Environ Earth Sci DOI 10.1007/s12665-015-4736-5
THEMATIC ISSUE
Data environment construction for virtual geographic environment Guonian Lu¨1,2,3 • Zhaoyuan Yu1,2,3 • Liangchen Zhou1,2,3 • Mingguang Wu1,2,3 Yehua Sheng1,2,3 • Linwang Yuan1,2,3
•
Received: 5 March 2015 / Accepted: 17 August 2015 Ó Springer-Verlag Berlin Heidelberg 2015
Abstract Virtual geographic environment (VGE) aims to express the real-world naturally, and support the complex geographic analysis. The data environment, fundamental of VGE, is expected to support the data management, analysis, sharing and application requirements of the massive complex geographic spatio-temporal data. In this paper, we summarized the key problems in the construction of the data environment of VGE. The unified spatio-temporal data model and a new data structure were developed according to the geographic rules. The organization and compress storage mechanism of massive spatio-temporal data were also developed. With these foundations, case studies, which integrate the global, regional and city scale data to operate complex data modeling and analysis, are performed. The results showed that the construction of the integrated data environment of VGE can largely improve the efficiency of GIS analysis, which also provides a potential new tool to support the complex geographic analysis. Keywords Virtual geographic environment Data environment Spatio-temporal data model Spatiotemporal data organization Geographic data analysis Geographic model simulation
& Guonian Lu¨
[email protected] 1
Key Laboratory of Virtual Geographic Environment, Ministry of Education, Nanjing, China
2
State Key Laboratory Cultivation Base of Geographic Environment Evolution (Jiangsu Province), Nanjing 210023, Jiangsu, China
3
Jiangsu Center for Collaborative Innovation in Geographic Information Resource Development and Application, Nanjing Normal University, No. 1 Wenyuan Road, Nanjing, China
Introduction The VGE is a new geographic language to express and extend geographic knowledge. It projects the real geographic world into digital world for geographic expression, analysis, visualization and interaction (Lu 2011; Lin et al. 2013a, b). Unlike the traditional GIS, the goal of VGE is to naturally express the real world, support complex geographic analysis models, and promote cooperation and interactivity between the real word and the digital world (Hu et al. 2014). According to the above functions, VGE can be divided into four subtypes: the data environment, modeling environment, expression environment and collaborative environment (Lu 2011). Compared with current GIS, the data environment of VGE has more complex requirements in data representation, object construction and model supporting. The main function of the data environment of VGE (hereafter, data environment) is to abstract and organize data to represent the real complex geographic world digitally. The abstraction and organization of the data should further support the management and integration of multiple-source geographic data and support the building of geographic scene, operation of geographic analysis models, visualizations, coordination and interactions (Lu 2011). The data environment is fundamental for data integration and analysis. Since the geographic objects and phenomena are complex and the functions and goals of geographic analysis and modeling are various, the data environment should organize data to represent not only discrete entity and continuous phenomena but also their geographic attributes and interaction. The data environment should support the virtual reality realization, complex geographic analysis and simulations to demonstrate geographic knowledge from different perspectives.
