The Rebuilding Boundary Of Map On Fractal

Fractal theory is a branch of modern mathematics, and it studies the objects that they have self-similarity between the part and the whole. The dimension of these objects can be discrete or continuous, in other words, they can be integer or fraction. There are a large number of such objects among nature, such as rivers, coastline, terrain, and so on. As Euclidean geometry describes rule geometric objects with dimensions and simple geometric structure, fractal geometry uses fractal dimension and fractal structure to describe the non-rule geometric objects. In the description of the non-inerratic geometric objects among nature, many studies show fractal theory than Euclidean geometry more suitable. This dissertation discusses fractal characteristics of the map border, and uses fractal theory to analyze, describe and rebuild them.This dissertation mostly studies the description of the map boundary and rebuilding techniques in the integrated map boundary. The main contents and results of this dissertation are as follows,①Introducing the correlative concept of fractal theory and the computing methods of fractal dimension.②Studying the extraction and denotation methods of the map boundary, proposed the EB(Extraction of Boundary) algorithm for the extraction of the map boundary.③Discussing the Douglas-Peuker algorithm in detail, and analyzing this algorithm defect in the curve rebuilding, proposed two advanced algorithms for opened curve and closed curve.④Researching under different scale rebuilding of the map boundary, AMMBR (Advanced Method of Map Boundary Rebuilding) algorithm is given on fractal dimension.⑤Designing the prototype for the map boundary rebuilding and verifying the effectiveness and feasibility of the methods and algorithms proposed in the dissertation.Based on the research of the map boundary's shape structure characteristic and its rule with the measure and the scale changing, the dissertation gives a set of method that can maintain the shape of map boundary reconstructed. The method can substantially reduce the preservation and operation points when the map boundary is rebuilt, and improve the efficiency of the map boundary rebuilding. The research work of the dissertation provides an effective method for the integrated map.