Guonian Lu

Multidimensional-unified topological relations computation: a hierarchical geometric algebra-based approach

This article presents a geometric algebra-based model for topological relation computation. This computational model is composed of three major components: the Grassmann structure preserving hierarchical multivector-tree representation (MVTree), multidimensional unified operators for intersection relation computation, and the judgement rules for assembling the intersections into topological relations. With this model, the intersection relations between the different dimensional objects (nodes at different levels) are computed using the Tree Meet operator. The meet operation between two arbitrary objects is accomplished by transforming the computation into the meet product between each pair of MVTree nodes, which produces a series of intersection relations in the form of MVTree. This intersection tree is then processed through a set of judgement rules to determine the topological relations between two objects in the hierarchy. Case studies of topological relations between two triangles in 3D space are employed to illustrate the model. The results show that with the new model, the topological relations can be computed in a simple way without referring to dimension. This dimensionless way of computing topological relations from geographic data is significant given the increased dimensionality of geographic information in the digital era.

A data description model for reusing, sharing and integrating geo-analysis models

Geo-analysis models are necessary tools for understanding various geo-processes and phenomena in Earth’s environment. Studying, reusing, sharing and integrating geo-analysis models can help researchers solve complicated and synthetic geo-problems with interdisciplinary knowledge, especially for researchers who collaborate with each other to build virtual geographic environments (VGEs). While the integration frameworks of geo-analysis models could permit their practical use, it is essential for model users to prepare data according to the specific requirements of the different geo-analysis models. Model users should invest adequate effort and time into preparing such model data, particularly when employing multi-disciplinary geo-analysis models. This paper proposed a data description model, the Universal Data eXchange (UDX) model that can reduce the effort and difficulties of model data preparation and pre-processing for model users. With the UDX model, researchers from interdiscipline can build a collaborative workspace in VGEs more conveniently. A hierarchical structure was employed in the UDX model for the flexible description of heterogeneous model data, and a set of basic data node types was designed to provide a relatively stable organization method for the various data contents. In the UDX model, the structural format data (e.g., the Shapefile and NetCDF data) and the flexible plain text data content can be described in a uniform way. In addition, model data information can be completely and unambiguously described with the items in the attachment libraries (e.g., unit and dimension library, semantic library, spatial reference library, and data description template library). Furthermore, two different model integration case studies were conducted to prove that various data processing methods and efforts can be accumulated and organized with the designed UDX data processing library.

Data environment construction for virtual geographic environment

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.

Change detection for 3D vector data: a CGA-based Delaunay–TIN intersection approach

In this paper, conformal geometric algebra (CGA) is introduced to construct a Delaunay–Triangulated Irregular Network (DTIN) intersection for change detection with 3D vector data. A multivector-based representation model is first constructed to unify the representation and organization of the multidimensional objects of DTIN. The intersection relations between DTINs are obtained using the meet operator with a sphere-tree index. The change of area/volume between objects at different times can then be extracted by topological reconstruction. This method has been tested with the Antarctica ice change simulation data. The characteristics and efficiency of our method are compared with those of the Möller method as well as those from the Guigue–Devillers method. The comparison shows that this new method produces five times less redundant segments for DTIN intersection. The computational complexity of the new method is comparable to Möller’s and that of Guigue–Devillers methods. In addition, our method can be easily implemented in a parallel computation environment as shown in our case study. The new method not only realizes the unified expression of multidimensional objects with DTIN but also achieves the unification of geometry and topology in change detection. Our method can also serve as an effective candidate method for universal vector data change detection.

A function-based linear map symbol building and rendering method using shader language

Maps are widely used to visualize geo-information so that map users can develop related understandings about the real world. Such a process for communicating information is largely dependent on the rendering of map elements using different symbols (points and linear and area symbols). To meet the demand of more dynamic and comprehensive visualization in map rendering, it is essential to improve the rendering efficiency. This paper focuses on these research topics, especially the difficulty in constructing and drawing linear map symbols. By employing shader language, a function-based linear symbol building and rendering method is presented in this paper. The basic idea of this function-based method is to build a map-rendering solution that employs graphic processing unit (GPU) acceleration technology to improve the rendering efficiency. A ‘function’ is used to represent the algorithm that draws certain simple or complex linear map symbols. This function reflects the structure of a linear map symbol (describing the symbol construction information) and also the rendering process of the symbolized linear map elements (handled on a per-pixel basis by the shader program). Based on the Open Geospatial Consortium (OGC), Styled Layer Descriptor (SLD) specifications, four basic line types (i.e., solid lines, dashed lines, gradient color lines, and transition lines) are implemented in the proposed method, and the implementation of line markers, line joins and line caps is also discussed. Three experiments are conducted to demonstrate improvements in map rendering. The results show that a variety of linear map symbols can be constructed in a uniform way, which suggests that the proposed method addresses the difficulty in drawing linear map symbols. With this method, the efficiency of rendering linear map elements is substantially improved compared to using the graphics device interface plus (GDI+) and anti-grain geometry (AGG) methods; it also provides an applicable approach for developing map rendering systems. Using this function-based concept, the complexity of building linear map symbols and drawing linear map elements can be decreased.

