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两种测地坐标系之间的坐标转换 总被引：10，自引：0，他引：10
从数学上论证以长度量为坐标参数的测地坐标系与大地坐标系能够成为表述3维欧氏空间中点位的正则坐标系的条件及限定区域,然后着重阐述了测地坐标系与大地坐标系相互转换的基本原理和方法,并用算例验证了其正确性,从而为进一步实现测地坐标系应用于DEM和3 DGIS建模提供了可能,这就为最终解决在统一的真3维坐标系统中建立DEM和3 DGIS奠定了基础. 相似文献
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施一民 《武汉大学学报(信息科学版)》2003,28(6):710-713
为真正实现大城市中的精密定位 ,提出了直接采用区域性椭球面上的测地坐标代替高斯平面直角坐标以作控制网点平面位置的表述 ,分析了测地坐标系的优良性质 ,阐述了采用测地坐标系实现大城市精密定位的原理和方法 ,初步探索了其应用的可行性 相似文献
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Algorithms for geodesics 总被引：2，自引：0，他引：2
Charles F. F. Karney 《Journal of Geodesy》2013,87(1):43-55
Algorithms for the computation of geodesics on an ellipsoid of revolution are given. These provide accurate, robust, and fast solutions to the direct and inverse geodesic problems and they allow differential and integral properties of geodesics to be computed. 相似文献
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《制图学和地理信息科学》2013,40(2):131-147
Part of a cuboctahedron-based geodesic map projection by Buckminster Fuller is expanded to spherical quadrilaterals with opposite sides equal. Points on such a quadrilateral can be described by intersections of geodesics, which provide parameterized coordinate values in a Geodesic Coordinate System. Through a linear transform of the geodesic coordinates, a spherical quadrilateral maps to a parallelogram. The resulting map has the same constant scale on all four sides. Within the map, all lines parallel to the sides correspond to geodesics on the globe. Spherical rectangles, spherical squares, and diamonds (spherical rhombi) are specifically examined; various tiling sets of diamonds can be used to cover the globe. Non-projection applications in geometry, astronomy, and computer graphics are described. 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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在利用ＧＩＳ进行空间分析的过程中，常常会遇到求取某一连通域内两点间最短路径和相应的距离这类问题，传统上使用的欧氏距离对此有较大的局限性。本文把测地距离的概念引入到矢量型ＧＩＳ中，并讨论了测地距离的若干性质；在此基础上，提出了一种简便有效的求取矢量型ＧＩＳ中两点间测地距离的方法，并编写了相应的程序。实际应用表明文中所提出的方法是切实可行的，有效地克服了欧氏距离的局限性。 相似文献
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To generate highly compressed digital elevation models (DEMs) with fine details, the method of Poisson disk sampling in geodesic metric is proposed. The main idea is to uniformly pick points from DEM nodes in geodesic metric, resulting in terrain-adaptive samples in Euclidean metric. This method randomly selects point from mesh nodes and then judges whether this point can be accepted in accordance with the related geodesic distances from the sampled points. The whole process is repeated until no more points can be selected. To further adjust the sampling ratios in different areas, weighted geodesic distance, which is in relation to terrain characteristics, are introduced. In addition to adaptability, sample distributions are well visualised. This method is simple and easy to implement. Cases are provided to illustrate the feasibility and superiority of the proposed method. 相似文献
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Abstract The Arc of the Geodesic.—In the first part of this paper a method was given for computing the azimuth of a geodesic. The method gives the convergence of the geodesic correctly up to the second power of e the eccentricity. The formula (9), however, also depends on the assumption that σ, the arc-length of the geodesic, can be obtained with sufficient accuracy from the Supplemental Dalby Theorem, that is to say, by a purely spherical computation. It is, therefore, needful to show that this supposition is justifiable; a means must in fact be indicated for verifying the assumption. 相似文献
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一种四叉树和测地线活动轮廓模型相结合的海陆影像分割方法 总被引：1，自引：0，他引：1
