Global Multi-resolution Half-Honeycomb Trapezoid Grid

In order to break through the limitationof thelatitude/longitudegrid and hexagon grid, a new subdivision unit, Half-honeycomb Trapezoid, is proposed. Based on the summarization of the geometric properties and subdivision performance of Half-honeycomb Trapezoid, a new discrete global topographic grid system is established, and its compatibility with hexagonal grid is analyzed. At last, the visualization of multi-resolution global grid is achieved.

Construction of quality evaluation indicator system for diamond discrete global grid systems

Although the uniformity of diamond discrete global grid is essential for calculations and searches,geometric deformations increase with the level of divisions.The Good child Criteria provides a basis for evaluating the quality of the global grid.However,some indicators in the criteria are redundant and contradictory,and the existing indicator system has limitations.Directly using the indicator system may render the evaluation of the diamond grid unreliable.In this study,we summarized the evaluation indicators for grid quality basedon the Good child Criteria,calculated the correlations between these indicators using different diamond grid systems,and constructed reliable evaluation systems based on similarities and differences.The selected grid systems are classified into two groups:non-equal-area and equal-area grids.Their quality evaluation systems are composed of Size-Shape-Topology Factor and Geometry-Topology Factor,respectively.The proposed quality evaluation systems utilize a minimal number of indicators selected from each factor to provide a comprehensive description of the diamondgrid’s characteristics.This approach simplifies the complexity of the evaluations while improving their reliability and credibility.

地理空间数据等积全球格网多模式三维扩展方法

全球离散格网系统是新型地理空间数据组织框架,等面积格网由于在采样和空间分析方面的独特优势而备受关注,但相关研究囿于地球表面,缺乏扩展至三维广域空间的一般方法。本文首先提出将等积球面格网系统扩展为球体格网系统的多种剖分模式,并实现其统一数学描述和详细数学证明;然后引入体积和紧致度指标定量评价不同剖分模式的体元性质,并与球体退化八叉树格网(SDOG)、大圆弧八叉树格网(SGOG)作对比;最后初步探索了本文方法的应用案例,讨论了不同应用需求下选择剖分模式的原则。对比试验结果表明,退化剖分的体元各项指标均优于规则剖分,等体积和退化剖分的体积性质优于SDOG,紧致度性质优于SGOG。本文多剖分模式三维扩展方法不仅符合国际标准等体积的要求,而且兼顾常规剖分设计选项,为不同应用需求提供了参考依据。

Algebraic encoding scheme for aperture 3 hexagonal discrete global grid system

Discrete Global Grid Systems(DGGSs) are spatial references that use a hierarchical tessellation of cells to partition and address the entire globe. They provide an organizational structure that permits fast integration between multiple sources of large and variable geospatial data sufficient for visualization and analysis. Despite a significant body of research supporting hexagonal DGGSs as the superior choice, the application thereof has been hindered owing in part to the lack of a rational hierarchy with an efficient addressing system. This paper presents an algebraic model of encoding scheme for the Aperture 3 Hexagonal(A3H) DGGS. Firstly, the definition of a grid cell, which is composed of vertices, edges, and a center, is introduced to describe fundamental elements of grids. Secondly, by identifying the grid cell with its center, this paper proves that cell centers at different levels can be represented exactly using a mixed positional number system in the complex plane through the recursive geometric relationship between two successive levels, which reveals that grid cells are essentially special complex radix numbers. Thirdly, it is shown that through the recursive geometric relationship of successive odd or even levels, the mixed positional number system can also be applied to uniquely represent cell centers at different levels under specific constraint conditions, according to which the encoding scheme is designed. Finally, it is shown that by extending the scheme to 20 triangular faces of the regular icosahedron,multi-resolution grids on closed surfaces of the icosahedron are addressed perfectly. Contrast experiments show that the proposed encoding scheme has the advantages of theoretical rigor and high programming efficiency and that the efficiency of cross-face adjacent cell searching is 242.9 times that of a similar scheme. Moreover, the proposed complex radix number representation is an ideal formalized description tool for grid systems. The research ideas introduced herein can be used to create a universal theoretical framework for DGGSs.

