基于Gauss-Chebyshev积分的道路平曲线计算

doi:10.13278/j.cnki.jjuese.20180304

吉林大学学报(地球科学版) ›› 2019, Vol. 49 ›› Issue (3): 902-908.doi: 10.13278/j.cnki.jjuese.20180304

• 地球探测与信息技术 • 上一篇

基于Gauss-Chebyshev积分的道路平曲线计算

郑连林¹, 姚连璧^1,2

1. 同济大学测绘与地理信息学院, 上海 200092;
2. 同济大学现代工程测量国家测绘地理信息局重点实验室, 上海 200092

收稿日期:2018-11-21 出版日期:2019-06-03 发布日期:2019-06-03
作者简介:郑连林(1992-),男,硕士研究生,主要从事工程测量研究,E-mail:9527npc@tongji.edu.cn
基金资助:
国家自然科学基金项目（41771482）；"十三五"国家重点研发计划项目（2016YFB1200602-02）

Horizontal Coordinates Computation in Route Survey Based on Gauss-Chebyshev Quadrature Rules

Zheng Lianlin¹, Yao Lianbi^1,2

1. College of Surveying and Geoinformatics, Tongji University, Shanghai 200092, China;
2. Key Laboratory of Modern Engineering Surveying, National Administration of Surveying, Mapping, and Geo-Information, Shanghai 200092, China

Received:2018-11-21 Online:2019-06-03 Published:2019-06-03
Supported by:
Supported by National Natural Science Foundation of China (41771482) and National Key Research and Development Program of China During the 13th Five -Year Plan Period (2016YFB1200602-02)

摘要/Abstract

摘要： 道路平曲线坐标计算中可能会采用线元法，其中线元类型有直线、圆曲线和缓和曲线。本文采用改进的线元表对平曲线数据进行预处理，讨论了Gauss-Chebyshev积分公式的应用并通过数值计算实验研究了高斯点数量对待定点计算的影响，在此基础上使用Gauss-Chebyshev积分方法和5点改进型Gauss-Chebyshev积分方法解决平曲线计算中的定积分计算问题。为验证Gauss-Chebyshev积分的计算效果，选取某铁路一段平曲线作为计算数据，指定16个临近点作为数值实验对象，实验结果显示反算所得各点里程和偏距与起始给定的数值一致。

关键词: 线元(积木)法, 平曲线, 数值计算方法, Gauss-Chebyshev积分公式

Abstract: In order to calculate the coordinates of the points on a horizontal curve, building block method is usually used to establish an integrated mathematical model. There are three types of line elements:straight line, circular curved line,and transition curved line. In this article, how to utilize building block method for data pretreatment is introduced, the Gauss-Chebyshev quadrature rule is taken as a universal computational method, and the effect set by the count of Gauss points on the accuracy of unknown points is also discussed by means of numerical experiments. On the basis,the Gauss-Chebyshev quadrature rules and the improved 5-point Gauss-Chebyshev quadrature rules are used to approximate the value of the definite integral so as to compute coordinates of the unknown points on horizontal curves. To test how the Gauss-Chebyshev quadrature rules work in computing coordinates, mileage, and deviations, a portion of plane curve on a railway is selected as calculation data, and 16 adjacent points are selected as objects of a numerical experiment. The result shows that all the mileage and deviations acquired by the inverse computation are consistent with the initial given values.

Key words: building block method, horizontal curve, numerical computing, Gauss-Chebyshev quadrature rules

中图分类号:

P258

郑连林, 姚连璧. 基于Gauss-Chebyshev积分的道路平曲线计算[J]. 吉林大学学报(地球科学版), 2019, 49(3): 902-908.

Zheng Lianlin, Yao Lianbi. Horizontal Coordinates Computation in Route Survey Based on Gauss-Chebyshev Quadrature Rules[J]. Journal of Jilin University(Earth Science Edition), 2019, 49(3): 902-908.

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基于Gauss-Chebyshev积分的道路平曲线计算

Horizontal Coordinates Computation in Route Survey Based on Gauss-Chebyshev Quadrature Rules

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