基于Voronoi图的方向区域查询方法

针对空间中方向区域查询效率不高的问题,通过引入Voronoi图,利用其特性对数据空间进行划分,提出了基于Voronoi图的方向区域查询方法.该方法在基于Delaunay三角网生成的Voronoi图索引结构基础上,将首结点与查询对象连线形成有向线段,利用Voronoi图可以通过邻接生成点延展的特点确定查询对象的位置,通过...     

Voronoi图的构建与查询方法

Voronoi图在图像处理、网络数据分析、空间信息检测、空间定位查询和路网轨迹分析等领域具有重要作用.为了有效构建Voronoi图,研究了利用Delannay三角网和影响区域对Voronoi图进行构建和动态更新的方法.探讨了基于Voronoi图进行空间近邻关系查询的主要方法.基于研究的方法,设计和开发了Voronoi图的生成与应用系统,该系统具有较好的应用性能.     

GIS中投影加权Voronoi图及竞争三角形生成算法研究

在GIS空间分析中，为了定位和分析空间区域中含权对象的竞争区域，提出了加权Voronoi图的新形式——投影加权Voronoi图，该图是从常规Voronoi图和一般加权Voronoi图的平面剖分模型出发，首先引入了能够产生空间竞争区域的空间投影剖分模型，然后由此形成空间中的三角形空隙，即竞争三角形，同时归纳了形成竞争三角形的3种加权方式，并分析了其生成算法和特性，计算机的模拟结果显示，将竞争三角形作为空间的竞争区域是可行的，最后论述了它在GIS空间分析中广泛的应用前景。     

广义Voronoi图求解多机器人运动规划

在拥挤环境中,由于障碍物的边界形状比较复杂,需要使用广义Voronoi图表示空间环境。且在多移动机器人的运动规划过程中,需要协调多个机器人的运动,必须得到Voronoi图通道的宽度。为此提出了一种计算拥挤障碍物环境中生成的广义Voronoi图及其通道宽度的算法。并在生成的Voronoi图上利用A*算法对多个机器人进行路径规划,并利用分布式方法协调多个机器人运动。对协调两个机器人运动的过程进行了仿真,仿真结果表明利用提出的算法生成的具有通道宽度信息的Voronoi图能够满足多移动机器人运动规划的需要。     

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。     

分区加权Voronoi图的性质及其面积计算

分区加权Voronoi图是Voronoi图和加权Voronoi图的推广,可以用来模拟移动通信中基站发射天线分扇区以不同功率向周围发射时所覆盖区域的形状。首先,给出了分区加权Voronoi图的性质、定理及相关证明;其次,分析了分区加权Voronoi图中的各种区域,并给出了一种计算相应区域面积的算法;最后,利用分区加权Voronoi图模拟石家庄市部分城区中的基站建设情况,并对模拟产生的重复覆盖、服务区和盲区面积进行了计算。     

粗糙域Voronoi图离散生成算法研究

Voronoi图是计算几何的一个重要分支,粗糙域Voronoi图是Voronoi图概念在复杂生成面上的扩展。提出了粗糙域Voronoi图的概念并利用A‘算法计算生成面上点与各母点的最短路径对其进行离散生成。为了降低粗糙域Voronoi图离散生成算法的复杂度,对粗糙域下A’算法估价函数权值与粗糙域粗糙特性的关系进行了深入探索。实验结果表明,A’算法估价函数权值与粗糙域粗糙特性正相关,并以此获得r算法估价函数的最优权,大大降低了粗糙域Voronoi图离散生成算法的复杂度。     

面向位置服务的K-Vretr隐私保护方法

针对K匿名、空间泛化等隐私保护方法中匿名区域受攻击造成用户隐私泄露的问题,提出一种基于K匿名机制的K-Vretr方法.首先,引入Voronoi图模型,利用离散的Voronoi图特性,分析同类信息点,生成K匿名集发送给LBS服务器;其次,定义关系矩阵,计算出用户位置与目标信息点之间的邻近关系;再次,应用二次剩余假设模型,...     

一种基于点集自适应分组构建Voronoi 图的并行算法

论文提出一种基于点集自适应分组构建Voronoi 图的并行算法,其基本思 路是采用二叉树分裂的方法将平面点集进行自适应分组,将各分组内的点集独立生成 Voronoi 图,称为Voronoi 子图;提取所有分组内位于四边的边界点,对边界点集构建Voronoi 图,称为边界点Voronoi 图;最后,针对每个边界点,提取其位于Voronoi 子图和边界点Voronoi 图内所对应的两个多边形,进行Voronoi 多边形的合并,最终实现子网的合并。考虑到算法 耗时主要在分组点集的Voronoi 图生成,而各分组的算法实现不受其他分组影响,采用并行 计算技术加速分组点集的Voronoi 图生成。理论分析和测试表明,该算法是一个效率较高的 Voronoi 图生成并行算法。     

突发威胁情况下的无人机航迹重规划

为了提高Voronoi图在航迹规划方面的实用性,提出了一种改进型的Voronoi图构造模型。该模型通过引入威胁源的不可穿越区域边界,利用折中原理,在Delaunay三角网的基础上构建航迹拓扑空间。改进型的Voronoi图模型拓展了传统模型的航迹段数量,提高了航迹段对威胁的敏感性,使规划的航迹更为合理。其次,在分析突发威胁对于航迹拓扑空间影响的基础上,提出了一种基于改进型Voronoi图的航迹重规划模型,并结合D*算法对突发情况下的航迹重规划进行了研究,规划出了理想航迹。     

Generating and updating multiplicatively weighted Voronoi diagrams for point,line and polygon features in GIS

