay graph of circles (the dual graph of the Voronoi diagram of circles) can be computed exactly, and in a much simpler way, by computing the eigenvalues of a two by two matrix.","PeriodicalId":148710,"journal":{"name":"4th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2007)","volume":"115 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134007764","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: 4
Using the Delaunay Triangulation/ Voronoi Diagram to extract Building Information from Raw LIDAR Data 使用Delaunay三角剖分/ Voronoi图从原始激光雷达数据中提取建筑信息
4th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2007) Pub Date : 2007-07-09 DOI: 10.1109/ISVD.2007.40
R. Tse, C. Gold, D. Kidner
{"title":"Using the Delaunay Triangulation/ Voronoi Diagram to extract Building Information from Raw LIDAR Data","authors":"R. Tse, C. Gold, D. Kidner","doi":"10.1109/ISVD.2007.40","DOIUrl":"https://doi.org/10.1109/ISVD.2007.40","url":null,"abstract":"An increasing need for automated 3D city reconstruction models is being driven by a variety of applications, from tourism to disaster management. The arrival of LIDAR (light detection and ranging) - airborne laser altimetry - now provides rapid elevation models of terrain and buildings. LIDAR data contains X, Y and Z coordinates only, it does not provide any building information. The challenge is to convert the data into CAD-type models containing walls, roof planes and terrain which can be rapidly displayed from any 3D viewpoint. This paper shows an alternative method to locate building blocks and identify the roof structures with the use of the Delaunay triangulation and its dual Voronoi diagram.","PeriodicalId":148710,"journal":{"name":"4th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2007)","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125614036","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: 11
Greedy Beta-Skeleton in Three Dimensions 贪婪-三维骨架
4th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2007) Pub Date : 2007-07-09 DOI: 10.1109/ISVD.2007.27
Hisamoto Hiyoshi
{"title":"Greedy Beta-Skeleton in Three Dimensions","authors":"Hisamoto Hiyoshi","doi":"10.1109/ISVD.2007.27","DOIUrl":"https://doi.org/10.1109/ISVD.2007.27","url":null,"abstract":"In two dimensions, the beta-skeleton is one of the most practical methods for reconstructing smooth curves from a given unorganized point set because of its provable guarantee. In three dimensions, however, the beta-skeleton cannot be used for surface reconstruction because it may contain unwanted holes omnipresently, no matter how high sampling density is. To overcome this difficulty, an extension of the beta-skeleton, called greedy beta-skeleton, is proposed. It is shown by computational experiments that the unwanted holes do not appear in the greedy beta-skeleton even when the dimension is three. In addition, the greedy beta-skeletons are computed for several practical inputs, and their fairness is examined. Computation results for some variants of the greedy beta-skeleton are also reported.","PeriodicalId":148710,"journal":{"name":"4th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2007)","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132351384","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: 4
Apollonius diagrams and the Representation of Sounds and Music 阿波罗尼乌斯图和声音和音乐的表现
4th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2007) Pub Date : 2007-07-09 DOI: 10.1109/ISVD.2007.7
Alex McLean, F. Leymarie, Geraint A. Wiggins
{"title":"Apollonius diagrams and the Representation of Sounds and Music","authors":"Alex McLean, F. Leymarie, Geraint A. Wiggins","doi":"10.1109/ISVD.2007.7","DOIUrl":"https://doi.org/10.1109/ISVD.2007.7","url":null,"abstract":"We introduce the use of weighted medial graph structures to represent sounds and musical events. Such structures permit the building of hierarchical neighborhood relationships (symmetries) while mapping time to a weight (of a note, or event). This is useful to relate perceptual organisations (groupings in the sense of Gestalt theory) both visually and aurally. We treat time in a cinematographic way, effectively using a space- time representation. The use of colour, modulation (of waveforms), orientation, speed, etc., allows us to integrate multiple musical features in our dynamic diagrams. We provide illustrations, including animations, of our ideas.","PeriodicalId":148710,"journal":{"name":"4th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2007)","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125066164","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
Time Convex Hull with a Highway 时间凸壳与高速公路
4th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2007) Pub Date : 2007-07-09 DOI: 10.1109/ISVD.2007.38
Teng-Kai Yu, D. T. Lee
{"title":"Time Convex Hull with a Highway","authors":"Teng-Kai Yu, D. T. Lee","doi":"10.1109/ISVD.2007.38","DOIUrl":"https://doi.org/10.1109/ISVD.2007.38","url":null,"abstract":"We consider the problem of computing the time convex hull of a set of points in the presence of a straight-line highway in the plane. The traveling speed in the plane is assumed to be much slower than that along the highway. The shortest time path between two arbitrary points is either the straight-line segment connecting these two points or a path that passes through the highway. The time convex hull, CHt(P), of a set P of n points is the smallest set containing P such that all the shortest time paths between any two points lie in CHt(P). In this paper we give a Theta(n log n) time algorithm for solving the time convex hull problem for a set of n points in the presence of a highway.","PeriodicalId":148710,"journal":{"name":"4th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2007)","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125388168","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: 4
Degeneracy of Angular Voronoi Diagram 角Voronoi图的简并性
4th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2007) Pub Date : 2007-07-09 DOI: 10.1109/ISVD.2007.14
H. Muta, Kimikazu Kato
{"title":"Degeneracy of Angular Voronoi Diagram","authors":"H. Muta, Kimikazu Kato","doi":"10.1109/ISVD.2007.14","DOIUrl":"https://doi.org/10.1109/ISVD.2007.14","url":null,"abstract":"Angular Voronoi diagram was introduced by Asano et al. as fundamental research for a mesh generation. In an angular Voronoi diagram, the edges are curves of degree three. From view of computational robustness we need to treat the curves carefully, because they might have a singularity. We enumerate all the possible types of curves that appear as an edge of an angular Voronoi diagram, which tells us what kind of degeneracy is possible and tells us necessity of considering a singularity for computational robustness.","PeriodicalId":148710,"journal":{"name":"4th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2007)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129413270","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
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