A dynamic evacuation simulation framework based on geometric algebra

Abstract Integrating dynamic analysis models into geographic information system (GIS)-based evacuation simulations is important yet complex. Different models must be smoothly assembled according to the data processing flow to obtain a dynamic, data-forced evacuation simulation. However, because of the diversity of data types and dynamic data updating among different models, closely integrated evacuation simulations are complex and inefficient. In this study, geometric algebra (GA) is introduced to develop a dynamic evacuation simulation framework for a hazardous gas diffusion scheme. In the framework, geospatial data are first integrated into a unified virtual scene with different forms of multivector representation. The major simulation models of gas diffusion, risk assessment, and dynamic evacuation routing compose the major steps of the evacuation simulation. On the basis of the generalized multivector structure, dynamic exchange and updating geospatial data at different evacuation steps can be performed seamlessly with the multivector structure and GA operators. The framework is tested with a case study of a three-dimensional residential area, which shows that our framework can support the integration of dynamic evacuation processes and the model integration is direct and smooth. This framework may also provide a new solution for the integration and dynamic data updating in spatiotemporal GIS.

Geographic scenario: a possible foundation for further development of virtual geographic environments

ABSTRACT It has been two decades since virtual geographic environments (VGEs) were initially proposed. While relevant theories and technologies are evolving, data organization models have always been the foundation of VGE development, and they require further exploration. Based on the comprehensive consideration of the characteristics of VGEs, geographic scene is proposed to organize geographic information and data. We empirically find that geographic scene provides a suitable organization schema to support geo-visualization, geo-simulation, and geo-collaboration. To systematically investigate the concept and method of geographic scene, Geographic Scenario is proposed as the theory on developing geographic scene, and corresponding key issues of the Geographic Scenario are illustrated in this article. Prospects of the proposed method are discussed with the hope of informing future studies of VGEs.

A model-service deployment strategy for collaboratively sharing geo-analysis models in an open web environment

ABSTRACT Geo-analysis models can be shared and reused via model-services to support more effective responses to risks and help to build a sustainable world. The deployment of model-services typically requires significant effort, primarily because of the complexity and disciplinary specifics of geo-analysis models. Various modelling participants engage in the collaborative modelling process: geo-analysis model resources are provided by model providers, computational resources are provided by computational resource providers, and the published model-services are accessed by model users. This paper primarily focuses on model-service deployment, with the basic goal of providing a collaboration-oriented method for modelling participants to conveniently work together and make full use of modelling and computational resources across an open web environment. For model resource providers, a model-deployment description method is studied to help build model-deployment packages; for computational resource providers, a computational resource description method is studied to help build model-service containers and connectors. An experimental system for sharing and reusing geo-analysis models is built to verify the capability and feasibility of the proposed methods. Through this strategy, modellers from dispersed regions can work together more easily, thus providing dynamic and reliable geospatial information for Future Earth studies.

A characteristic bitmap coding method for vector elements based on self-adaptive gridding

Spatial index is a key component of Geographic Information Systems (GISystems). To date, an increasing number of spatial indexes have been developed to enhance the efficiency of spatial analysis and spatial query. Approximate expressions are adopted in the foundation of spatial index construction, to assist data organisation, e.g., bounding box of vector elements can be employed to build R-tree index. However, R-tree index using such bounding box expresses elements approximately, which usually results in redundancy and excessiveness due to inherent roughness of this method. This study proposes a characteristic bitmap coding method, termed the QCODE method, which generates approximate expressions of vector elements based on self-adaptive gridding. Based on the sizes of vector elements, this method selects the grid at an appropriate level in a self-adaptive manner, discretises the vector elements into grids through a rasterisation operation, as well as compresses and encodes this information as the code of a characteristic bitmap, i.e., the QCODE. The ‘bit’ data type is used in the design of QCODE to restrict the approximate expression of vector elements into finite bytes, providing more precise filtering as compared to the case in which only bounding box is used. With its distinct characteristics, the QCODE is introduced for the improvement of R-tree index. The results of experiments show that, combined with R-tree index, this method can reduce the filtering amount of vector elements as required for spatial analysis, and accelerate the execution efficiency of the entire process of GIS spatial analysis.

A discrete global grid system for earth system modeling

ABSTRACT To support Earth system modeling, we propose a discrete global grid system that expresses multi-resolution spatial data. Specifically, a unified coding model that expresses a grid of nodes, edges, and cells is constructed for a triangular discrete global grid system. To fulfill the requirements of practical applications, we design a code-based topological query method for this grid system and an algorithm to transform between grid codes and geographic coordinates. We evaluate the Global Finite Volume Community Ocean Model (Global-FVCOM) on the triangular discrete global grid system in the proposed uniform coding model. The ocean tidal waves simulated by the Global-FVCOM running on the coded grid are then compared with results obtained using a traditional irregular spherical grid system, and the results display comparable accuracy. The uniform coding model proposed in this paper provides a triangular discrete global grid system that can represent multi-resolution spatial data and can be used in Earth system models. This unified coding model can also be applied to the geographic coordinate system made up of latitudes and longitudes, as well as diamond and hexagonal grids.