海陆影像分割对于后续的海岸线提取、潮间带地形反演、海岸演化状况分析等都具有十分重要的意义。本文在分析了四叉树、测地线活动轮廓(GAC)模型和Canny边缘检测算子等在海陆影像分割中优缺点的基础上,提出了一种四叉树、Canny算子和GAC模型相结合的海陆影像分割方法。该方法综合利用上述各方法的优点,将Canny算子边缘检测结果融入到基于四叉树初分割的GAC模型中,重构边界停止函数,演化水平集方程,实现海陆影像分割。试验结果表明,该方法具有海陆影像分割速度快、精度高、可靠性强和自动化程度高等优点,对于弱边缘以及严重凹陷边缘,都能实现自动和准确分割。 相似文献
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B. R. Bowring 《Journal of Geodesy》1977,51(1):17-32
To deal specifically with the case of a nearly antipodal geodesic of given terminal positions, an equation in azimuth is produced
for solution by the Newton-Raphson Method of successive approximation. When the azimuth is in the region of 90° it is found
that an approach is best made by a development in series when the aim is precision calculation. Degeneracy is examined theoretically
and graphically. 相似文献
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The differential equations which generate a general conformal mapping of a two-dimensional Riemann manifold found by Korn
and Lichtenstein are reviewed. The Korn–Lichtenstein equations subject to the integrability conditions of type vectorial Laplace–Beltrami
equations are solved for the geometry of an ellipsoid of revolution (International Reference Ellipsoid), specifically in the
function space of bivariate polynomials in terms of surface normal ellipsoidal longitude and ellipsoidal latitude. The related
coefficient constraints are collected in two corollaries. We present the constraints to the general solution of the Korn–Lichtenstein
equations which directly generates Gau?–Krüger conformal coordinates as well as the Universal Transverse Mercator Projection
(UTM) avoiding any intermediate isometric coordinate representation. Namely, the equidistant mapping of a meridian of reference
generates the constraints in question. Finally, the detailed computation of the solution is given in terms of bivariate polynomials
up to degree five with coefficients listed in closed form.
Received: 3 June 1997 / Accepted: 17 November 1997 相似文献
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Markov chains have frequently been applied to match the probable routes with a set of GPS trip data that a pilot vehicle is emitting over a specific graph road network. This class of map- matching (MM) algorithms presently demonstrates and involve statistical and ad-hoc measures to drive the Markov chain transitional probabilities in picking the best route combinations constrained over the graph road network. In this study, we have devised an adaptive scheme to modify the Markov Chain (MC) kernel window as we move along the GPS samples to reduce the mistakes that can happen by the use of narrower MC widths. The measure for temporarily increasing the MC window width is chosen to be the ratio between the geodesic distance of current route to the actual geodesic distance between each pair of GPS samples. This adaptive use of MC has shown to have hardened the results significantly with tolerable computational cost increase. The details of the overall algorithm are depicted by the example routes extracted from various vehicle trips and the results are shown to validate the usefulness of the algorithm in practice. 相似文献
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B. R. Bowring 《Journal of Geodesy》1983,57(1-4):109-120
Various ways of solving the longitude equation of the inverse solution for the geodesic on the reference ellipsoid are examined, and a special development is given to deal with the nearly antipodal situation. 相似文献
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Voronoi图是地学计算中的一个基本结构,但是在地形曲面上,它还缺乏能与平面Voronoi图媲美的精度和成熟的算法。在离散地形曲面的不规则三角网格网上引入计算几何的测地距离场,从格网边上的距离场奇点逐步生长代表平分线的双曲线,由双曲线的排列得到离散曲面的精确划分,再将划分的面片聚类,生成精确的测地Voronoi图(geodesic Voronoi diagram,GVD)。然后,从定量与定性两方面对精确Voronoi图进行了检验,证明GVD可以给地形曲面空间分析带来基础性改进。基于奇点生长和双曲线排列的直接算法避免了现有算法对格网面片的过度细分与预处理,整体上直观易行,为数字地形分析发展严密的Voronoi图分析提供了有益探索。 相似文献