Journal of Jilin University(Earth Science Edition) ›› 2019, Vol. 49 ›› Issue (3): 902-908.doi: 10.13278/j.cnki.jjuese.20180304

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

Zheng Lianlin1, Yao Lianbi1,2   

  1. 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)

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

CLC Number: 

  • P258
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