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Expressing the geographic characteristics, processes, and mechanisms in a unified framework to form the data environment is challenging. Complex data should be represented and analyzed comprehensively using methods from different perspectives (Chen et al. 2011; Yue et al. 2013). Geometries and graphs, algebraic equations, time series, information spectrums, etc., should be integrated in VGE (Chen et al. 2013). Unifications should be accomplished to integrate the spatio-temporal references, different dimensional representation and different coordination/grids transformation. Discrete objects, continuous processes and abrupt/gradual changes should also be unified in a single framework. Therefore, it is better to change the foundation of the data environment from the classic cartographic model to the integrated scene model, which can integrate various different elements/information in a complete model. In this way, it supports the integration of the representation and computation at local, regional, global and even universal space scales (Hart and Dolbear 2013; Pueyo and Patow 2014; Wright 2012). Currently, the data environment is mostly constructed on the base of the classical GIS, which is mainly focused on data management and visualization based on cartographic model (Goodchild et al. 2012). This leads to several problems of the data representation and computation. (1) The cartographic models represent spatial objects with geometries and organize data into different feature layers. The geometries are mostly represented based on the Euclidean geometry. Due to the relative coordinate and dimensional isolation characteristics of the Euclidean geometry, multidimensional objects are represented as separate pieces. The computation between different dimensional objects is complicated. The computation structure and integration of ambiguous heterogeneous data are also complicated (Yuan et al. 2013; Zhou et al. 2010). (2) The spatial and temporal dimensions are separated and difficult to support both continuous and discrete geographic processes (Pultar et al. 2010; Richardson 2013; Yuan et al. 2010). Many geographic characteristics, such as spatiotemporal variance and processes, interactions and relationships between different elements, are not fully represented (Yu et al. 2012; Zheng et al. 2013). (3) The present GIS data organizations are highly unstructured. Since the dimensions and structure complexities are largely increased, the contradiction between high-dimensional unstructured data representation and linear data organization in computers is growing obvious. These also make the introduction of modern computational technologies (e.g., parallel computation; heterogeneous computation) into VGE more complex (Yue et al. 2013). All the above problems largely hinder the development of VGE as well as the spatio-temporal model analysis.
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In this paper, we developed a unified framework for the construction of the data environment to support complex geographic analysis. We presented the spatio-temporal unified data model, which integrates multiple geo-information to support the complex representation and analysis. New geographic rule-forced spatio-temporal indexes, data structures and data dispatches are designed. These technologies are implemented and deployed in case studies to illustrate the advantages of the new data environment. The paper is organized as follows: the theoretical foundations are provided in ‘‘Theoretical foundations’’. Key technologies including data model, data structures, and computation engines are discussed in ‘‘Key technologies’’. Two different case studies are studied in ‘‘Case studies’’. Finally, ‘‘Discussion and conclusion’’ are discussed in the last section.
Theoretical foundations The integration of geographic representation, model analysis and efficient computation is the key goal of building the data environment. From the abstract level, three different spaces should be considered to accomplish this goal. The first space is the geographic space, where real geographic objects and phenomena are placed and changed. The second space is the mathematical space, where the geographic objects and phenomena are abstracted and formally represented with mathematical structures. The third is the computational space, where special data models and data structures are designed to support the efficient data management, operation and computation. The interrelationship among the above three spaces should be fully considered and integrated during the data environment construction. The mathematical space is the bridge between geographic space and computational space. From the perspective of GIS field, the major components, GIS data models, data structures and computation engines are all concerned to the mathematical abstraction. For example, GIS data models abstract real world and project complex geographic phenomena into geometries for object representation. Data structures project high-dimensional spatiotemporal data into data sequences to fit the linear computer storage system. The computation engine implements the data operation and model calculation into machine instructions. Since common data types in GIS are represented as geometries and the geographic analysis models are represented or calculated with algebra, it is important to integrate the geometric expression and the algebraic computation of complex geographic objects and phenomenon in the data environment construction.
