Accuracy of quantized Voronoi diagrams

Quantization of spatial objects, which usually means vector‐to‐raster conversion in GIS and remote sensing, is a basic operation used for handling spatial data from data creation to visualization. Since quantization is an approximation of spatial objects, it inevitably yields errors in measuring their properties such as area, perimeter, diameter, and so forth. This paper discusses the accuracy of a quantized Voronoi diagram, a spatial tessellation generated from a set of points. A measure is proposed to evaluate the accuracy of the area of Voronoi regions calculated after quantization. In one‐dimensional space the measure is expressed as an explicit function of the expected number of generators in a cell. In two‐dimensional space, on the other hand, the measure is defined by an implicit function, whose approximation is derived in an explicit form. These functions permit us to evaluate the accuracy of quantization in relation to the size of lattice cells and the density of Voronoi generators. This leads to an appropriate choice of a lattice to keep the quality of a quantized Voronoi diagram at a desirable level.     

Revisiting John Snow's map: network-based spatial demarcation of cholera area

Dr. John Snow's cholera map is known as one of the pioneering examples of an epidemiology map, illustrating the spatial distribution of the victims from the cholera outbreak. This article revisits his map and expands on his attempt at visualizing the distribution of the victims by focusing on spatial demarcation using the sphere of influence along the street network by applying two analytical methods that are designed for analysis of network space. First, the article generates a network-based Voronoi diagram of the water pumps in the map that encompasses Snow's original version of the equidistance line that was drawn around a single pump. The article then presents a new, revised equidistance line that better reflects the circumstances around the time of the outbreak. This is followed by the construction of another set of boundaries derived by the application of a network-based clumping method. Comparing the demarcation lines produced with the two methods shows a sphere of influence which was unclear when using the network Voronoi diagram alone. Results from the analysis using the clumping method also confirm some of Snow's observations on the spatial distribution of the victims.     

Zone design of specific sizes using adaptive additively weighted Voronoi diagrams

Territory or zone design processes entail partitioning a geographic space, organized as a set of areal units, into different regions or zones according to a specific set of criteria that are dependent on the application context. In most cases, the aim is to create zones of approximately equal sizes (zones with equal numbers of inhabitants, same average sales, etc.). However, some of the new applications that have emerged, particularly in the context of sustainable development policies, are aimed at defining zones of a predetermined, though not necessarily similar, size. In addition, the zones should be built around a given set of seeds. This type of partitioning has not been sufficiently researched; therefore, there are no known approaches for automated zone delimitation. This study proposes a new method based on a discrete version of the adaptive additively weighted Voronoi diagram that makes it possible to partition a two-dimensional space into zones of specific sizes, taking both the position and the weight of each seed into account. The method consists of repeatedly solving a traditional additively weighted Voronoi diagram, so that each seed's weight is updated at every iteration. The zones are geographically connected using a metric based on the shortest path. Tests conducted on the extensive farming system of three municipalities in Castile-La Mancha (Spain) have established that the proposed heuristic procedure is valid for solving this type of partitioning problem. Nevertheless, these tests confirmed that the given seed position determines the spatial configuration the method must solve and this may have a great impact on the resulting partition.     

The color‐magnitude diagram of NGC 2264

Existing photometry for NGC 2264 tied to the Johnson & Morgan (1953) UBV system is reexamined and, in the case of the original observations by Walker (1956), reanalyzed in order to generate a homogeneous data set for cluster stars. Color terms and a Balmer discontinuity effect in Walker's observations were detected and corrected, and the homogenized data were used in a new assessment of the cluster reddening, distance, and age. Average values of E_{B – V} = 0.075 ± 0.003 s.e. and V₀ –M_V = 9.45 ± 0.03 s.e. (d = 777 ± 12 pc) are obtained, in conjunction with an inferred cluster age of ∼5.5 × 10⁶ yr from pre‐main‐sequence members and the location of the evolved, luminous, O7 V((f)) dwarf S Mon relative to the ZAMS. The cluster main sequence also contains gaps that may have a dynamical origin. The dust responsible for the initial reddening towards NGC 2264 is no more than 465 pc distant, and there are numerous, reddened and unreddened, late‐type stars along the line of sight that are difficult to separate from cluster members by standard techniques, except for a small subset of stars on the far side of the cluster embedded in its gas and dust and background B‐type ZAMS members of Mon OB2. A compilation of likely NGC 2264 members is presented. Only 3 of the 4 stars recently examined by asteroseismology appear to be likely cluster members. NGC 2264 is also noted to be a double cluster, which has not been mentioned previously in the literature (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On open cluster physical parameters from 2MASS data

