The Research Of Mathematics Foundation Of Large Scale Topographic Map In Modern Engineering

Map has a long history and is possibly the earliest one among the three great inventions as information dissemination tools of primitive human, the other two being music and language. It takes the geo-space concept from geodesy, depicting geo-information by simulative products integrated with visible and measurable characteristic. Being limited to use and manufacture of paper-based media, calculation and measure tools and so on, map projection methods have been adopted to convey space. The reason that Cartography became a new science from ancient knowledge is the use of map projection which has a history of more than two thousand years. With the revolution of computing capacity in recent50years, map projection calculation has turned to be a task not as arduous as it used to be. Therefore, designing and applying more accurate map projection, which has got a high attention in science and technology field, is an effective method with minimum cost to improve the quality of basic geo-information products.Survey technology has had a rapid development in the past half century and the measurement accuracy has improved more than five orders of magnitude, but the projection solutions of series topographic map still remain unchanged. In some practices of large scale engineering survey, cadastral survey, especially precision engineering survey, particularly in large-scale high-speed railway network construction, current Gauss projection method cannot satisfy the demand of practical engineering and measurement accuracy, which is an urgent problem needed to be solved. In order to meet the construction requirement, independent coordinate system is adopted through confining the deformation of side length in a certain range in precision engineering survey projects like high-speed railway construction. Each independent coordinate system, however, is isolated, without due respect to extensions and connections among complex objects. Modernized precision engineering project is a unified system in its own right, which cannot be treated in isolation and static state. Take the treelike-extension structure of high-speed rail network as an example, scientific data management can be achieved only by constructing a unified coordinate system, which will further optimize benefits of a project by planning as a whole the various processes of the project such as survey, design, construction and maintenance, among others. Therefore, it is of significance to establish a map projection system of high precision in order to meet the requirements of the mathematical foundation of large scale maps in modern engineering.This dissertation put forward the global treelike-extension map projection of high precision. Concentrated on the linear or treelike-extension characteristics of large scale engineering survey, this new Gauss map projection set the central meridian length ratio between0.9999988and0.9999992with15’zone as its longitude differential, based on classic Gauss projection. With maximum length deformation confined to1.2per million and1.6per million, its precision improved by about2～3orders of magnitude contrary to3°zone projection, and about3～4orders to6°, which surpasses the precision requirement and development of precise survey. The traditional versions of various Gauss projections can only be fine-tuned while can’t improve the precise level. At the same time this paper compared with previous Gauss projection applying3°and6°zone, and stropped into the high precision nature of global treelike-extension map projection.Then some experiments searching map sheets which contain linear features and joining principle of map sheets was given in order to explore its applications. Established the large scale map projection system for modern engineering survey including survey, mapping, planning, design, layout and construction, which has the characteristics of minimum length deformation and none angle deformation, with the fact that it can almost be fit to Euclidean space, as well as the strength of high precision of global unified mathematical foundation for linear, treelike-extension geographical features together with the planning and construction of small and medium-sized cities.At the same time, expanded the number scheme of original series of topographic maps for scientific unified data management of all kinds of engineering large scale map, extended the original scale series of1:5,000～1:1,000,000to1:500～1:2,000which fit to modern precise survey and cadastral maps. The new15’zone method, distinctly improved the precision of projection, provided a unified map projection foundation in accordance with the precision requirement of earth control network for large and super large precise survey such as highway, railway, magnetic levitation and high precise cadastral map, strongly supported the precise survey. It’s even more significant to closely link GIS coordinate system to CAD coordinate system of large precision projects.Converted the original geographic information of these features in1:50,000and larger than the1:50,000topographic maps as well as all corresponding DLG data in ARCGIS into this map projection system by project transformation, which can be regarded as space data of standard Euclidean space. With non-angle deformation, minimum