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The extension from the Euclidean geometry to nonEuclidean geometry generalized the mathematical expression of the representation space, metrics and relationships. Modern abstract algebra systems (e.g., Riemannian algebra, algebraic topology, Matrix algebra) are integrated and extended under the non-Euclidean geometry framework. Therefore, introducing and integrating modern mathematical theory, including non-Euclidean geometry, algebraic topology, abstract algebra, etc., as a foundation of VGE data model construction will largely extend the expression and analysis ability of VGE. With the extension of the mathematical expression, different kinds of data and analysis models can be reconstructed to make the data and model efficiently integrated. Introducing non-Euclidean geometry into data environment is accomplished by projecting geographic space into mathematical space and then designing the computational space according to the mathematical space. Here, the geometric algebra and the cell-complex theory are integrated to construct the VGE data environment. Geographic objects and phenomena should firstly be expressed as mathematical expressions, such as multivector or manifolds (Yuan et al. 2013; Zhou et al. 2010). The abstract, generalized and flexible characteristics of mathematical expression can then simplify the expression objects in different coordinate systems. Highly abstract expression and operation space of this modern mathematics can support the representation and analysis of the highly dimensional data inherently and expand the computation power for massive data. With the powerful mathematical representation and transformation, unified data models and data structures [e.g., multi-dimensional unified data model (Yuan et al. 2011)] can be designed to support organization, storage and computation of relevant spatio-temporal data. Powerful mathematical operators and theoretical calculations can be applied to support complex geographic analysis. The mathematical expressions of data are easier to be organized efficiently to fit both the data management and analysis requirements. Mathematical parameterization expression, operator-based computation and unified computation structures can then be developed to support advanced computational technologies (e.g., parallel computation, heterogeneous computing) to achieve better efficiency and analytical ability. According to the above ideas, we constructed the framework of the data environment as depicted in Fig. 1. A spatio-temporal unified data model is firstly constructed to deal with the unified expression of continuous and discrete objects and phenomena. Heterogeneous spatio-temporal data, including spatio-temporal fields, complex 3D scenes, videos, images, etc., are parsed from semantic and structural layer. Geo-information, such as geometric structures, semantics, and relations, is extracted and integrated with
the geometric algebra (GA) data model. Thus, various kinds of data, including body elements, voxels, surfaces, etc., can be represented by this data model in a fusion structure. To reduce the data transition between memory and external storage, the geographic characteristics and laws are integrated to design the new VGE data structure and spatio-temporal data indexing. The organization of massive unstructured spatio-temporal data is also developed to support the unified expression of complex geographic scene. Meta-data model, data adapters and data sharing mechanisms are developed to support the complex VGE computation. To increase the computational efficiency, distributed spatio-temporal data accelerator, massive spatiotemporal data scheduling and distribution mechanisms as well as the spatio-temporal computation engine are developed.
Key technologies Data model The main function of the GIS data model is to support the data representation and spatial analysis. The VGE data model should be extended from the GIS data model to further support the global scale data discretization, various geographic analysis models and complex geographic data representation. Multiple geo-information (e.g., attributes, semantics, and spatio-temporal relations) should be integrated in the VGE data model. It is also indispensable for the VGE data model to support the representation of multidimensional objects and dynamical geographic processes. According to the spatio-temporal frameworks and real geographic world abstract, a unified spatio-temporal data model, which is compatible with different dimensions, coordinates and computation models, may offer a good opportunity to improve the representation and analysis ability of VGE. Here, non-Euclidean geometry and algebraic topology are introduced to construct the VGE data model. The unification properties of non-Euclidean geometry support the unified representation of different dimensional manifold and non-manifold, continuous and discrete objects, in planar and spherical coordination (Groger and Plumer 2011; Yuan et al. 2013; Zhao et al. 2009). These objects can be represented as multivectors in the GA framework. The relations between various complex objects are represented by the algebraic topology (Shen et al. 2010; Zhou et al. 2010). Since both the non-Euclidean geometry and algebraic topology are symbolically computed, the data model not only has a unified representation framework for complex objects and processes, but also effectively inherits the existing algorithms and models. For example, the
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Environ Earth Sci Fig. 1 The overall framework of data environment
