Uncertain Voronoi diagram

In this paper, we introduce the fuzzy Voronoi diagram as an extension of the Voronoi diagram. We assume Voronoi sites to be fuzzy points and then define the Voronoi diagram for this kind of sites, then we provide an algorithm for computing this diagram based on Fortune's algorithm which costs O(nlogn) time. Also we introduce the fuzzy Voronoi diagram for a set of fuzzy circles, rather than fuzzy points, of the same radius. We prove that the boundary of this diagram is formed by the intersection of some hyperbolae, and finally we provide an O(n³logn)-time algorithm to compute the boundary.     

A nearly optimal deterministic parallel Voronoi diagram algorithm

We describe ann-processor,O(log(n) log log(n))-time CRCW algorithm to construct the Voronoi diagram for a set ofn point-sites in the plane.A preliminary version of this paper was presented at the 17th EATCS ICALP meeting at Warwick, England, in July 1990.Supported by the US NSF under Grants CCR 890221 and CCR 8906949.Supported by the US NSF under Grants CCR 8810568, CCR-9003299, and IRI-9116843, and by the NSF and DARPA under Grant CCR 8908092.Supported by the EU Esprit program under BRAs 3075 (ALCOM) and 7141 (ALCOM II).     

A simple GPU-based approach for 3D Voronoi diagram construction and visualization

In this paper we propose a simple GPU-based approach for discrete incremental approximation of 3D Voronoi diagram. By constructing region maps via GPU. Nearest sites, space clustering, and shortest distance query can be quickly answered by looking up the region map. In addition, we propose another representation of the 3D Voronoi diagram for visualization.     

Polygon offsetting using a Voronoi diagram and two stacks

The generation of the trimmed offset of a simple polygon is a conceptually simple but important and computationally non-trivial geometric problem for many applications. This article presents a linear time algorithm to compute a trimmed offset of a simple polygon consisting of arcs as well as line segments in a plane. Assuming that a Voronoi diagram of the polygon is available, the algorithm uses two stacks: T-stack and C-stack. The T-stack contains intersections between an offset and Voronoi edges, and the C-stack contains an offset chain which is a part of the trimmed offset. The contents of both stacks are pushed into and popped from the stacks in a synchronized fashion depending on the events that occur during the offsetting process.     

一般城市Voronoi图的结晶生成

城市Voronoi图是以L1平面上任意两点之间花费的最短时间为距离的一种新型Voronoi图,它要求交通网络路线仅为水平或垂直方向。然而,客观世界中存在大量曲线交通路线。为了使城市Voronoi图理论研究进一步贴近现实,进而应用于实际,将交通路线扩展为曲线,提出了一种新的城市Voronoi图——一般城市Voronoi图,给出了一般城市Voronoi图的定义、性质和结晶生成算法。     

一种基于Voronoi图的高效异常检测方法

提出了一种新的基于Voronoi图的异常检测方法。采用Voronoi图来确定对象间的邻近关系,定义了一种新的异常因子,算法的时间复杂性为O（nlogn）。实验结果表明,同现有的算法相比具有较高的检测效率和准确性。     

Robustness of k-gon Voronoi diagram construction

In this paper, we present a plane sweep algorithm for constructing the Voronoi diagram of a set of non-crossing line segments in 2D space using a distance metric induced by a regular k-gon and study the robustness of the algorithm. Following the algorithmic degree model [G. Liotta, F.P. Preparata, R. Tamassia, Robust proximity queries: an illustration of degree-driven algorithm design, SIAM J. Comput. 28 (3) (1998) 864-889], we show that the Voronoi diagram of a set of arbitrarily oriented segments can be constructed with degree 14 for certain k-gon metrics (e.g., k=6,8,12). For rectilinear segments or segments with slope +1 or −1, the degree reduces to 2. The algorithm is easy to implement and finds applications in VLSI layout.     

