Geometric Characterization And Quantitative Research On Urban Form

The cities are the material space and environment of human activities, and their forms reflect the main features of the city. The conception of the city has a long history,but the city as a research object is almost late. And the research on the urban morphology is later. The quantitative research of urban form can help us explore the urban form, make the research results more scientific and persuasive, and provide a clear basis and theoretical support.As a cross subject, the urban morphology has received more and more attention.The research on urban morphology mainly focuses on the morphological evolution, the driving mechanism of urban evolution, the elements of urban forms and so on. But the quantitative method of urban form is slow relatively, and the research result is relatively insufficient. In the concrete quantification, scholars often adopted the quantitative methods of other subjects, and these methods may not be applicable to urban form. With the perspective of spatial frequency, the quantitative methods applied to urban form have been researched from point, line, surface aspects for urban form by means of the analysis, reference, improvement, verification and so on.The main achievements and innovations of this paper focused on the following aspects:1. there were mainly four aspects in the results of the research on urban point group.A method based on frequency domain restoration technique was proposed to quantify the distribution range of the point group. The limitation of the traditional statistical indexes lies in the ability to express the shape, which leads to the possibility of prescission between the quantitative data and the guidance from the shape. While thecity form is varied and its profile is fraught with uncertainty. A method was put forward in the third chapter, which characterized the general contour based on the morphological characteristics of the point group, and applied the method of frequency domain transform and low-pass filtering. The range shape after restoration depends on the position distribution of the point group.A quantitative method for point group center location based on distributed range was proposed. The result of traditional point group center calculation method is to characterize the statistical average of all the points, which may be outside the range of the point group. The significance of the central position in the urban morphology is greatly reduced. In the third chapter, I put forward the method to calculate the center range with adjusting the distribution range and then calculate the center position.A method was proposed to quantify density relationship of the point group. In the traditional quantization, the value of the density of the point group is often acquired by calculating the ratio of the number of all points and the specified range. The ratio value is a constant, and it is difficult to measure the internal density relations of the city. In the third chapter, by using the method of frequency domain transform, the filter and the fitting point, the final results reflected the density distribution of the point group for fuzzy state.A quantitative method for the complexity of range configuration is proposed. The range shape can be understood as a region shape, and the indexes in the traditional quantitative methods are often one characteristic of a certain aspect. Although the general features can reflect the regional shape, it lacks descriptive ability and persuasion.It is difficult to directly define the shape complexity, because the shape is a high-level,abstract concept and it is difficult to be reflected by one or several standards. In the third chapter of this thesis, with the frequency domain transform and band-pass filtering for the form distribution range, morphological edge radial energy distribution was reflected in the one-dimensional data. According to the one-dimensional Fourier transform, the entropy was calculated. the result effectively reflected the degree of disorder in the edge energy, indirect expressed form complexity.2. there were mainly three aspects in the results of the research on urban line group.A quantitative method for the distribution range of line group is proposed, and a method to quantify density distribution based on line group range is proposed. There are a lot of linear factors in the urban form. The linear factors in the city form reflect the important information of the regional skeleton and contour. The parameters related to the distribution range of the linear group are usually specified, therefore, the result is a constant. The key reason lies in the extensive and mechanical properties of the distribution range of the specified line group. In the fourth chapter, a method was put forward to recover the corresponding region by the point group. According to the point order(the connection direction between point and point) in the line group, the method of generating line group distribution range is further developed.An index for the complexity of the linear group directions named as line direction entropy was proposed. The direction is an important feature of linear form and an important reference to a city for human cognitive ability. In a city, the form of line group or the direction of complexity should be quantified as the reference and the basis of cognition. But the corresponding quantitative methods and indicators have not yet emerged. In the fourth chapter of this thesis, a method was put forward as that:according to the several main directions of an urban form and the proportion for the lines in each direction, the entropy index was calculated.3. there were mainly two aspects in the results of the research on urban surface group.A two dimensional entropy index is presented to reflect the degree of disorder of surface group distribution. In the whole space of the surface distribution of different attributes in the urban form, some scholars used the principle of entropy to quantify the degree of disorder in the group, but the result can not reflect the spatial distribution information in the form. In the fifth chapter, with the space surface group information distribution and the joint probability for a single flat surface and its around, the disorder degree of a system was calculated according to the entropy, and the spatial distribution information was included in the calculation of entropy.Comprehensive representation of urban basic spatial form. The location, direction,area, and the group of the urban represent the structural characteristics of the urban space. In the fifth chapter, the overall form of the urban space is characterized by someindexes in the previous chapters.4. The inverse application of fractal theory named as polyform was put forward.Fractal geometry is characterized by self similarity and non scale, which is characterized by fractal dimension. Form of this kind of graphics inspired researchers and designers greatly, so it is in the urban morphology. Fractal graphics is often in continuous recursive fragmentation. As the quantity index, the fractional dimension characterizes evolutionary process in the urban morphology. The actual urban morphology, however, needs not only the values of quantities calculation, but also the simple and condensed expression for the form that is hard to provide through the fractal theory. In the fourth chapter, the polyform method was put forward, which is the main function: to simplify and linearize the urban form, to simulate the abstraction and refinement when the human used land. The process is opposite to that of the fractal process, while the repetition and aggregation of the morphological rules were recursive.