spatial metrics like distance, directions, etc., can be directly supported with the GA-operators (Yuan et al. 2011). The solid 3D entitles can be organized and represented using the L-Rep model (Zhou et al. 2010). The object movements can be expressed as versor equations and the smooth interpolations are becoming direct (Yuan et al. 2012). Analysis algorithms like voronoi, network analysis and topological analysis can be directly supported (Yuan et al. 2014a, b). The topological and structure relations can be expressed and calculated using the cell-complex theory (Wang et al. 2008b; Zhou et al. 2010). This will greatly improve the multidimensional expression, analysis and modeling of VGE. GA, a description language of both Euclidean and nonEuclidean geometry (Hestenes 1986), is used to integrate geometrical expression and algebra computation. In our previous works, the GA data models that can efficiently support the vector data, spatio-temporal field and network data representation are developed. Preliminary studies suggest that the GA data model can well support the unified spatio-temporal object/phenomena expression and analysis (Yuan et al. 2011, 2013). In VGE data environment, multiple geo-information including spatio-temporal elements, relations, semantics and attributes should be integrated in a single framework. So the GA Data model was extended to be compatible with the cell-complex structure. The VGE data model is logically formalized and organized (Fig. 2a). In the conception layer, the unified space–time [four dimensional (x, y, z, t) space], rather than the separated space–time, is used in the VGE data model to project the geographic space to the mathematical space. The unified multidimensional representation in GA can directly support
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the unified representation of the unified space–time, thus can support the complex space–time representation. Discrete and continuous changes are modeled with versor equations (Luo et al. 2012; Yuan et al. 2013). The logical layer of VGE data model is mainly constructed based on the cell-complex structure. The L-Rep structure of geometries is used and modified to be embedded into the GA data model. The GIS data are parsed into components of spatial, temporal, attribution, semantics and relations components (Miao et al. 2009; Wang et al. 2008a, b). These components are then represented as hierarchical multivector sets according to a unified structure to integrate multiple geo-information. Multivector is mathematical structures that can be operated with GA operators, thus the powerful computation model. With the multivector representation, GA-MUC (Yuan et al. 2012), is applied to support the complex geographic analysis models. Due to the coordinate-free and multidimensional-unified characteristics of the GA representation and computation, high possibility of the dependency of coordinates of current expression and calculation mode can be avoided. The GA representation also has the potential to directly support the geographic expression, computation and analysis model construction from the data model layer, thus the construction and operation efficiency of GIS analysis models can be greatly increased (Luo et al. 2013a; Yu et al. 2012, 2013). To achieve consistency of the existing GIS data, vector, spatio-temporal field and network data are modeled independently in the VGE data model (Fig. 2b). These different implementations are integrated with various representation forms of multivector structure. The multidimensional-
Environ Earth Sci Fig. 2 VGE data model
unified vector data model is mainly constructed based on the Grassmann structure of GA to organize multidimensional objects in a unified framework (Yuan et al. 2010). Since the expression, storage and calculation are all unified in the multivector structure, the organization, expression and analysis for complex geography scene are simple and direct (Yuan et al. 2011). The spatio-temporal field data are represented by the tensors (Luo et al. 2013c). Tensor operators (e.g., slices, fibers) and tensor analysis methods
(e.g., principal tensor decomposition) are used for data operation, feature extraction and visualization. The hierarchical tensor decomposition is used to support continuous data compression and updating (Yuan et al. 2015). For network data, the node as well as k-walks routes are represented in the Cl(n, n) space, where n is the number of nodes. Then, topologies among nodes, edges and routes of networks can be directly calculated with Clifford adjacent matrix, and the network routes are extended and traversed
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with the oriented meet product (Yuan et al. 2014b). In the GA representation and analysis of networks, the network topology and path certain constraints can be generated algebraically. Thus, solving the dynamic network analysis and multi-type constrained optimal path problem becomes simple and efficient (Feng et al. 2014; Luo et al. 2013b; Yu et al. 2010). Data structure According to the VGE data presented above, various VGE data structures are designed for different types of geospatial data storage and computation. Data structures link the logical structure of data model and efficient computer storage and computation. It is also a key GIS component to accelerate the computational performance of GIS operations and computations (e.g., query and topological analysis). Well-designed data structure can increase the flexibility, stability and performance of the VGEs. The spatio-temporal data are multidimensional and highly unstructured, yet both the internal and external memories are linear, which can only access and compute data linearly. Although there are several methods to project highdimensional spatio-temporal data to one dimensional linear space, distribution characteristics (e.g., spatio-temporal proximity and aggregation) of the original data usually cannot be maintained. Since complicated and various distributed geographic spatial data should be projected to fix length and uniform memory space, the performance of accessing spatio-temporal data is highly related to the order of data organization (Lee 2001). This leads to the difficulty of prediction of the object numbers and space occupations of the spatio-temporal data, which further increase the complexity in effective load balance (Zheng et al. 2009). Since most current data structures are static rather than dynamic and accessing spatio-temporal data are usually