基于最小包络矩形算法的大曲率地面石材铺贴优化研究

Study on Optimization of Stone Laying Scheme of Subway Platform with Large Curvature Based on Minimum Envelope Rectangle Algorithm

随着现代建筑风格的多样化,异形公共建筑地面铺砖(石材)工程逐年增多,其中大曲率界面铺砖优化设计方案需求也越发强烈。本文基于优化算法对平面不规则多边形采用最小包络矩形方法,结合某地铁大曲率弧形站台地面石材铺贴工程,开展铺砖方案优化研究。与以往研究相比,该方法用于解决不规则图形凸化处理后矩形件的优化布局问题,再根据矩形旋转角度分割网栅,最后基于优化算法生成铺砖效果示意图,并对该站台改进铺砖算法前后的用砖数量进行对比,结果表明:利用待铺设砖块的规格作为各种矩形网格分割的基础,可以实现对任意多边形的改进分割方案;该站台使用类平行四边形和类梭形进行铺砖,对比传统铺贴方案,类梭形方案用砖数量减少了19块,切割次数减少了9次,类平行四边形方案用砖数量减少了109块,切割次数减少了38次,操作复杂度明显降低。可见,最小包络矩形算法可优化任意多边形的切割方案,为大曲率公共建筑地面铺砖工程提供解决思路,对相关工程设计与施工具有参考意义。

With the diversification of modern architectural styles,the project of laying bricks(stones)on the ground of special-shaped public buildings is increasing year by year,and the demand for optimal design scheme of laying bricks with large curvature interface is becoming stronger and stronger.In this paper,based on the optimization algorithm,the minimum envelope rectangle method is used for irregular polygons,and the optimization of tile laying scheme is carried out in combination with the stone paving project of a subway platform with large curvature.Compared with previous studies,this method is used to solve the problem of optimal layout of rectangular parts after convex treatment of irregular figures,and then divide the grid according to the rotation angle of the rectangle.Finally,a schematic diagram of tile laying effect is generated based on the optimization algorithm,and the number of bricks used in the platform before and after the improved tile laying algorithm is compared.The results show that the improved partition scheme of arbitrary polygons can be realized by using the specifications of bricks to be laid as the basis of various rectangular grid segmentation.The platform uses parallelogram-like and shuttle-like paving bricks.Compared with the traditional paving scheme,the number of bricks in the shuttle-like scheme is reduced by 19,and the cutting times are reduced by 9 times.The number of bricks in the parallelogram-like scheme is reduced by 109,and the cutting times are reduced by 38 times,which obviously reduces the operation complexity.It can be seen that the minimum envelope rectangle algorithm can optimize the cutting scheme of any polygon,provide a solution for the brick laying project of public buildings with large curvature,and have reference significance for the design and construction of related projects.