Geometrical Structure And Fourier Transform Of Hexagonal Discrete Global Grid System

With the rapid development of earth observation,satellite navigation and mobile communication,the data obtained and accumulated is transited from a structured type easily processed to an unstructured one which is very hard for process.Characteristics of big data have arisen nascently.Current models and related processing methods cannot meet the practical demand completely.Discrete global grid system is a reference model of digital multi-resolution earth,which can help to establish the new model of data association and integration with geographical location and make up for the shortcomings of the current spatial data organization,processing and application.This paper takes the aperture 3 discrete global grid system as the main object of study,makes a deep analysis of its geometric structure and encoding scheme,builds the Discrete Fourier Transform model of grids in the sphere and realizes the algorithm of fast transform.Work is as follows:1.From the perspective of the characteristics and application requirements of spatial data,this paper states the necessity of research on using discrete global grid systems to process geospatial data,analyzes research status of this field and raises questions of current questions and structural arrangement of it.2.It is proved that the planar aperture 3 hexagonal grid system is ‘number' in a special form and an encoding scheme is designed according to this.Then the mapping mechanism from infinite two-dimensional planar grids to finite and closed grids in three-dimension is stated,which reveals the geometric structure of the aperture 3 hexagonal grid system.The accuracy and superiority of conclusions above are verified by contrast experiments.3.The mathematical model of resampling from rectangular grids to hexagonal grids is built and it is proved that equal-area resampling has the smallest information distortion in the aspect of cells' corresponding relationship according to analysis.The Discrete Fourier Transform model of the aperture 3 hexagonal grid system is built.The two-dimensional transform kernel is converted into an one-dimensional one which lowers the processing difficulty and in the help of Cooley-Tukey algorithm,fast discrete Fourier transform is implemented.The accuracy and superiority of the algorithm are verified by contrast experiments.