共查询到20条相似文献，搜索用时 31 毫秒
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地图投影反解变换的一种新方法 总被引：6，自引：1，他引：5
通常地图投影反解变换有2种方法,即多项式拟合法和投影方程解析法.多项式法利用已知控制点的坐标对应关系,通过最小二乘法拟合求解地图投影反解变换的多项式函数,其优点是反解模型与地图投影无关,算法具有通用性,缺点是反算精度较低.解析法根据地图投影正算公式,在一定条件下通过解方程求得地图投影反解变换解析式,其优点是反解变换精度高,缺点是解法复杂.本文利用计算数学方法,根据地图投影变换的基本数学原理,提出了一种新的地图投影反解变换方法,双向迭代逼近法(BDIRA).具有反解变换精度高、收敛速度快、算法通用和GIS软件编程实现方便等特点. 相似文献
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The coordinate frame transformation (CFT) problem in geodesy is typically solved by a stepwise approach which entails both inverse and forward treatment of the available data. The unknown transformation parameters are first estimated on the basis of common points given in both frames, and subsequently they are used for transforming the coordinates of other (new) points from their initial frame to the desired target frame. Such an approach, despite its rational reasoning, does not provide the optimal accuracy for the transformed coordinates as it overlooks the stochastic correlation (which often exists) between the common and the new points in the initial frame. In this paper we present a single-step least squares approach for the rigorous solution of the CFT problem that takes into account both the intra-frame and inter-frame coordinate covariances in the available data. The optimal estimators for the transformed coordinates are derived in closed form and they involve appropriate corrections to the standard estimators of the stepwise approach. Their practical significance is evaluated through numerical experiments with the 3D Helmert transformation model and real coordinate sets obtained from weekly combined solutions of the EUREF Permanent Network. Our results show that the difference between the standard approach and the optimal approach can become significant since the magnitude of the aforementioned corrections remains well above the statistical accuracy of the transformation results that are obtained by the standard (stepwise) solution. 相似文献
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胡毓钜 《武汉大学学报(信息科学版)》1987,(2)
本文对编制城市游览图提出了变比例尺地图投影系统。通过由普通城市平面图向辅助球面作逆投影A,再由辅助球面向平面作非A投影,构成了变比例尺地图的数学基础。由不同性质的投影的组合,能起到适应不同城市街区结构的特点。使本系统具有相当的灵活性。文中还讨论了辅助球适宜的大小和不同方位投影之间的变换公式。文末试作了北京市的变比例尺地图。 相似文献
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A closed-form of Newton method for solving over-determined pseudo-distance equations 总被引：3，自引：0，他引：3
The Newton method has been widely used for solving nonlinear least-squares problem. In geodetic adjustment, one would prefer to use the Gauss–Newton method because of the parallel with linear least-squares problem. However, it is proved in theory as well as in practice that the Gauss–Newton method has slow convergence rate and low success rate. In this paper, the over-determined pseudo-distance equations are solved by nonlinear methods. At first, the convergence of decent methods is discussed after introducing the conditional equation of nonlinear least squares. Then, a compacted form of the Hessian matrix from the second partial derivates of the pseudo-distance equations is given, and a closed-form of Newton method is presented using the compacted Hessian matrix to save the computation and storage required by Newton method. At last, some numerical examples to investigate the convergence and success rate of the proposed method are designed and performed. The performance of the closed-form of Newton method is compared with the Gauss–Newton method as well as the regularization method. The results show that the closed-form of Newton method has good performances even for dealing with ill-posed problems while a great amount of computation is saved. 相似文献
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刘大海 《测绘科学技术学报》2012,(1):9-11
高斯投影复变换的数值计算简单快捷,具有重要的工程应用价值.从数值计算角度出发,使用计算机代数系统Mathcad,Matlab以及Mathematica对高斯投影复变换进行了改进:只需建立正算变换计算式而不再需要建立反算变换计算式.对于复方程,利用系统的求根函数直接求解.对于复积分,研究了积分级数分析法、椭圆积分函数法及... 相似文献
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地图投影计算机代数分析研究进展 总被引：1，自引：0，他引：1
地图投影是现代地图学的重要组成部分,涉及大量的椭圆函数幂级数展开、隐函数复合函数微分、椭圆积分、复变函数运算等一系列烦琐的数学分析过程,人工推导不但费时费力,而且容易出错,有时由于难以忍受的复杂性等各种原因,甚至根本无法实现。本文主要从椭球各纬度间正反解符号表达式、不同变形性质地图投影间的直接变换、高斯投影的复变函数表示、斜轴墨卡托投影数学分析、极区海图投影及变换等5个方面,论述了地图投影计算机代数分析取得的研究进展,讨论了该领域有待进一步解决的主要问题,对推动地图投影学的发展具有积极意义。 相似文献
