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 integratio...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 u展开更多
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 distr...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.展开更多
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...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.展开更多
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...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.展开更多
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 s...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.展开更多
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 geospa...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.展开更多
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 a...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.展开更多
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 ...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.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 41671410)the Postdoctoral Science Foundation of China (Grant No. 2013T60161)the Excellent Young Scholar Foundation of Information Engineering University (Grant No. 2016610802)
文摘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 u
基金This work is partly funded by the University of Southampton’s Marine and Maritime Institute(SMMI)and the European Research Council under the European Union’s Horizon 2020 research and innovation program(grant agreement number:723526:SEDNA).
文摘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.
基金the National Natural Science Foundation of China[grant number 41171314],[grant number 41023001]the Fundamental Research Funds for the Central Universities[grant number 2014619020203].Comments from the anonymous reviewers and editor are appreciated.
文摘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.
文摘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.
基金supported by the Special Science Fund for Innovation Ecosystem Construction of National Supercomputing Center in Zhengzhou[grant no 201400210100]the National Key Research and Development Program of China[grant no 2018YFB0505301].
文摘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.
基金supported in part by the National Science and Engineering Research Council(NSERC)of Canadathe PYXIS innovation inc.
文摘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.
基金the Natural Sciences and Engineering Research Council of Canada (NSERC-DG).
文摘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.
基金funded by the Natural Sciences and Engineering Research Council of Canada(NSERC).
文摘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.