random, the performance of the massive random query cannot be stable and predictable. Numerous different data structures, which are separated for different goals, are designed for different dimensional data organization and analysis. The separation of data structures increases the complexity of algorithm structures and lowers the efficiency. This separation also lowers the ability to support distributed/paralleled computing and cloud computing (du Mouza et al. 2009). The VGE data structure is designed by integrating the spatio-temporal distribution of geographic objects and phenomena in the data organization and indexing. The spatio-temporal distribution pattern of the data directly determines the space division and overlapping, data equilibrium and spatial proximity of objects between different data groups, which also determines the load balance of data query and accessing. The new data structure is composed
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of the integrated expression of multidimensional elements and complex coupled data objects in the geographic scene, geographic law and feature-driven data indexing (Fig. 3). Heuristic detection rules as well as the measurements and quantitative index of temporal distance, spatial distance, object distance and spatial similarity/heterogeneous are introduced to construct the multi-granularity hierarchical partition method of spatio-temporal data. Then, the batch hierarchical data indexing and incremental data updating methods are constructed on the foundation of the intrinsic spatio-temporal data distribution characteristics and geography laws. The new data-driven data structure, which integrates the internal and external memories and associates spatio-temporal indexing and scheduling method, is constructed. Based on the multivector structure in GA, a data structure called MVTree (Multivector-Tree) (Yuan et al. 2014a) is constructed based on the Grassmann structure. This MVTree integrates the dimensional construction structure, topological relations and metric relations in a unified data structure. Cell-complex chains are introduced to interlink topological objects in complex scenes. With the cellcomplex operators, the space and objects in complex scenes are separated into a series of related space units. Complete topological relationships of space/objects are computed in the algebraic topological space. The ‘‘distance function’’ and ‘‘distance effect function’’ as well as semivariant function, quadrat analysis and other quantitative analysis methods are introduced to explore the spatiotemporal distribution patterns of spatio-temporal data. A new spatio-temporal indexing structure, Pattern List, is constructed. By logging and analyzing the existing query pattern of the users, the Pattern List predicts the depth of the searching tree to optimize the search structure. For the data updating, the quantitative and qualitative changes are distinguished to avoid frequently searching space reconstruction. The batch data updating procedure is also optimized. Computation engine Highly abstract mathematical spaces and structures, which support the primary expression and analysis of high-dimensional data, also provide operators and algorithms for efficient geo-computation. Based on this, the computation engine is developed according to the algebraic computation from the mathematical foundations to support complex geographic analysis model computation. The major effect of the computation engine is to optimize the computation process with the algebraic computation. Since the VGE data representation is algebraic and the computation is operator based, the computation process optimization can be achieved by developing symbolical expansion and
Environ Earth Sci GA-based representation of multiple elements Geometric expression GeoObjMv=Obj.Points Obj.Lines Obj.Polygons Obj.Polyhedrons Attribute expression v=αe1010 esandstone +βetime e3000 AD erock =e1010 +γedepth e800 m etime =e0111 =αe1010 e1100 +αe0111 e1000 + edepth =e0100 γe1011 e0100 Action expression Evt(V) = T* Evt*T~ Cell complex chain-based topological representation Boundary operator
(b) Boolean operation based on cell complex
Association boundary operator
Operating functor
Pattern List index Dispersibility index calculation:
Objective function calculation:
(a) Data organization process
(c)
Multi-dimensional scene explore based on Pattern List
Fig. 3 VGE data structure
simplification mechanisms according to the characteristics of mathematical operators. The VGE computation engine is constructed according to different data types. For the vector data, the GA expressions and operators are integrated to support the unified algebraic computation. The computation under the GA framework is highly data adaptive and multidimensional unified, which can form computation templates to support complex computation (Yuan et al. 2012, 2013). For high-dimensional spatio-temporal field data, tensor algebra is introduced to unify the data representation, organization and computation. The tensor-based model, which is dimension-independent and highly computable, changes the data representation and storage from the tuple and table-based relational model into the cube-based multidimensional cube model (Yuan et al. 2010). Both the GA and tensor-based computation are operator-based algebraic computation, which can be optimized formally and symbolically. To integrate large-scale model simulations, the mathematical properties of different computational grids are firstly analyzed. The composite diamond mesh, which is constructed from the triangle and the hexagonal grid and has compatibility of both grids, is then designed. By coding the grid components of diamond vertex and diamond edges, the division, hierarchical structures and the query mechanisms are constructed. With this grid, the global grid subdivision based on the discrete rhombus cell is
constructed. Since the composite diamond mesh is compatible with the triangle and the hexagonal grid, the grid subdivision can also unify the grid for data management and computing.
