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- Title
等角圆锥投影基准纬度非迭代算法.
- Authors
焦晨晨; 李松林; 李厚朴; 边少锋; 钟业勋
- Abstract
Objectives: For the traditional conformal conic projection, Newton 's iterative method is generally used to solve the reference latitude. However, the method requires to be iterated repeatedly, which leads to relatively low computational efficiency and is not easy to be extended and utilized. Therefore, non-iterative expressions for the reference latitudes B0,B1,B2 of the spherical conformal conic projection are derived in this paper to facilitate theoretical analysis and numerical computation. Methods: In order to simplify the fussy iterative algorithm in calculating the reference latitude of the traditional conformal conic projection, the average latitude and the average latitude difference were introduced. With the help of the powerful computer algebra system Mathematica, the non-iterative algorithm of the conformal conic projection based on the sphere model is proposed. Compared with the traditional ellipsoid iterative algorithm, the country and provinces with different latitude differences are taken as examples. Results: Numerical examples show that the maximum relative error of the reference latitudes B0,B1,B2 calculated by the non-iterative formula of the sphere model derived is less than 2.011% and the relative error of length deformation is less than 1 × 10-6. For provinces with different latitude differences, the smaller the latitude difference, the closer the reference latitude calculated based on the sphere model to that based on the ellipsoid model, the smaller the relative error of length, and the closer the length deformation. Conclusions: The derived non-iterative expressions overcome the tedious iterative process and make the theoretical analysis more convenient, which enriches the map projection theory to a certain extent. The established mathematical model can be extended to the non-iterative algorithm for solving the reference latitude for rectifying and authalic conic projection under the sphere model and each conic projection under the ellipsoidal model, and the algorithm is applicable to the whole map of China and all provinces. Therefore, the non-iterative algorithm of spherical conic projection derived can be used to replace the traditional complex iterative algorithm in the process of making small and medium scale maps in China.
- Subjects
CHINA; NEWTON-Raphson method; SPHERICAL projection; MAP projection; NUMERICAL analysis; LATITUDE; ELLIPSOIDS
- Publication
Geomatics & Information Science of Wuhan University, 2023, Vol 48, Issue 2, p301
- ISSN
1671-8860
- Publication type
Article
- DOI
10.13203/j.whugis20200301