Improving regularity of Delaunay Triangulation of Khuzestan Bidbland Dome via Circle Packing Algorithm and Genetic Optimization

Document Type : Research Article


1 Department of Mathematics, Payame Noor University, Tehran, Iran

2 Laboratory of Algorithms and Computational Geometry, Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran

3 Department of Mathematics, Payame Noor University, Tehran


Professor Nooshin et al. defined structural regularity indicators quantitatively three decades ago and used various methods for improving the regularity of some structures, such as stepping projection, sphere packing concept, recursive techniques, etc, to create a special category of space structures (domes and flats) and grid shells that were designed in a multifaceted manner, and depending on the type of project, they used one or more of these indicators to analyze and compare the regularity of the structures The regularity studied in this research is related to increase of equal lengths or almost equal lengths, the reduction the count of elements with different lengths, the reduction of the number of length intervals and different shapes of faces while maintaining the geometric form. The aim of this research is to study the previous regularity indicators,  investigate and analyze the improving regularity of  Delaunay triangulation obtained from the points of the single layer dome of Bidboland Khuzestan with the proposed algorithm: using the circle packing algorithm and genetic optimization (using the minimization of different regularity indicators) to reach a suitable pattern. To analyze the improving regularity. we have presented algorithms for calculating the regularity indicators, we have calculated the numerical results of these indices and we have suggested a general definition for regularity degree. we show that each of these indices alone is not criteria for measuring and comparing the regularity of two structures. The results of this research are effective in improving the regularity of structures, form finding, and creating the optimal design of a structure.


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