Case studies Two different case studies are provided to illustrate how the above data model, data structures and computation engines are used in the VGE. The first case is the ground– surface–underground integrating city expression and modeling. The second case is the multi-scale data integration on the global, regional and city levels. The unified computation and model simulations with different computational grids are performed. Ground–surface–underground integrated city expression and modeling This case studies different data integration of Nanjing city in the VGE. The data include the ground 3D buildings, the surface vector data, underground strata layer and pipeline data. Since the scale information of different objects in the city level is various, the implications and the relationship between different scales of geographic phenomena and models are first explored. The VGE data model is then
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applied to synthesize the characteristics of ‘‘object models’’ and ‘‘field models’’. 2D representations are transformed into 3D surfaces and volumes using Delaunay restricted algorithms with the support of the data model. Then, these 3D entities are then organized according to the L-Rep model. To integrate different objects on the ground, surface and under the ground, cellular homology theory in algebraic topology is introduced to define the multidimensional spatial entity as the k-dimensional non-oriental manifold. Thus, complex objects (e.g., frame, surface, body elements) as well as non-manifold data can be represented in the cell-complex data model in a unified way. Different objects on the ground, surface and under the ground can then be represented by the adhesive relationship between different cells in the 0–3 dimension. Then, buildings, surfaces, and underground entities can be unified in a single scene (Fig. 4). Dynamic topological consistency and view-dependent LOD conditions are solved with the 3D free topology model constructed based on Poincare duality (Wu 2013). With this unified data model, algorithms, including region query, spatial intersection detection, Boolean calculation, grid discretization and object smoothing, etc., are constructed (Wang et al. 2008b; Zhou et al. 2010). Based on the flexible grid, simulations, such as salt rock creep cavity, are performed. The VGE integrated expression and modeling can support not only integrated representation, but also complex simulations. Therefore, the expression can increase the city-level management and analytical ability, which also provides a potential to develop the decision support systems based on VGE.
Global–regional-city scales integrated expression and modeling This case studies the data integration and model simulation support of the VGE at different spatial scales. Several methods are implemented to integrate data and simulation models at different scales. Discrete methods for 3D surface, tetrahedral meshes, regular and irregular hexahedral meshes are developed. These discretization methods fully take external boundary and internal feature constraints, such as point, line, surface, and holes, into account. Then, the computation of the 3D simulation models is supported by discretizing spatial objects with an optimized rule. An integrative model, which has a clearly defined structure and semantics, is built to integrate multi-source and heterogeneous data (Wang et al. 2006). The integration of point, line, surface, body, lattice element, and volume element expression is effectively supported for the realization of regional and city scale model. To integrate the global scale data and models, the dynamic multi-scale decomposition of the vector data is developed to support multiple representations of spatial data. Expression parameters, such as the scale and viewpoint, are determined in the 3D spheroid. With the global grid subdivision and coding scheme, the global data can be integrated. 3D modeling and visualization of global plate data are then interpreted in the global grid. The CSDDG (composite spherical diamond discrete grid) is used to support both the data management and model computation. The composite diamond discrete grid can be neatly transformed into other different grids
Scene data
Date type and structure parsering
NonManifold manifold
Vector
Field
MV-based representation Cell complex chain-based operators Compose
Bond
Bound
Cell complex chain embedding
Ground-Surface-Underground integrated
(a) Construction process Fig. 4 Ground–surface–underground integrated city expression and modeling
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(b) Examples
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Fig. 5 Global–regional-city scales integrated expression and modeling Table 1 Performance comparison of the Boolean operation (unit: seconds)
No. of triangles
L-Rep (Intersection)
32,768
0.59
1.24
0.73
2.51
0.83
3.22