length deformation, the data can be easily fit into the Euclidean CAD system. And all planning result data in CAD will also be systematically and easily transformed to ARCGIS data.It was pointed out that there are two ways to solve the conflicts between the geographic information metric space and the Euclidean metric space which is commonly used in machinery and civil engineering design through CAD, and that each of the two ways is suitable for certain occasions. On one hand, for the computer technical system aimed at geographic information analysis and decision-making, i.e., integration of military information system, Euclidean metric space data shall be transformed in equivalence to geographic information metric space data, which, being accurate, scientific and systematic, can be integrated into geographic information metric space. On the other hand, in traditional simulative fields using medium of paper-based maps, hand measurement, form analysis and evaluation, aesthetic design and decision making are all mainly based on human’s interaction, experience and judgment in Euclidean metric space. In such cases, geographic information metric space data shall be transformed in equivalence to Euclidean metric space data. That is to say, in traditional maps and CAD fields, among other interactive occasions, Euclidean metric space shall be adopted, which requires a transformation from a huge amount of data and common geographic information according to the required precision and distortion by using traditional map projection methods.The main research achievements of this dissertation include:1.Studied the theory and method of mathematics foundation of large scale maps, mainly analyzed existing limitations of the application of current Gauss-Kruger projection and its derivative projections, discussed the corresponding solutions, including the establishment of the mathematical basis for the map, the analysis of status quo of mathematics foundation of large scale maps in China, the precision requirement of map projections in survey and design of contemporary precise engineering projects, the precision requirement of spatial data in CAD design, the comparison of map projections at home and abroad, and the approach to a unified projection foundation according to the survey precision of the earth control network;2.Coded programs calculating Gauss-Kruger projection coordinates, length deformation, meridian convergence angle, vector length, fracture distance, providing data basis for accuracy analysis and choosing solutions;3.Searched map projection solutions surpass the precision requirement in precise survey, put forward highly precise global treelike-extension map projection, a new Gauss projection with length ratio of central meridian being0.9999988-0.9999992, using15’longitude differential as projection zone, whose maximum length deformation reached1.2per million and1.6per million. If length ratio of central meridian being0.9999990, the length deformation of mainland will not exceed one per one million, reformed the current zonal solutions of map projection in3°and6°;4.Developed equal-angle projection formula, length deformation formula, meridian convergence formula. Probed into the coordinate system, length deformation, application and property of the highly precise global treelike-extension map projection, drew conclusions of its characteristics from comparison with the original3°and6°zone Gauss projection. Demonstrated the topology continuity both in longitude and latitude direction of this projection system in1:50,000map so as to prove the continuous treelike-extension property of global projection system.5.Established the highly precise treelike-extension coordinate system of15’zone band based on the1:50,000map sheet of the high-speed rail between Wuhan and Guangzhou, transformed one mapsheet of the highly precise global treelike-extension coordinate system built in ARCGIS to the highly precise unified plane coordinate system by map translation, rotation;6.Presented the serial number solutions of1:500～1:2,000maps for unified mathematical basis of the large scale engineering survey, extended the current number solutions of1:1,000,000～1:5,000topographic maps to1:2000～1:500topographic maps, which means that number solutions of1:1,000,000～1:500were established; 7.Summarized the innovations and achievements of this paper, found out the deficiency and pointed out further research direction as well as its application.To sum up, this dissertation put forward the highly precise global treelike-extension map projection, a new Gauss projection with length ratio of central meridian being0.9999988-0.9999992, using15’longitude differential as projection zone, as well as a new number scheme for topographic maps by studying its properties and application; Based on geographic information science and technology, focused on the wide range of treelike-extension linear features in the ellipsoid space, this paper provided a widely used Euclidean metric space with high precise of1/80million for survey, design, layout, construction, test, management and so on in global extent, integrated GIS with CAD, the two mature fields for the first time. Thus a unified projection foundation in accordance with the precise requirement of earth control network was put forward for survey and design of modern precise engineering of large scale.