A sweepline algorithm for Euclidean Voronoi diagram of circles

Presented in this paper is a sweepline algorithm to compute the Voronoi diagram of a set of circles in a two-dimensional Euclidean space. The radii of the circles are non-negative and not necessarily equal. It is allowed that circles intersect each other, and a circle contains others.The proposed algorithm constructs the correct Voronoi diagram as a sweepline moves on the plane from top to bottom. While moving on the plane, the sweepline stops only at certain event points where the topology changes occur for the Voronoi diagram being constructed.The worst-case time complexity of the proposed algorithm is O((n+m)log n), where n is the number of input circles, and m is the number of intersection points among circles. As m can be O(n²), the presented algorithm is optimal with O(n² log n) worst-case time complexity.     

基于Voronoi图的定性路径

定性路径是定性空间推理的一个基本概念。给出了一个基于Voronoi图的定性路径表示与推理方法。该方法应用Voronoi图的邻近关系来表示定性位置和定性路径,即用运动点所在Voronoi区域的邻域来表示定性位置,用运动点所经过的定性位置序列来表示定性路径。设计并实现了一个定性路径推理算法,基于初始Voronoi图及不同时刻所有Voronoi区域的边数来动态更新Voronoi图邻近关系,可识别出运动点并找出定性路径。实验结果表明,该方法是可行的。     

Interaction interfaces in proteins via the Voronoi diagram of atoms

A protein consists of one or more chains where each chain is a linear sequence of amino acids bonded by peptide bonds. Chains in a protein interact with each other and the interaction is known to be one of the most fundamental factors which determine important physiological phenomena in the body. Hence, biologists have been investigating protein interactions since the early days of life science.While the studies on the interactions by biologists have emphasized the biological, chemical and/or physical aspects of the interactions, we approach the interactions from a geometric point of view.In this paper, we define an interaction interface using the Voronoi diagram of atoms in proteins. Based on a mathematical definition of the interaction interface, we provide a set of measures to characterize the inter- and intra-protein interactions.Given a Voronoi diagram of atoms in a protein consisting of a number of chains, we compute a geometric mid-surface, called an interaction interface, between each pair of chains in the protein. The interface consists of a set of faces where each face in the interface is a Voronoi face defined by two atoms belonging to different chains. Hence, the interface can be found in time in the worst case for m Voronoi faces in the Voronoi diagram. Then, a number of geometric and topological measures are derived from the interface to characterize the interaction.     

三维点集Voronoi图的算法实现

对现有三维点集Voronoi图的生成算法进行深入研究,提出并实现由Delaunay三角剖分构建Voronoi图的算法．首先采用随机增量局部转换计算Delaunay三角剖分,然后再根据对偶特性构建Voronoi图．该算法健壮性很高,适用于处理各种非完全共面三维点集．     

一种基于离散Voronoi图的手写体文字细化方法

基于一般图形Voronoi图的离散构造法,提出了一种新的文字图像细化算法。该方法首先对文字图像进行水平扫描和垂直扫描,通过游程匹配记录下所有端点游程,并对端点游程进行处理,接着计算文字图像的边界,在计算边界的同时根据端点游程划分出生成元。最后基于一般图形Voronoi图的离散构造法生成文字图像内部的Voronoi边,从而得到文字图像骨架。该方法直接从图像的边界入手,解决了当前已有算法从图像边界近似多边形入手的问题。该方法速度较快,尤其在大篇幅文字图像的细化速度方面具有显著优势,且简单易行,可以较精确地获取文字图像的骨架。     

Constructing the Voronoi diagram of a set of line segments in parallel

In this paper we give a parallel algorithm for constructing the Voronoi diagram of a polygonal scene, i.e., a set of line segments in the plane such that no two segments intersect except possibly at their endpoints. Our algorithm runs inO(log² n) time usingO(n) processors in the CREW PRAM model.The research of M. T. Goodrich was supported by NSF under Grants CCR-8810568 and CCR-9003299 and by NSF/DARPA under Grant CCR-8908092. C. K. Yap's research was supported in part by NSF Grants DCR-8401898 and CCR-9002819.     