The near infrared range has opened a new window to study stellar populations in the Galaxy, in the Local Groud and beyond. Despite the large and growing use of these data, insufficient efforts have been made in the direction to calibrate stellar physical parameters such as age, reddening and distance. This can also be achieved using near infrared and optical data together. Furthermore, the huge amounts of photometric data available now and in the incoming years, demand the development of automated and statistical isochrone fittings to cope with such data. With this in mind, we analyse 2MASS data in order to determine physical parameters for a sample of 9 open clusters. As a first step, we determined the age, reddening and distance values for each cluster applying the classical isochrone fitting (by eye). Subsequently, we employed an automated procedure which compares synthetic colour-magnitude diagrams to observed ones, making use of the likelihood statistics to find the best solution. We also carried out structural analyses of the clusters using stellar radial density profiles. Both classical and statistical isochrone fittings revealed that there can be disagreement between physical parameters obtained from near infrared data analysis and the literature corresponding ones, most based on optical and UV data. Concerning the observed cluster structures, they were studied for the first time. We found evidence of various dynamical stages in the sample.     

按Voronoi算法分析不均匀土层上的桩筏基础

现有桩筏基础分析方法仅能利用地基分层考虑土层的竖向不均匀性,对土层水平向不均匀性的分析却是无能为力。为了改进现有方法,首先计算地基多个勘察孔在水平面上的Voronoi图,利用Voronoi图最近影响范围特性,通过把多边形范围内土层按最近勘察孔的土层资料替代的方法,近似分析水平向不均匀土层上的桩筏基础。分析时按Bowyer-Watson算法计算Delaunay三角形,然后用间接法得到Voronoi图,借助C++计算机语言编制程序分析桩筏基础。通过一个桩筏基础计算模型,对比分析采用多个勘察孔和一个勘察孔土层资料桩筏基础的分析结果,发现土层水平向差异较大时,基础沉降、桩顶反力分布,筏板弯矩等结果差别较大。故对土层不均匀性较明显地基上的桩筏基础设计,宜采用Voronoi图算法应用全部勘察孔资料进行分析。     

基于Voronoi图的新疆塔里木盆地城镇影响范围分析

确定塔里木盆地城镇影响范围,是新疆城镇体系规划、城市经济区划的一项基本工作,具有现实意义.建立城镇综合实力指标体系,运用Voronoi图在空间分割和地图制图应用中的诸多特性,提供一种新的城镇空间影响范围的划分方法,来实现对塔里木盆地城镇空间影响范围的生成和界定.结果表明:综合实力指数较高的城镇的影响范围一般会超过其所在市县的行政范围,较低的则小于其行政范围;盆地北部、西北部城镇密度较大的区域,城镇的辐射半径较小,影响范围绝对面积不大,南部、东南部城镇密度较小的区域,城镇的辐射半径大,影响范围绝对面积较大.此外,塔里木盆地南部县域的中心城镇的辐射范围呈现为竖向的条块状,并与其行政区划基本吻合,反映出塔里木盆地南部绿洲经济相对的独立性和完整性.     

Voronoi图在地图制图中的应用

在搜集整理Voronoi相关文献与资料的基础上,首先简要介绍了Voronoi图及其应用领域,然后着重从地图信息识别与提取、地图综合和自动注记等方面总结了它在地图制图学中的应用情况,最后分析并探讨了应用中遇到的问题和今后的发展方向。指出Voronoi图在地图制图中的应用是由其特殊的几何与拓扑性质决定的,加权Voronoi图、广义Voronoi图及3DVoronoi图的引入使得其应用有着更远大的前景。     

Subsurface Meridional Circulation in the Active Belts

Temporal variations of the subsurface meridional flow with the solar cycle have been reported by several authors. The measurements are typically averaged over periods of time during which surface magnetic activity existed in the regions where the velocities are calculated. The present work examines the possible contamination of these measurements due to the extra velocity fields associated with active regions plus the uncertainties in the data obtained where strong magnetic fields are present. We perform a systematic analysis of more than five years of GONG data and compare meridional flows obtained by ring-diagram analysis before and after removing the areas of strong magnetic field. The overall trend of increased amplitude of the meridional flow towards solar minimum remains after removal of large areas associated with surface activity. We also find residual circulation toward the active belts that persists even after the removal of the surface magnetic activity, suggesting the existence of a global pattern or longitudinally-located organized flows.