ELASTIC WAVES IN 3-D DISCRETE GRIDS

Wave motion in finite element models presents some characteristics different from those of wave motion in continuum, which leads to the errors and other special phenomena in finite element simulation of wave motion. The wave propagation in a 3-D finite element model is studied by utilizing the formal solution in the paper, and the corresponding dispersion relations are derived. Then the main properties of wave motion in 3-D grids such as dispersion, cut-off frequency and polarization drift are discussed. Characteristics different from those of wave motion in 2-D grids are revealed.

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.

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.

Optimal orientations of discrete global grids and the Poles of Inaccessibility

Spatial analyses involving binning often require that every bin have the same area,but this is impossible using a rectangular grid laid over the Earth or over any projection of the Earth.Discrete global grids use hexagons,triangles,and diamonds to overcome this issue,overlaying the Earth with equally-sized bins.Such discrete global grids are formed by tiling the faces of a polyhedron.Previously,the orientations of these polyhedra have been chosen to satisfy only simple criteria such as equatorial symmetry or minimizing the number of vertices intersecting landmasses.However,projection distortion and singularities in discrete global grids mean that such simple orientations may not be sufficient for all use cases.Here,I present an algorithm for finding suitable orientations;this involves solving a nonconvex optimization problem.As a side-effect of this study I show that Fuller’s Dymaxion map corresponds closely to one of the optimal orientations I find.I also give new high-accuracy calculations of the Poles of Inaccessibility,which show that Point Nemo,the Oceanic Pole of Inaccessibility,is 15 km farther from land than previously recognized.

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.

Interactive data styling and multifocal visualization for a multigrid web-based Digital Earth

Globe-based Digital Earth(DE)is a promising system that uses 3D models of the Earth for integration,organization,processing,and visualization of vast multiscale geospatial datasets.The growing size and scale of geospatial datasets present significant obstacles to interactive viewing and meaningful visualizations of these DE systems.To address these challenges,we present a novel web-based multiresolution DE system using a hierarchical discretization of the globe on both server and client sides.The presented web-based system makes use of a novel data encoding technique for rendering large multiscale geospatial datasets,with the additional capability of displaying multiple simultaneous viewpoints.Only the data needed for the current views and scales are encoded and processed.We leverage the power of GPU acceleration on the client-side to perform real-time data rendering and dynamic styling.Efficient rendering of multiple views allows us to support multilevel focus+context visualization,an effective approach to navigate through large multiscale global datasets.The client–server interaction as well as the data encoding,rendering,styling,and visualization techniques utilized by our presented system contribute toward making DE more accessible and informative.

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.

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.

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.

Voxel modeling and association of ubiquitous spatiotemporal information in natural language texts

The ubiquitous spatiotemporal information extracted from Internet texts limits its application in spatiotemporal association and analysis due to its unstructured nature and uncertainty.This study uses ST-Voxel modeling to solve the problem of structured modeling and the association of ubiquitous spatiotemporal information in natural language texts.It provides a new solution for associating ubiquitous spatiotemporal information on the Internet and discovering public opinion.The main contributions of this paper include:(1)It proposes a convolved method for ST-Voxel,which solves the voxel modeling problem of unstructured and uncertain spatiotemporal objects and spatiotemporal relation in natural language texts.Experiments show that this method can effectively model 5 types of spatiotemporal objects and 16 types of uncertain spatiotemporal relation founded in texts;(2)It realizes the unknown event discovery based on voxelized spatiotemporal information association.Experiments show that this method can effectively solve the aggregation of ubiquitous spatiotemporal information in multi-natural language texts,which is conducive to discovering spatiotemporal events.The selection of convolution parameters in voxel modeling is also discussed.A parameter selection method for balancing the discovery capability and discovery accuracy of spatiotemporal events is given.

Numerical analysis of horizontal temperature distribution in large buildings by thermo-aeraulic zonal approach

The commercial and public services sectors including shopping centers,worship buildings,theatres,and other types,account for more than 20%of the electricity consumption in the world.These building typologies are characterized by large spaces and high and temporary occupation.Besides,the horizontal temperature distribution in these buildings becomes one of the important parameters on occupant's comfort and energy efficiency.In the present study,a thermo-aeraulic zonal model using TRNSYS and CONTAM simulation tools is developed to analyze the spatial temperature distribution in a large building.Parametric studies relating to mesh discretization of building volume are performed to optimize the computational time and convergence.Extensive computational simulation is carried out to analyze the impact of building height,internal loads,natural ventilation and climatic conditions on the spatial temperature distribution,building energy performance,and thermal comfort.The developed simulation model in this study is effective to predict the horizontal temperature distribution with reasonable computation time compared to CFD simulations.The results show that the internal heat gains lead to an increase in the horizontal temperature gradient which should not be negligible especially in the case of large buildings.On the other side,natural night ventilation can reduce the peak tempearture in building by 3℃ for normal occupation building with limited internal gains.Furthermore,good spatial temperature distribution can decrease annual building energy needs about 32%.It can be helpful for architects and building developers to make an optimal choice regarding to building envelope and HVAC design.

Arithmetic and Fourier transform for the PYXIS multi-resolution digital Earth model

This paper investigates a multi-resolution digital Earth model called PYXIS,which was developed by PYXIS Innovation Inc.The PYXIS hexagonal grids employ an efficient hierarchical labeling scheme for addressing pixels.We provide a recursive definition of the PYXIS grids,a systematic approach to the labeling,an algorithm to add PYXIS labels,and a discussion of the discrete Fourier transform on PYXIS grids.

A virtual globe-based vector data model:quaternary quadrangle vector tile model

This study proposes a virtual globe-based vector data model named the quaternary quadrangle vector tile model(QQVTM)in order to better manage,visualize,and analyze massive amounts of global multi-scale vector data.The model integrates the quaternary quadrangle mesh(a discrete global grid system)and global image,terrain,and vector data.A QQVTM-based organization method is presented to organize global multi-scale vector data,including linear and polygonal vector data.In addition,tilebased reconstruction algorithms are designed to search and stitch the vector fragments scattered in tiles to reconstruct and store the entire vector geometries to support vector query and 3D analysis of global datasets.These organized vector data are in turn visualized and queried using a geometry-based approach.Our experimental results demonstrate that the QQVTM can satisfy the requirements for global vector data organization,visualization,and querying.Moreover,the QQVTM performs better than unorganized 2D vectors regarding rendering efficiency and better than the latitude–longitude-based approach regarding data redundancy.