GIScience research challenges for realizing discrete global grid systems as a Digital Earth

Increasing data resources are available for documenting and detecting changes in environmental,ecological,and socioeconomic processes.Currently,data are distributed across a wide variety of sources(e.g.data silos)and published in a variety of formats,scales,and semantic representations.A key issue,therefore,in building systems that can realize a vision of earth system monitoring remains data integration.Discrete global grid systems(DGGSs)have emerged as a key technology that can provide a common multi-resolution spatial fabric in support of Digital Earth monitoring.However,DGGSs remain in their infancy with many technical,conceptual,and operational challenges.With renewed interest in DGGS brought on by a recently proposed standard,the demands of big data,and growing needs for monitoring environmental changes across a variety of scales,we seek to highlight current challenges that we see as central to moving the field(s)and technologies of DGGS forward.For each of the identified challenges,we illustrate the issue and provide a potential solution using a reference DGGS implementation.Through articulation of these challenges,we hope to identify a clear research agenda,expand the DGGS research footprint,and provide some ideas for moving forward towards a scaleable Digital Earth vision.Addressing such challenges helps the GIScience research community to achieve the real benefits of DGGS and provides DGGS an opportunity to play a role in the next generation of GIS.

Intelligent geospatial maritime risk analytics using the Discrete Global Grid System

Each year,accidents involving ships result in significant loss of life,environmental pollution and economic losses.The promotion of navigation safety through risk reduction requires methods to assess the spatial distribution of the relative likelihood of occurrence.Yet,such methods necessitate the integration of large volumes of heterogenous datasets which are not well suited to traditional data structures.This paper proposes the use of the Discrete Global Grid System(DGGS)as an efficient and advantageous structure to integrate vessel traffic,metocean,bathymetric,infrastructure and other relevant maritime datasets to predict the occurrence of ship groundings.Massive and heterogenous datasets are well suited for machine learning algorithms and this paper develops a spatial maritime risk model based on a DGGS utilising such an approach.A Random Forest algorithm is developed to predict the frequency and spatial distribution of groundings while achieving an R2 of 0.55 and a mean squared error of 0.002.The resulting risk maps are useful for decision-makers in planning the allocation of mitigation measures,targeted to regions with the highest risk.Further work is identified to expand the applications and insights which could be achieved through establishing a DGGS as a global maritime spatial data structure.

Wahi, a discrete global grid gazetteer built using linked open data

Discrete global grid systems have become an important component of Digital Earth systems.However,previously there has not existed an easy way to map between named places(toponyms)and the cells of a discrete global grid system.The lack of such a tool has limited the opportunities to synthesize social place-based data with the more standard Earth and environmental science data currently being analyzed in Digital Earth applications.This paper introduces Wāhi,the first gazetteer to map entities from the GeoNames database to multiple discrete global grid systems.A gazetteer service is presented that exposes the grid system and the associated gazetteer data as Linked Data.A set of use cases for the discrete global grid gazetteer is discussed.

EASE-DGGS:a hybrid discrete global grid system for Earth sciences

Although we live in an era of unprecedented quantities and access to data,deriving actionable information from raw data is a hard problem.Earth observation systems(EOS)have experienced rapid growth and uptake in recent decades,and the rate at which we obtain remotely sensed images is increasing.While significant effort and attention has been devoted to designing systems that deliver analytics ready imagery faster,less attention has been devoted to developing analytical frameworks that enable EOS to be seamlessly integrated with other data for quantitative analysis.Discrete global grid systems(DGGS)have been proposed as one potential solution that addresses the challenge of geospatial data integration and interoperability.Here,we propose the systematic extension of EASE-Grid in order to provide DGGS-like characteristics for EOS data sets.We describe the extensions as well as present implementation as an application programming interface(API),which forms part of the University of Minnesota’s GEMS(Genetic x Environment x Management x Socioeconomic)Informatics Center’s API portfolio.

Spatial prediction of sparse events using a discrete global grid system;a case study of hate crimes in the USA

Spatial prediction of any geographic phenomenon can be an intractable problem.Predicting sparse and uncertain spatial events related to many influencing factors necessitates the integration of multiple data sources.We present an innovative approach that combines data in a Discrete Global Grid System(DGGS)and uses machine learning for analysis.A DGGS provides a structured input for multiple types of spatial data,consistent over multiple scales.This data framework facilitates the training of an Artificial Neural Network(ANN)to map and predict a phenomenon.Spatial lag regression models(SLRM)are used to evaluate and rank the outputs of the ANN.In our case study,we predict hate crimes in the USA.Hate crimes get attention from mass media and the scientific community,but data on such events is sparse.We trained the ANN with data ingested in the DGGS based on a 50%sample of hate crimes as identified by the Southern Poverty Law Center(SPLC).Our spatial prediction is up to 78%accurate and verified at the state level against the independent FBI hate crime statistics with a fit of 80%.The derived risk maps are a guide to action for policy makers and law enforcement.