A Voronoi diagram is an interdisciplinary concept that has been applied to many fields. In geographic information systems (GIS), existing capabilities for generating Voronoi diagrams normally focus on ordinary (not weighted) point (not linear or area) features. For better integration of Voronoi diagram models and GIS, a raster-based approach is developed, and implemented seamlessly as an ArcGIS extension using ArcObjects. In this paper, the methodology and implementation of the extension are described, and examples are provided for ordinary or weighted point, line, and polygon features. Advantages and limitations of the extensions are also discussed. The extension has the following features: (1) it works for point, line, and polygon vector features; (2) it can generate both ordinary and multiplicatively weighted Voronoi diagrams in vector format; (3) it can assign non-spatial attributes of input features to Voronoi cells through spatial joining; and (4) it can produce an ordinary or a weighted Euclidean distance raster dataset for spatial modeling applications. The results can be conveniently combined with other GIS datasets to support both vector-based spatial analysis and raster-based spatial modeling.     

线段加权Voronoi图的离散生成算法的研究与实现

线段加权Voronoi图是对普通Voronoi图在生成元以及权重两方面加以推广而产生的.给出用离散的方法来生成线段加权Voronoi图,无须复杂计算,容易实现.另外利用其解决绿化问题,会达到良好的划分及可视效果.     

基于四叉树结构的加权Voronoi图生成算法

针对普通Voronoi图研究的局限性和加权Voronoi算法的低效率问题,提出基于四叉树结构的加权Voronoi图生成方法。核心思想是利用四叉树结构的层次性,获取未膨胀节点的搜索区域和相关生长源,以时间消耗值替代加权距离,并以节点的最短时间消耗值为依据查找归属生长源。推理了基于四叉树结构计算模型的几个基本性质。实验结果表明,本方法能实现生长源的快速膨胀,有效降低时间复杂度,其时间复杂度小于均匀格网结构,可操作性强,具有较好的实用价值。     

线段加权的Voronoi图

本文将点上加权的Ｖｏｒｏｎｏｉ图推广到线段上加权的Ｖｏｒｏｎｏｉ图，证明了该图的两线段间的Ｖｏｒｏｎｏｉ边是二次曲线，给出了所有情形下两线段间的Ｖｏｒｏｎｏｉ边的具体形状和画法及线段加权的Ｖｏｒｏｎｏｉ图Ｖｎ的画法。     

Approximation of Generalized Voronoi Diagrams by Ordinary Voronoi Diagrams

A numerically robust algorithm for the ordinary Voronoi diagrams is applied to the approximation of various types of generalized Voronoi diagrams. The generalized Voronoi diagrams treated here include Voronoi diagrams for figures, additively weighted Voronoi diagrams, Voronoi diagrams in a river, Voronoi diagrams in a Riemannian plane, and Voronoi diagrams with respect to collision-avoiding shortest paths. The construction of these generalized Voronoi diagrams is reduced to the construction of the ordinary Voronoi diagrams. The methods proposed here can save much time which is otherwise necessary for writing a computer program for each type of generalized Voronoi diagram.     

基于MapReduce的加权Voronoi图并行算法设计及应用

针对大规模数据的加权Voronoi图实现的复杂性和计算精度低问题, 采用欧氏距离法, 设计和实现了一种基于MapReduce编程模型的并行栅格加权Voronoi图的生成算法, 并将其成功应用于石家庄桥东区超市的推荐服务。该算法计算精度高, 同时可适用于任意点、线、面及复合发生元的加权Voronoi图的计算。实验结果表明, 算法在处理大规模栅格数据时能明显提高栅格Voronoi图的生成速度, 并能为用户推荐综合因素优选的超市。     

Quasi-triangulation and interworld data structure in three dimensions

It is well-known that the Voronoi diagram of points and the power diagram for weighted points, such as spheres, are cell complexes, and their respective dual structures, i.e. the Delaunay triangulation and the regular triangulation, are simplicial complexes. Hence, the topologies of these diagrams are usually stored in their dual complexes using a very compact data structure of arrays.The topology of the Voronoi diagram of three-dimensional spheres in the Euclidean distance metric, on the other hand, is stored in a radial edge data structure which is not as compact as the data structure used for the Voronoi diagram of points and the power diagram for weighted points.In this paper, we define a dual structure of the Voronoi diagram of three-dimensional spheres called a quasi-triangulation and present its important properties. Based on the properties of a quasi-triangulation, we propose a data structure, called an interworld data structure, based on arrays to compactly store the topology of the quasi-triangulation with a guaranteed query performance.     

Exploration of Empty Space among Spherical Obstacles via Additively Weighted Voronoi Diagram

Properties of granular materials or molecular structures are often studied on a simple geometric model – a set of 3D balls. If the balls simultaneously change in size by a constant speed, topological properties of the empty space outside all these balls may also change. Capturing the changes and their subsequent classification may reveal useful information about the model. This has already been solved for balls of the same size, but only an approximate solution has been reported for balls of different sizes. These solutions work on simplicial complexes derived from the dual structure of the ordinary Voronoi diagram of ball centers and use the mathematical concept of simplicial homology groups. If the balls have different radii, it is more appropriate to use the additively weighted Voronoi diagram (also known as the Apollonius diagram) instead of the ordinary diagram, but the dual structure is no longer a simplicial complex, so the previous approaches cannot be used directly. In this paper, a method is proposed to overcome this problem. The method works with Voronoi edges and vertices instead of the dual structure. Additional bridge edges are introduced to overcome disconnected cases. The output is a tree graph of events where cavities are created or merged during a simulated shrinking of the balls. This graph is then reorganized and filtered according to some criteria to get a more concise information about the development of the empty space in the model.