准确获取采空区体积是矿山实施空区周边资源安全开采的重要基础性依据,也是矿山实施空区处理及其灾变监控的重要基础性工作。针对传统采空区三角网模型四面体算法易出现重叠计算的问题,本文以采空区三维激光探测系统(CMS)获取的原始数据为依据,在自主研发的采空区三维探测建模软件生成的采空区三角网模型的基础上,改进了传统采空区三角网模型四面体算法,提出了以激光探头为中心点连接所有三角网的四面体累积求和算法,实现对采空区体积的精确求解。算法首先确定了四面体求解的中心点,通过中心点与三角网模型中的所有三角片面连接形成四面体,然后运用四面体的有向体积相加实现对采空区体积的求取。实际应用表明,改进后的采空区体积四面体算法具有精度高、适用性好等优点。
To obtain an accurate size of mine goaf is an important criterion of resource exploitation surrounding mine goaf region. What is more, it is also important groundwork of mine goaf treatment and disaster monitoring. In view of the traditional goaf triangulation model tetrahedron algorithm which is prone to cause the overlap computation problem, this paper takes the original data of three-dimensional laser system CMS acquisition as the standard criterion, and puts forward a tetrahedron cumulative sum algorithm that takes laser probe as the center point to connect all the triangulation. Thus, the accurate solution of the goaf's volumes is determined. On the basis of the goaf triangulation network model generated by self-developed products-3D modeling software of goaf detection, the traditional tetrahedron algorithm of mining goaf triangulation model is improved. First of all, the center point of tetrahedral solution is determined by the algorithm, then a tetrahedron is formed through the connection of the center point and triptychs of the triangle network model. Finally, the mining goaf's volume is calculated by summing up the tetrahedral directed volumes. Actual application shows that the improved tetrahedron algorithm of mining goaf tetrahedral volume has the advantages of high precision and wide application range.
[1] 王国焘, 罗周全, 鹿浩, 等. CMS在矿山开采安全中的应用[J]. 有色金属(矿山部分), 2009, 61(5): 53-56, 65. Wang Guotao, Luo Zhouquan, Lu Hao, et al. Application of CMS in mining safety[J]. Nonferrous Metals (Mine Section), 2009, 61(5): 53-56, 65.
[2] 罗周全, 鹿浩, 袁节平, 等. CMS辅助金属矿山采空区回采技术研究[J]. 有色金属(矿山部分), 2008, 60(6): 1-4. Luo Zhouquan, Lu Hao, Yuan Jieping, et al. Surveys of excavation mining technology of metal mine with 3D cavity monitoring system[J]. Nonferrous Metals (Mine Section), 2008, 60(6): 1-4.
[3] 罗周全, 刘晓明, 张木毅, 等. 大规模采场三维探测及回采指标可视化计算[J]. 中南大学学报: 自然科学版, 2008, 27(2): 323-330. Luo Zhouquan, Liu Xiaoming, Zhang Muyi, et al. Stope 3D monitoring and its mining index visible calculation[J]. Journal of Central South University: Science and Technology Edition, 2008, 27(2): 323-330.
[4] 徐伟恒, 冯仲科, 苏志芳, 等. 一种基于三维激光点云数据的单木树冠投影面积和树冠体积自动提取算法[J]. 光谱学与光谱分析, 2014, 34 (2): 465-471. Xu Weiheng, Feng Zhongke, Su Zhifang, et al. An automatic extraction algorithm for individual tree crown projection area and volume based on 3D point cloud data[J]. Spectroscopy and Spectral Analysis, 2014, 34(2): 465-471.
[5] 张小青, 朱光, 侯妙乐, 等. 基于四面体的不规则表面文物体积计算[J]. 测绘通报, 2011(10): 50-52. Zhang Xiaoqing, Zhu Guang, Hou Miaole, et al. Volume calculation of surface irregular cultural relic based on tetrahedron[J]. Bulletin of Surveying and Mapping, 2011(10): 50-52.
[6] 王泉德. 任意三角网格模型体积的快速精确计算方法[J]. 计算机工程与应用, 2009, 45(18): 32-34, 58. Wang Quande. Fast and accurate volume calculation method for arbitrary triangular meshes[J]. Computer Engineering and Application, 2009, 45 (18): 32-34, 58.
[7] 徐志, 许宏丽. 一种基于凸包近似的快速体积计算方法[J]. 计算机工程与应用, 2013, 49(21): 177-179, 185. Xu Zhi, Xu Hongli. Fast algorithm of computing volume based on convexhull[J]. Computer Engineering and Applications, 2013, 49(21): 177-179,185.
[8] Ratnikova N, Huang C H, Sanchez- Hernandez A, et al. CMS space monitoring[J]. Journal of Physics, 2014, 513(4): 36-42.
[9] Sakuma T, McCauley T. Detectorand event visualization with sketch up at the CMS experiment[J]. Journal of Physics, 2014, 513(2): 22-32.
[10] 罗周全, 刘晓明, 杨彪, 等. 采空区精密探测技术应用研究[J]. 矿业研究与开发, 2006, 26(增2): 87-90. Luo Zhouquan, Liu Xiaoming, Yang Biao, et al. Research on precision detection of mined area[J]. Mining Research and Development, 2006, 26 (Suppl 2): 87-90.
[11] 罗贞焱. 基于CMS探测的采空区三维可视化系统研究[D]. 长沙: 中南大学, 2010. Luo Zhenyan. The research of goaf's 3D visual system based on MS detection[D]. Changsha: Central South University, 2010.
[12] Liu H. An Improved refinement algorithm of triangular mesh subdivision based on minimum weight theory[J]. Applied Mechanics and Materials, 2014(2): 2552-2555.
[13] Sun D, Sun Y, Tian Z, et al. Rapidly getting intersection algorithm for triangular mesh surface models[J]. Journal of Beijing University of Technology, 2012, 38(8): 1121-1124, 1135.
[14] Dai C, Liu H, Dong L. A comparison of objective functions of optimizationbased smoothing algorithm for tetrahedral mesh improvement[J]. Journal of Theoretical and Applied Mechanics, 2014, 52(1): 151-163.
[15] Bronson J, Levine J A, Whitaker R. A multimaterial tetrahedral meshing algorithm with guarantees[J]. IEEE Transactions on Visualization and Computer Graphics, 2014, 20(2): 223-237.
