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1.
《测量评论》2013,45(71):30-37
AbstractIn the last instalment of this paper it was explained that, owing to the immense size of the country, the co-ordinate system adopted by the Central Land Survey for the mapping of China consists of a number of zones bounded by parallels of latitude, the survey in each zone being based on the Lambert conical orthomorphic projection. The great extent of each zone in longitude, some sixty-five degrees, necessitated the development of series which would converge reasonably quickly, and, for this purpose, series were obtained in which a vertical distance between the parallel passing through the given point and the central parallel was used instead of the co-ordinates themselves. The series already given provided for the conversion of geographical co-ordinates into rectangulars and the inverse problem, while the present instalment deals with the scale factor and the transformation of co-ordinates from one zone to another, concluding with some numerical examples. 相似文献
2.
在测量与地图制图中,等量纬度求解大地纬度是一种常见的投影反解计算,就该反解问题的几种不同算法进行研究,包括迭代法、等量纬差求解大地纬度的级数展开式及等量纬度求解大地纬度的直接算法。利用Mathematica对后两种算法的计算公式进行了详细推导,给出了其高阶系数展开式,同时对现有算法中存在的问题进行了解析。兰勃脱等角投影算例表明,所推导的公式其计算精度可达(1×10-7)″~(1×10-8)″,完全满足测量与地图投影高精度的要求。 相似文献
3.
Sebastian Orihuela 《The Cartographic journal》2013,50(2):158-165
The Lagrange projection represents conformally the terrestrial globe within a circle. This is achieved by compressing the latitude and longitude and by applying the new coordinates into the equatorial stereographic projection. The same concept can be generalized to any conformal projection, although the application of this technique to other analytical functions is less known. In this work, the general Lambert–Lagrange projection formula is proposed and the application of the modified coordinates is discussed on projections: stereographic, conformal conic and Gauss–Schreiber. In general, the results are merely a curiosity, except for the case of Gauss–Schreiber, where the use of coordinates with altered scale can be applied in the optimization of conformal projections. 相似文献
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针对中国地理格网(1°、10°等多级格网系统)的分割方法,设计了一种适合该格网系统的新型地图投影——分层组合投影。从微分几何的观点出发,把地球椭球按等纬度分割成若干层圆台,分别建立每个圆台的投影模型,即可得到一种地图投影。这种投影还可根据格网间隔的不同进行细分,从而发展成为一种适合多分辨率格网模型的动态地图投影。通过对该投影进行变形计算表明,该投影可以保持等角,而且面积和长度变形都很小,特别是在高纬度地区,与Mercator投影相比变形明显减小。 相似文献
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The Gauss conformal mappings (GCMs) of an oblate ellipsoid of revolution to a sphere are those that transform the meridians into meridians, and the parallels into parallels of the sphere. The infinitesimal-scale function associated with these mappings depends on the geodetic latitude and contains three parameters, including the radius of the sphere. Gauss derived these constants by imposing local optimum conditions on certain parallel. We deal with the problem of finding the constants to minimize the Chebyshev or maximum norm of the logarithm of the infinitesimal-scale function on a given ellipsoidal segment (the region contained between two parallels). We show how to solve this minimax problem using the intrinsic function fminsearch of Matlab. For a particular ellipsoidal segment, we get the solution and show the alternation property characteristic of best Chebyshev approximations. For a pair of points relatively close in the ellipsoid at different latitudes, the best minimax GCM on the segment defined by these points is used to approximate the geodesic distance between them by the spherical distance between their projections on the corresponding sphere. This approach, combined with the best locally GCM if the points are on the same parallel, is illustrated by applying it to some case studies but specially to a 10° × 10° region contained between portions of two parallels and two meridians. In this case, the maximum absolute error of this spherical approximation is equal to 2.9 mm occurring at a distance about 1,360 km. This error decreases up to 0.94 mm on an 8° × 8° region of this type. So, the spherical approximation to the solution of the inverse geodesic problem by best GCM can be acceptable in many practical geodetic activities. 相似文献
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针对在东西向的高速铁路工程项目建设过程中,现今采用的高斯投影所能控制的范围小,需要建立较多投影带,投影带边缘变形大,各投影带间坐标转换复杂,不利于数据共享等突出问题,本文提出采用兰勃特投影的新方式。首先介绍切、割兰勃特投影的原理和坐标转换方法;其次通过分析高斯投影和兰勃特投影在郑徐高铁项目中的对比应用,得出兰勃特投影更适合东西向高速铁路工程坐标系统建设的结论。对类似线形工程项目具有一定的指导意义。 相似文献
10.
《测量评论》2013,45(60):220-221
AbstractThe problem of computing marginal scales of latitude and longitude on a rectangular map on the Transverse Mercator projection, where the sheet boundaries are projection co-ordinate lines, may be solved in various ways. A simple method is to compute the latitudes and longitudes of the four corners of the sheet, and then, assuming a constant scale, to interpolate the parallels and meridians between these corner values. Although it is probably sufficiently accurate for practical purposes, this method is not precise. It is not difficult to adapt the fundamental formulce of the projection to give a direct solution of the problem. 相似文献
11.
