The Optimization Method of the Sector Partition Based on Metamorphic Voronoi Polygon

Voronoi diagram is founded by using computational geometry based on originaldistribution of the waypoints, and then the elements from Voronoi diagram are metamorphosed by usingthe rule for airsppce partition, and the controller's workload is accounted in each element that ismade up of Metamorphic Voronoi polygon. Then in accordance with the rule about balance ofcontroller's workload, Simulated Annealing algorithm (SA) is used to achieve the optimization ofcombination of those elements , and the new resolution has satisfied the restriction of two rulesfor airspace partition. Therefore, the boundaries of the aggregates of these elements are theoptimal borderlines of sectors. The result of actual airspace design example validates therationality of the sector optimization method presented in this paper.

3D Sector Optimum Partition of Airspace

A new method for sector optimum partition of airspace is proposed by dividing the fright altitude into several layers according to the distribution characteristics of the controller＇s workloads in an airspace. On the basis of the original distribution of the waypoints at each level of altitude, the sweel5 line algorithm of Voronoi diagram is used to divide them into certain polygons （ elements）, and the controller＇s workloads are calculated in each Voronoi polygon. Then by the rule about balance of controller＇s workload and by adding conditions of control handover or coordination for the sector, a mathematical model for the controller＇s workload based sector optimization is built. By the model, the Voronoi polygons are optimally partitioned. As a result, a 3D sector optimum partition of the whole airspace is formed by combining the sector optimum partitions at every layer. The actual airspace partition for Xiamen Airport has proved the reasonability and effectiveness of the 3D sector optimum partition of airspace proposed.

Spatial Characteristics Analysis of Urban Expansion in Luoyang, China

The characteristics of urban space expansion reflect the changes of urban spatial layout and structure, as well as the orientation of urban development in the future. This paper uses the regional sector division method to divide the urban land into 8 orientations, based on the urban land space compaction index, and designs a sector partition compaction index. Based on the remote sensing image data of 1990, 2000, 2010, and 2020, the spatial characteristics of urban land expansion of Luoyang are analyzed by using the partition compaction index, expansion intensity index, fractal dimension, and standard deviation ellipse. The results show that: from 1990 to 2020, the urban overall planning of Luoyang has effectively guided the urban development, the urban land expands rapidly, the urban land compaction has been maintained at a low level, and the urban form has been tending to be reasonable;the urban land centroid gradually shifts to the southwest, and the distribution axis rotates clockwise from southwest-northeast to northwest-southeast, and the directionality of distribution gradually disappears;the urban land has gone through the development process of land filling-enlarging-refilling. The urban land expansion is relatively active in the region with an azimuth of 90°- 225°, and the urban expansion in the north of Luo River is relatively stable and is always filling mode.