基于Delaunay三角剖分生成Voronoi图算法

针对Delaunay三角网生长算法和间接生成Voronoi图算法构网效率不高的问题,提出了一种Delaunay三角网生长法间接生成Voronoi图的改进算法。该算法以点集凸壳上一边快速生成种子三角形,定义了半封闭边界点的概念,在三角形扩展过程中动态删除封闭点及半封闭边界点,加快Delaunay三角网生成速度。然后又定义了有序目标三角形的概念,该算法能迅速查找点的有序目标三角形,生成无射线的Voronoi图;考虑凸壳上点的特性,借助三个无穷点生成带射线的Voronoi图。通过实验结果分析表明,改进的算法执行效率有了很大提高。     

不同交通网络速度的Voronoi图的结晶生成

针对以欧氏距离为度量的Voronoi图所分割必须是均质空间的局限性,为了体现实际分析中的交通网络所导致的空间不均质性,在现有Voronoi图理论成果的基础上,提出了以交通时间距离为度量的基于交通网络的Voronoi图的概念,运用结晶生成法通过C#软件编程实现了不同交通网络速度的基于交通网络的Voronoi图的生成程序。该方法进一步完善和丰富了Voronoi图理论,拓展了Voronoi图的应用范围,体现了实践应用价值。     

基于Voronoi图的障碍不确定数据的聚类算法

数据采集过程中普遍存在不确定性,并且在现实地理空间中,不确定数据之间可能存在障碍物间隔。为解决障碍空间中不确定数据的聚类问题,提出APPGCUO算法,该算法包括三个过程:在障碍物约束下采用R树节点最小最大值方法提出的RPT-OUCure算法,用以生成局部最优解,提高生成局部最优解的效率;继而利用近似骨架的理论提出GIABO算法,以局部最优解生成有效初始解,避免划分聚类算法中任意初始解的不足;最后结合Voronoi图的特性提出VPT-KMediods算法,减少不确定数据的积分运算量。实验结果表明,APPGCUO算法具有较高的聚类效率和质量。     

基于Voronoi图的群体队形控制方法

影视作品中采用群体队形控制技术来制作大量角色处于某种队形运动的场景，但许多群体队形技术往往侧重于对自由移动的个体角色进行控制，而忽视了对队形运动的整体控制，导致场景画面缺乏美感性、整体性和条理性。针对这些问题，提出了基于Voronoi图的群体队形控制方法。首先，将群体队形进行Voronoi图空间划分，建立一个包含所有智能体的队形网格；然后，提出一种新的群体队形形变算法，采用人工势能场和相对速度障碍法进行合理避障，再结合弹簧系统使群体队形在形变过程中尽可能保持整体稳定；最后，采用Lloyd算法快速恢复到目标队形。实验结果表明，该方法可以很好地模拟群体队形变换运动，适用各种复杂场景，具有美感、整体、条理的队形变换效果。     

基于Voronoi图的时间序列线性模式查询算法

时间序列线性模式查询在实际中具有广泛的应用,也是时间序列挖掘的基础。利用Voronoi图的基本原理,提出了一种新的线性模式KL相似性度量,给出了实现线性模式查询的最优算法。     

基于近似Voronoi图的移动机器人实时路径规划

运用Voronoi图理论及人工势场理论,研究了一种基于近似Voronoi图的移动机器人实时路径规划的方法,用来实现未知室内环境中移动机器人的自主导航。该方法朝向预先定义的目标点位置来探测室内环境,生成近似Voronoi图,同时利用人工势场法进行避障,生成一条能达到目标点的安全、光滑路径。仿真结果表明,该方法简单且易于实现,同时能够减少规划时间。