A novel method of determining the optimal polyhedral orientation for discrete global grid systems applicable to regionalscale areas of interest

The polyhedral discrete global grid system(DGGS)is a multi-resolution discrete earth reference model supporting the fusion and processing of multi-source geospatial information.The orientation of the polyhedron relative to the earth is one of its key design choices,used when constructing the grid system,as the efficiency of indexing will decrease if local areas of interest extend over multiple faces of the spherical polyhedron.To date,most research has focused on global-scale applications while almost no rigorous mathematical models have been established for determining orientation parameters.In this paper,we propose a method for determining the optimal polyhedral orientation of DGGSs for areas of interest on a regional scale.The proposed method avoids splitting local or regional target areas across multiple polyhedral faces.At the same time,it effectively handles geospatial data at a global scale because of the inherent characteristics of DGGSs.Results show that the orientation determined by this method successfully guarantees that target areas are located at the center of a single polyhedral face.The orientation process determined by this novel method reduces distortions and is more adaptable to different geographical areas,scales,and base polyhedrons than those employed by existing procedures.

Location coding and indexing aperture 4 hexagonal discrete global grid based on octahedron

将正八面体上下相邻的两个三角形面片合并成一个四分体,建立二维坐标系,在此基础上采用六边形格网单元的层次编码方案,分析了不同位置格网单元的编码特征,提出了一种"孔4双轴查找算法",实现了相应的邻接单元及父、子单元查找,并进行了相关实验及对比分析。结果表明,该算法和传统的Vince算法相比较,邻接单元查找速度提高了约900倍,父单元和子单元的查找速度均提高了约120倍。

Construction of rhombic triacontahedron discrete global grid systems

Discrete Global Grid System(DGGS)is a new multi-resolution geospatial data modeling and processing scheme for the digital earth.The icosahedron is commonly regarded as an ideal polyhedron for constructing DGGSs with small distortions;however,the shape of its face is triangular,making it difficult to incorporate the matrix structure used for geospatial data storage and parallel computing.To overcome this limitation,this study utilizes the rhombic triacontahedron(RT)as the basic polyhedron to construct DGGSs.An equal-area projection between the surface of RT and the sphere is developed and used to design a grid-generation algorithm for the aperture 4 hexagonal DGGS based on RT.Compared with the equal-area DGGS based on the icosahedron,the proposed scheme results in smaller angular projection distortions,with the mean and standard deviation decreasing by 41.6%and 30.9%,respectively.The grid cells of the RT DGGS also achieve more optimized geometric characteristics in shape compactness,length deviation,and angle deviation than those in the icosahedron DGGS.Additionally,the cross-surface computation efficiency provides advantages in code conversion to latitude and longitude and proximity queries.Furthermore,the use of RT offers a new and better framework within the context of DGGS research and application.

An open-source web service for creating quadrilateral grids based on the rHEALPix Discrete Global Grid System

The foundation of modern Digital Earth frameworks is the Discrete Global Grid System(DGGS).To standardize the DGGS model,the Open Geospatial Consortium(OGC)recently created the DGGS Abstract Specification,which also aims to increase usability and interoperability between DGGSs.To support these demands and aid future research,open implementations are necessary.However,several OGC conformant DGGSs are not available for researchers to use.This has motivated us to develop an open-source web service that allows users to create quadrilateral grids based on the rHEALPix DGGS.In this paper,we describe the implementation of the web service,including issues and limitations,and demonstrate how discrete global grids and regional grids can be created.Lastly,we present examples that show how vector data sets can be modeled and integrated at different levels of resolution–a key benefit of the DGGS model.

An optimized hexagonal quadtree encoding and operation scheme for icosahedral hexagonal discrete global grid systems

Although research on the discrete global grid systems (DGGSs) has become an essential issue in the era of big earth data,there is still a gap between the efficiency of current encoding and operation schemes for hexagonal DGGSs and the needs of practical applications. This paper proposes a novel and efficient encoding and operation scheme of an optimized hexagonal quadtree structure (OHQS) based on aperture 4 hexagonal discrete global grid systems by translation transformation. A vector model is established to describe and calculate the aperture 4 hexagonal grid system. This paper also provides two different grid code addition algorithms based on induction and ijk coordinate transformation. We implement the transformation between OHQS codes and geographic coordinates through the ij,ijk and IJK coordinate systems. Compared with existing schemes,the scheme in this paper greatly improves the efficiency of the addition operation,neighborhood retrieval and coordinate transformation,and the coding is more concise than other aperture 4 hexagonal DGGSs. The encoding operation based on the ijk coordinate system is faster than the encoding operation based on the induction and addition table. Spatial modeling based OHQS DGGSs are also provided. A case study with rainstorms demonstrated the availability of this scheme.

