The Study Of GIS Computational Model Based On Geometric Algebra

Spatial analysis is the core function of geographic information science as well as the basic for ensuring better progress in geographic information system application. As the development of observation technologies including Internet of things, air survey, satellite remote sensing, and so on, the geographic data have become more and more rich. Lots of high-dimension and multi-factor intensive GIS spatial data have appeared. At the same time, the corresponding calculating regulations of GIS spatial data lag behind. It results in the problem that existing analyzing methods can’t analyze effectively the above data. Most of existing spatial data analyzing methods have deficiencies in self-adaptive expression of multi-dimension objects, unified analysis of spatial data and construction of multi-dimension unified analyzing framework. The multi-dimension expression structure and unified calculating structure of geometric algebra (GA) are introduced to innovate upon the expression and calculation methods from underlying theory, and to define calculating and analyzing regulations oriented to multi-dimension and multi-factor complex data. It is an effective way of breaking the bottle neck in current GIS application and overcoming the drawbacks of conventional GIS analyzing methods.This thesis researches the GA-based GIS spatial calculating model which is founded on early studies of our research group on GA-based GIS theory, methods and applications. This paper researches the multi-dimension expression features of GA and the expression models of geographic space, studies the construction of GIS calculating space based on GA, and then explores the build of GA-based GIS spatial calculating methods and models. In this thesis, the constructing methods and calculating strategies of GA-based GIS algorithms are studied systematically, and finally the above theories are validated by system realizing and cases demonstrating. The main research achievements are as follow:1. The embedding model from geographic space into GA space is designed by using the multi-dimension expression features of GA and the GA-based GIS calculation space is constructed. The build of calculation structure of GIS basic objects and multi-factor syncretic objects is realized using blade and multivector. The corresponding multivector calculating regulations and operators and algorithms library aimed at different characters of different GA models are defined, and are expanded to multivector. On the basic of reversibility of geometric product, the general strategies of solving problems in GA framework are structured and the general process of GIS spatial calculating from spatial definition to objects expression to problem formulation to GA solution are designed.2. On the basic of direct computability of geometric objects and unity of calculating regulations in GA space, the multi-dimension unified analyzing framework is structured, and the algorithm models are constructed which is founded on the analysis of conventional methods. It designs the corresponding dimension-embedding and algorithm solving strategies for multi-dimension vectors, high-dimension field and internet data. The synthetic expression of multivector and multi-dimension features is proposed. The computing regulations and models of multi-dimension data are provided in the paper and then the cases are demonstrated. The construction and expressing methods of multi-dimension unified field space are designed. It realizes the unified calculation of field feature parameters using differential operation and feature space projection of GA and further builds the unified analyzing methods of multi-dimension field data. The unified expression structures and expanding methods of nodes, edges and routes in GIS internet are constructed by using the dimensional computation of GA. And then embedding methods of different kinds of route constraints are designed to realize the solution of optimal path in node-type and mixed type constraints internet.3. The GA-based GIS computation engine are designed which provides the basic theories of the implementations of GA algorithms. The data structures of storage class and calculating class are constructed in GA space and GIS space, and then the operation interface and the data flow of the computation engine are accomplished. The code and system implementation is developed in the three-tier architecture which includes computation space, operator library and algorithm solving. The process templates of GIS computation are formulated to realize the particular GIS applications, and finally an embedded plug-in mechanism for GIS algorithms is proposed.4. At last, the GA-based multidimensional space computation system is implemented with the execution of integrated modeling instance and dynamic calculation instance, which can verify the main conclusions of the thesis. In the system we realize the unified expression and integrated analysis of the multidimensional vector data, the three dimensional field data and multi-constrained network data. Under the condition of multicomponent geography scene, the GIS analysis algorithms including computation of the dynamic space relationship, structural analysis of the pollution status and planning of the optimal path are designed which consider the distribution of pollutants. All the case studies suggest that GA-based GIS computational model is qualified the computation of multicomponent, multidimensional and dynamic geographic scene.The studies in this thesis show that the GA-based GIS spatial computation methods can meet the analyzing need of multi-dimension, multi-factor and structure complex GIS spatial data. With the support of designed GA operators and algorithms library, simple, intuitive and expandable GIS spatial solution templates can be constructed. The unified analyzing and algebraic solving of GIS problems in complicated and dynamic scenes are realized by the design of GIS computation engine based on GA. The GA-based GIS spatial computing methods are expected to provide complicated GIS spatial computing problems with a complete calculating framework and solving model and promote the development of a new generation of GIS which is characterized by multi-element synthetic analysis.