Research On Metric Grid Of Natural Shapes

Spatial analysis is the main feature of GIS and one of the main factors in evaluating GIS. Regardless of theoretical research or practical application for current GIS, Spatial analysis is in relatively backward level. Incomple data is the major reason. Based on the idea of "Zero Initialization of Spatial Data", this dissertation describes spatial information as a general form-<x,U> with raster data structure. Location data is stored evidently and spatial relations required can be calculated by certain operations.The study on Geographical information in the past is concentrated on entities while ignoring the space. This dissertation devotes to the interaction effects between entities and those between entities and space from the combinative view of entity and space. The entities referred in this dissertation can be any arbitrary natural shapes. Specifically this dissertation makes some researches as follows:Firstly, this dissertation summarizes research situation of spatial analysis based on certain metric space at home and abroad. It sums up the existing research in terms of metric, spatial analysis, spatial relations and spatial data model. Metric space is the base and datum in spatial analysis in GIS. Spatial analysis is the most notable feature of GIS distinguished from other information systems. Spatial relationships are the "bridge" connecting spatial database and applications. Spatial data model is the theoretical basis for spatial data organization and design for spatial database. Therefore, these factors constitute the foundation of spatial analysis based on metric.Secondly, this dissertation analyses the limitations of existing topology data model which explicitly describes the relationships. It points out that an ideal GIS should cover a wide range of uses as far as possible, so it could not give up any spatial relationship in initialization. Based on the idea of "a model represents a geographical thinking", This dissertation used the idea of "zero Initialization of GIS spatial data" advanced by Professor Hu as the theoretical foundation for spatial analysis, a fundamental solution to the bottlenecks of "data not prepared while needed, prepared but not used and prepared but will not be used" in the development of GIS.Thirdly, the concepts of parallel and perpendicular in geometry are introduced to general metric space that can be Euclidean or non-Euclidean metric space and they find expressions in equi-distance and gradient lines groups. The concept of parallel is given by the point set which has the same distance to a certain entity. After the distance transformation, Full space was measured corresponding to entities. The points set that has the constant distance "a" is parallel to another points set that has the constant distance "b" where the distance is measured out to the same entity. The concept of perpendicular can be given by the maximum rate of distance change that is the one of gradient line.Fourthly, based on the first law in geography advanced by Waldo Tobler (1970): "Everything is related to everything else, but near things are more related than distant things" and the viewpoint advanced by Goodchild (1992):"The distance between events or objects is often an important factor in interactions between them" this dissertation analyzes the spatial interactions between the most close entities. It points out that the way of the interaction between entities is in accordance with the path of the gradient line.Fifthly, this dissertation gives the concepts of generalized polar coordinates based on plolar coordinates used in relative geography metric space. Generalized polar coordinates describe the interaction way that entites affect space, so any arbitratry spatial point has a nearest-entity-based metric expression of (distance, direction).Sixthly, the concept of metric grid is introduced which is constituted of two groups of mutually orthogonal curves—the equi-distance and gradient lines groups. Two things can be completed in the metric grid:the first, using the form of generalized polar coordinate, we can measure the distance and direction of an arbitrary point based on the most neighbor entity; the second, corresponding relations can be analyzed in the interaction process between different entities and this dissertation indicates that there are several situations of corresponding relations, such as one-to-one, one-to-many and many-to-one.Seventhly, based on the idea that the Medial Axis of polygon is the Voronoi diagram of all components, this dissertation studies the interaction among them. It primarily points out that the Medial Axis of polygon is the combination of bisector, parabola and perpendicular bisector, which has a complete corresponding ralations with the Medial Axis in geometry, and then analyses the corresponding relations between the components of polygon and Medial Axis. After analysis, this dissertation indicates that the relations may be either quite a number of one-to-one correspondence or focus-to-parabola or point-to-perpendicular bisector correspondence.Eightly, one case study is maritime boundary delimitation between China and Japan:this dissertation primarily analyses the corresponding relations of opposite coastlines if adopting the method of medial-line, and then points out the irrationality of this proposition. The first step is implementing distance transformation, and then obtaining the Voronoi diagram that also means the medial-line between China and Japan. The second step is picking up some special points using the method of Douglas, in order to get the gradient lines, tracing back these points to the certain entity. The last step is analyzing the corresponding relations of opposite coastlines and pointing out that most Chinese coastlines are continuous while those of Japan are not the same condition.Finally, another case study is the minimum spanning tree algorithm in the presence of arbitrary obstacles. The metric grid is constituted in the interaction process of point entities in space with obstacles. Firstly, we find the shortest path between points that is also the shortest gradient line. Secondly, the entire shortest path between the nearest points constituted the Delaunay triangulation. Lastly, minimum spanning tree is gained by greedy strategy according to the Delaunay triangulation.