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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) ,2026,45(6):91-99.

辛普森积分模型在复杂地表面积计算中的应用分析

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 山东 济南  250014；4.山东建筑大学 测绘地理信息学院 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，开展辛普森积分模型在复杂地表面积计算中的适用性分析与优化应用研究。  方法 首先对现有地表曲面拟合法、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；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，分别采用辛普森模型与传统计算模型及ArcGIS，SuperMap，GeoScene等GIS软件，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，将辛普森计算模型作为计算服务与高性能并行计算框架结合，以IntelliJ IDEA为开发环境，以JAVA为开发语言，利用Apache Hadoop分布式计算平台，实现辛普森模型的并行计算策略。 结果 结果表明，辛普森积分模型具有更优的计算精度和效率。计算地表面积时，将DEM精度插值到1 m可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结合的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地解决了实际应用中计算精度低和效率低等问题，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应用，并取得了显著效果。

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

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”项目（2022KJ201）

收稿日期:2024/01/17

修回日期:2024/04/26

出版日期:2026/10/09

Application analysis of Simpson integral model in complex surface area calculation

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， Shandong， China；2.Shandong Yuanhong Survey Planning and Design Co.， Ltd.， Jinan  250014， Shandong， China；3.Shandong Public Resource Trading Center， Jinan  250014， Shandong， China；4.School of Surveying and Geo-Informatics， Shandong Jianzhu University， Jinan  250100， Shandong， China

Abstract: Objectives To address the difficulty of surface area calculation in complex terrain， this study applies and optimizes the Simpson integral model for complex surface area calculation.  Methods First， existing surface area algorithms—including surface fitting， triangulated irregular network （TIN）， the slope-based method， and Simpson integral—are reviewed and compared. Then， two study areas， Shanghe County （flat terrain） and Pingyin County （rugged terrain）， are selected to validate the Simpson model against traditional methods and commercial GIS software （ArcGIS， SuperMap， and GeoScene） in terms of accuracy and efficiency. Finally， the Simpson model is integrated with a high-performance parallel computing framework， with IntelliJ IDEA serving as the development environment， Java as the programming language， and Apache Hadoop as the distributed computing platform， to implement a parallel computing strategy.  Results Comparative results demonstrate that the Simpson integral model achieves higher accuracy and efficiency. When DEM resolution is interpolated to 1 m， both the accuracy and efficiency of the single-process Simpson model are improved. The parallel implementation improves computational efficiency by about 80% compared with the single-process version. Conclusions The proposed high-performance parallel Simpson integral model effectively resolves the trade-off between accuracy and efficiency in large-scale applications. This computing service has been successfully applied in the “One Map” 3D terrain area calculation for natural resources management in Shandong Province， yielding significant practical benefits.

Key words: calculation of surface area; simpson integral model; DEM;model optimization; high performance parallel computing