Computing geodetic coordinates from geocentric coordinates 总被引：1，自引：1，他引：0
H. Vermeille 《Journal of Geodesy》2004,78(1-2):94-95
A closed-form algebraic method to transform geocentric coordinates to geodetic coordinates has previously been proposed. The validity domain of latitude and height formulae in the vicinity of the Earths core is specified. A new expression of longitude is proposed, excluding indetermination and sensitivity to round-off error around the ±180 degrees longitude discontinuity. 相似文献
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为简化传统正轴等角圆锥投影求解基准纬度时繁琐的迭代算法,引入平均纬度和平均纬差的概念,借助计算机代数系统Mathematica,在平均纬差处级数展开,导出了基于球体模型的正轴等角圆锥投影求解基准纬度的非迭代算法。以全国和不同纬差的省区为例,将其与传统椭球迭代算法进行对比分析。结果表明,推导的基于球体模型的非迭代公式计算基准纬度B0、B1、B2的相对误差最大值为2.011%,长度变形的相对误差小于1×10-6,基本可满足全国以及各省区地图制图的精度要求,从而验证了所研究算法的精确性与实用性。 相似文献
14.
Mathematical equations to transform geodetic to grid coordinates on the Lambert conical orthomorphic projection are derived
in a form stable enough to allow computations to be made on the Mercator and Polar Stereographic projections as special cases. 相似文献
15.
J. C. Bhattacharji 《Journal of Geodesy》1980,54(2):225-233
The Everest spheroid, 1830, in general use in the Survey of India, was finally oriented in an arbitrary manner at the Indian
geodetic datum in 1840; while the international spheroid, 1924, in use for scientific purposes; was locally fitted to the
Indian geoid in 1927. An attempt is here made to obtain the initial values for the Indian geodetic datum in absolute terms
on GRS 67 by least-square solution technique, making use of the available astro-geodetic data in India, and the corresponding
generalised gravimetric values at the considered astro-geodetic points, as derived from the mean gravity anomalies over1°×1° squares of latitude and longitude in and around the Indian sub-continent, and over5° equal area blocks covering the rest of the earth’s surface. The values obtained independently by gravimetric method, were
also considered before actual finalization of the results of the present determination. 相似文献
16.
《测量评论》2013,45(65):131-134
Abstract1. In geodetic work a ‘Laplace Point’ connotes a place where both longitude and azimuth have been observed astronomically. Geodetic surveys emanate from an “origin” O, whose coordinates are derived from astronomical observations: and positions of any other points embraced by the survey can be calculated on the basis of an assumed figure of reference which in practice is a spheroid formed by the revolution of an ellipse about its minor axis. The coordinates (latitude = ?, longitude = λ and azimuth = A) so computed are designated “geodetic”. 相似文献
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Longitude–latitude grids are commonly used for surface analyses and data storage in GIS. For volumetric analyses, three‐dimensional meshes perpendicularly raised above or below the gridded surface are applied. Since grids and meshes are defined with geographic coordinates, they are not equal area or volume due to convergence of the meridians and radii. This article compiles and presents known geodetic considerations and relevant formulae needed for longitude–latitude grid and mesh analyses in GIS. The effect of neglecting these considerations is demonstrated on area and volume calculations of ecological marine units. 相似文献
18.
L. A. Kivioja 《Journal of Geodesy》1971,45(1):55-63
By choosing sufficiently small elements of the length of the geodetic line, or of the latitude or longitude difference, the
other two can be computed at each element and the results can be accumulated to solve the problem with more than twenty significant
number accuracy if desired. Ten to twelve number accuracy was computed in the examples of this paper. The geodetic line elements
are kept in correct azimuth by Clairaut’s equation for the geodetic line. The computers can do millions of necessary computations
very economically in a few seconds. All other published methods solving the direct or indirect problem can be reliably checked
against results obtained by this method. The run of geodetic lines around the back side of the Ellipsoid is outlined. 相似文献
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Simple and highly accurate formulas for the computation of Transverse Mercator coordinates from longitude and isometric latitude 总被引：2，自引：0，他引：2
A conformal approximation to the Transverse Mercator (TM) map projection, global in longitude λ and isometric latitude q, is constructed. New formulas for the point scale factor and grid convergence are also shown. Assuming that the true values
of the TM coordinates are given by conveniently truncated Gauss–Krüger series expansions, we use the maximum norm of the absolute
error to measure globally the accuracy of the approximation. For a Universal Transverse Mercator (UTM) zone the accuracy equals
0.21 mm, whereas for the region of the ellipsoid bounded by the meridians ±20° the accuracy is equal to 0.3 mm. Our approach
is based on a four-term perturbation series approximation to the radius r(q) of the parallel q, with a maximum absolute deviation of 0.43 mm. The small parameter of the power series expansion is the square of the eccentricity
of the ellipsoid. This closed approximation to r(q) is obtained by solving a regularly perturbed Cauchy problem with the Poincaré method of the small parameter.
Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users. 相似文献