On the isolatitude property of the rHEALPix Discrete Global Grid System

Digital Earth frameworks provide a way to integrate,analyze,and visualize large volumes of geospatial data,and the foundation of such frameworks is the Discrete Global Grid System(DGGS).One approach in particular,the rHEALPix DGGS,has the rare property of distribution of cell nuclei along rings of constant latitude(or isolatitude rings).However,this property is yet to be explored.In this paper,we extend existing work on the rHEALPix DGGS by proposing a method to determine the isolatitude ring on which the nucleus of a given cell falls by converting a cell identifier to isolatitude ring without recourse to geodetic coordinates.In addition,we present an efficient method to calculate the geodetic latitude of a cell’s nucleus via its associated isolatitude ring.Lastly,we use the proposed methods to demonstrate how the isolatitude property of the rHEALPix DGGS can be utilized to facilitate latitudinal data analysis at multiple resolutions.

基于全球离散格网的空域冲突检测算法设计

为了快速检测空域冲突、及时进行冲突消解,针对现有空域冲突检测算法计算量大、速度慢问题,设计了一种空域冲突检测算法。该算法采用正二十面体剖分方式,将空域格网化;结合矩阵运算,大大降低了空域冲突检测运算量。该算法在大规模空域冲突检测时能够快速、准确地检测出空域冲突位置和冲突空域编号。

广域六角格兵棋地图构建方法与机动推演应用

兵棋推演是预演战争、模拟作战的科学方法,全球化趋势对兵棋推演的推演范围和灵活程度提出了更高要求。采用六边形全球离散格网系统建立广域多尺度兵棋地图,并在推演案例中检验了其作用。首先,提出栅格及矢量数据六角格量化方法;其次,建立环境要素与作战要素联合作用的部队机动时间效能模型,设计了最优路径规划算法;最后,构建兵棋地图,并以部队海陆两栖机动推演为例加以验证。实验结果表明,六边形全球离散格网系统兼具数据建模和分析计算功能,既可被用于构建海陆广域多尺度兵棋地图,又可作为作战推演的统一计算框架,弥补了传统兵棋地图空间范围受限、尺度变换不灵活的缺陷,具有较好的应用前景。

文本中空间信息的结构化建模与语义定位

互联网上存在大量包含空间信息的文本,本文针对此类文本中描述事件位置的空间语义建模方法不统一、模糊处理方法不恰当等问题,利用方形离散格网建立结构化语义表达模型,使用统一的形式对方向、距离、拓扑3类基本语义及其组合形成的复杂语义进行表达,并使用卷积方法定量化空间语义中的模糊概念,将不确定的语义描述投影到地理空间,最终通过多句空间语义确定事件发生的地理位置。试验表明:①结构化语义表达模型能适用于包含多种空间关系的语义,在多语义联合建模求并时能确定未知事件发生的地理范围;②语义定位的可信度与语义类型、参考实体类型、参考实体数量及正确语义占比等因素有关,当参考实体数量较多时,能在正确语义数量小于错误语义数量的情况下确定事件发生的地理位置范围。

菱形三十面体六边形全球离散格网系统构建算法

全球离散格网系统是递归剖分整个地球空间形成的多分辨率离散地球参考模型,有助于建立以空间位置为主键的多源数据关联融合新模式。正二十面体的三角面不利于建立格网单元行列索引,且生成的球面格网单元存在较大形状差异,对此,该文采用面数更多、结构更优的菱形三十面体构建六边形全球离散格网系统。首先,在单个菱形面上建立离散斜坐标系描述多种孔径六边形剖分产生的多分辨率格网;其次,根据菱形三十面体的几何属性确定跨面单元归属,据此拼接各面上的多分辨率单元,构成封闭三十面体上的格网系统;最后,通过Snyder等积多面体投影将封闭菱形三十面体上的格网系统映射至球面。实验结果表明,相比二十面体的同类成果,菱形三十面体六边形全球离散格网系统的几何属性和应用潜力更好,有助于建立地球空间信息数据的高精度承载模型。

全球离散格网的建模方法及基本问题

全球离散格网(Discrete Global Grid,DGG)模型是数字地球及空间信息格网的基础,不同的建模方法不但影响空间数据的存储和管理效率,而且影响全球GIS的操作功能。该文介绍了DGG的评价标准,将DGG的建模方法归纳为3种类型:经纬度格网模型、自适应格网模型和正多面体格网模型,重点分析了不同类型球面离散格网模型的几何结构、单元特征和应用模式。最后,提出了DGG在Global GIS中亟待解决的基本问题,包括编码、精度、应用、误差、整合和定位问题。