冯永玉,刘伟,李维平,等.辛普森积分模型在复杂地表面积计算中的应用分析[J].河南理工大学学报(自然科学版), doi: 10.16186/j.cnki.1673-9787.2024010045.

FENG Y Y，LIU W，,LI W P，et al. Application analysis of Simpson integral model in complex surface area calculation [J]. Journal of Henan Polytechnic University( Natural Science), doi:10.16186/j.cnki.1673- 9787. 2024010045.

辛普森积分模型在复杂地表面积计算中的应用分析(网络首发)

冯永玉¹，刘伟 ²，李维平³，王学 ²，邢华桥⁴，王燕¹

（1.山东省国土空间数据和遥感技术研究院 山东 济南 250001；2.山东元鸿勘测规划设计有限公司 山东 济南 250014；3.山东省公共资源交易中心 250014；4.山东建筑大学 山东 济南 250100）

摘 要：[目的]为了解决复杂地表环境下地表面积计算难的问题，本文开展了辛普森积分模

型在复杂地表面积计算中的应用分析工作。[方法]首先对现有的地表曲面拟合法、空间三角

网构建法、坡度计算法和辛普森积分法等地表面积计算理论模型进行总结归纳，并对其进行

优缺点分析；其次，以地势平坦的商河县和地势较为起伏的平阴县为研究区域，将辛普森模

型与传统的计算模型及 ArcGIS、SuperMap、GeoScene 等 GIS 软件，分别从精度、效率等方面开展地表面积计算结果的对比验证；最后，把辛普森计算模型作为计算服务与高性能并

计算框架相结合，以 IntelliJ IDEA 为开发环境，以 JAVA 为开发语言，利用 Apache Hadoop

分布计算平台，实现辛普森模型的并行计算策略。[结果]多重对比分析结果表明辛普森积分

模型具有更优的计算精度和效率；此外，当地表面积计算时将 DEM 精度插值到 1m 时，能有效提高单一进程下辛普森积分模型的计算效率和精度；计算服务与高性能并行计算框架的结合辛普森计算模型比单一进程下辛普森积分模型表面面积计算效率提升了 80%左右。[结论]基于辛普森积分模型的高性能并行计算，很好的解决了实际应用中计算精度低、效率低的问题，计算服务已在山东省自然资源三维立体“一张图”地形面积计算关键技术中进行了应用，取得了显著的效果。

关键词：地表面积计算;辛普森积分模型;DEM;模型优化;高性能并行计算

中图分类号：P962

doi: 10.16186/j.cnki.1673-9787. 2024010045.

基金项目: 国家自然科学基金资助项目（41801308）；山东省优秀青年基金资助项目（ZR2022YQ36）；山东省高等学校“青创团队计划”（2022KJ201）

收稿日期：2024-01-17

修回日期：2024-04-26

网络首发日期：2024-08-06

Application analysis of Simpson integral model in complex surface area calculation（Online）

FENG Yongyu¹,LIU Wei²,LI Weiping³,WANG Xue²,XING Huaqiao⁴,WANG Yan¹

(1.Shandong Geographical Institute of Land Spatial Data and Remote Sensing Technology ,Jinan 250001,Shangdong,China;2.Shandong Yuanhong Survey Planning and Design Co.,Ltd., Jinan 250014,Shangdong,China;3.Shangdong Public Resource Trading Center, Jinan 250014,Shangdong, China;4.Shandong Jianzhu University, Jinan 250100,Shangdong,China)

Abstract：[Objectives] In order to solve the problem of difficult calculation of surface area in complex surface environment, this paper carries out the application analysis of Simpson's integral model in the calculation of complex surface area. [Methods] Firstly, the existing surface area calculation theoretical models such as surface surface fitting method, spatial triangulation network construction method, slope calculation method and Simpson integral method were summarized, and their advantages and disadvantages were analyzed; secondly, based on the flat terrain Shanghe County and Pingyin County, which has relatively undulating terrain, were used as the research areas. The Simpson model was compared with traditional calculation models and GIS software such as ArcGIS, SuperMap, and GeoScene to compare and verify the surface area calculation results in terms of accuracy and efficiency. Finally, combine the Simpson computing model as a computing service with a high-performance parallel computing framework, use IntelliJ IDEA as the development environment, use JAVA as the development language, and use the Apache Hadoop distributed computing platform to implement the parallel computing strategy of the Simpson model. [Results] The results of multiple comparison analysis show that the Simpson's integral model has better calculation accuracy and efficiency; in addition, when the DEM accuracy is interpolated to 1m when calculating the local surface area, the calculation efficiency and accuracy of the Simpson's integral model can be effectively improved in a single process; calculation The combination of the service and the high-performance parallel computing framework makes the Simpson calculation model more efficient than the surface area calculation of the Simpson integral model in a single process by about 80%. [Conclusions] High-performance parallel computing based on Simpson's integral model can effectively solve the problems of low calculation accuracy and low efficiency in practical applications. The computing service has been used as a key technology in the three-dimensional "one map" terrain area calculation of natural resources in Shandong Province. It has been applied and achieved remarkable results.

Keywords：Calculation of surface area; Simpson integral model; DEM; Model optimization; High

performance parallel computing

CLC:P962