131,072
1.1
10.36
1.19
21.39
1.55
30.63
524,288
2.66
201.19
4.56
370.16
5.02
830.28
according to the grid unit coding of neighboring relationship and the expression levels. Then, the finite difference, finite element and finite volume methods are directly supported. Here, the Chinese offshore 2D vertical tidal wave model (FVCOM) is used to demonstrate the integration of the triangle grid and composite spherical diamond grid (Fig. 5c). The model is forced by the ETOPO-1 water depth data. The motion of the China offshore tidal wave is simulated and visualized. The results suggest that the VGE data environment supports not only the data integration of different scales, but also the complex model simulations. Therefore, it can largely benefit the data integration and model analysis abilities. Performance comparison The performance comparison of the data representation, query, computation and visualization is conducted with a common GIS software. To verify the efficiency of the
IRIT (Intersection)
L-Rep (Union)
IRIT (Union)
L-Rep (Subtraction)
IRIT (Subtraction)
proposed L-Rep model-based Boolean operation of 3D entities, we compared the performance of the proposed algorithm with the geometric modeling engine IRIT (Elber 2015). Solid models with different sizes are operated with Intersection, Union and Subtraction operations with our solution and by the according methods within the IRIT engine, respectively. The results of analysis and comparison are provided in Table 1. Clearly, when the size of the object increases, our L-Rep model has obvious performance advantages compared with IRIT. The query performance of the VGE framework with the pattern list spatial index is also compared with the modern MongoDB and PostGIS databases within the same hardware and software environment. Different numbers of points, lines and maps are queried randomly using the box query from different databases. The time cost comparison is depicted in Fig. 6. From Fig. 6, we can clearly see that our indexing pattern list has large advantage in the performance of simple query like points and lines. In the map
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integrated more closely in the VGE. According to the development of earth observation technology, sensor networks, mobile Internet, etc., more file types, such as sensor network data, multimedia file types (video, audios, etc.), natural languages and text, should also be integrated in the VGE for a more comprehensive representation. Thirdly, the standardization of the VGE data environment can be further improved. A more complete description of the elements, relationships, operations, constraints and other aspects should be standardized as specification and abstract templates. Unified and customizable multi-dimensional spatial data representation and exchange model should be established to integrate the multi-source and heterogeneous data. In this way, various geographic analysis models could be seamlessly integrated to support the coupled multi-model analysis and simulation.
Fig. 6 Query performance comparisons
query experiment, although the dataset is much more complex, our pattern list is the quickest compared with MongoDB and PostGIS.
Acknowledgments This work was supported by the NSCF Project (Grant No. 41231173; 41471319) and the PAPD program. We acknowledge Prof. A-Xing Zhu and Prof. Ming Chen for their helpful comments on our paper. Compliance with ethical standards Conflict of interest of interest.
The authors declare that they have no conflict
Discussion and conclusion References The expression and analysis of supporting complex geographic objects and continuous geographic phenomena are one of the hottest topics in the development of VGE. In this manuscript, we presented the VGE data framework composed by the VGE data model, data structures and computation engine. The experiments suggest that the integrated VGE data environment can support complex analysis with integrated multiple geo-information. It can also better use the computational power of modern computation architectures and hybrid computation. Since the VGE data environment is developed from the perspectives of geographical cognition and knowledge representation, the VGE data environment can be more suitable for the geographical description of the world. In addition, the VGE data environment has strong computation ability and can support geographic analysis model directly. Although the VGE data environment is constructed, a lot of work can be further conducted to improve the VGE data environment. First, the generalization of the information representation can be improved. VGE should represent not only geographical objects and phenomena but also geographical rules and knowledge. Data objects, knowledge, rules and constraints should be represented in a unified way. Second, wider data integration should be
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