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James D. Turner 《Journal of Geodesy》2009,83(2):139-145
The Cartesian-to-Geodetic coordinate transformation is re-cast as a minimization algorithm for the height of the Satellite
above the reference Earth surface. Optimal necessary conditions are obtained that fix the satellite ground track vector components
in the Earth surface. The introduction of an artificial perturbation variable yields a rapidly converging second order power
series solution. The initial starting guess for the solution provides 3–4 digits of precision. Convergence of the perturbation
series expansion is accelerated by replacing the series solution with a Padé approximation. For satellites with heights < 30,000 km
the second-order expansions yields ~mm satellite geodetic height errors and ~10−12 rad errors for the geodetic latitude. No quartic or cubic solutions are required: the algorithm is both non-iterative and
non-singular. Only two square root and two arc-tan calculations are required for the entire transformation. The proposed algorithm
has been measured to be ~41% faster than the celebrated Bowring method. Several numerical examples are provided to demonstrate
the effectiveness of the new algorithm. 相似文献
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Fourier-based multi-scale representation and progressive transmission of cartographic curves on the internet 总被引：1，自引：0，他引：1
ABSTRACTAutomatic generation of multi-scale representations from the same spatial data source has been the research focus in map generalization for a long time. Based on the Fourier technique, this paper proposes a continuous, multi-scale representation model for progressive transformation of cartographic curves on the Internet. In our method, all the curves, whether closed or open, are depicted as periodical functions which are further expressed as Fourier series. The convergence degrees of the Fourier series are explored for different kinds of curves, and truncating frequencies are derived based on the similarity between the original and reconstructed curves. Using information theory and the Radical Law in cartography, the relationship between map scales and Fourier frequencies is established. Based on the proposed multi-scale model, we also introduce the principles and implementation of a progressive transmission method. Our method is evaluated using the contours from a topographic map. The results show that our model is a valid approach to multi-scale representation of cartographic curves. 相似文献
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AbstractThe analysis of remote sensing (RS) images, which is often accomplished using unsupervised image classification techniques, requires an effective method to determine an appropriate number of classification clusters. This paper proposes a preliminary analytical method to evaluate the input parameters for unsupervised RS image classification. Our approach involves first analysing the colour spaces of RS images based on the human visual perception theory. This enables the initial number of clusters and their corresponding centres to be automatically established based on the interaction of different forces in our supposed force field. The proposed approach can automatically determine the appropriate initial number of clusters and their corresponding centres for unsupervised image classification. A comparison of the experimental results with those of existing methods showed that the proposed method can considerably facilitate unsupervised image classification for acquiring accurate results efficiently and effectively without any prior knowledge. 相似文献
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《制图学和地理信息科学》2013,40(3):167-182
One of the most fundamental steps in map creation is the transformation of information from the surface of a globe onto a flat map. Mapmakers have developed and used hundreds of different map projections over the past 2,000 years, yet there is no perfect choice because every map projection uniquely alters some aspect of space during the transformation process. Detailed information about the type, amount, and distribution of distortion is essential for choosing the best projection for a particular map or data set. The distortion inherent in projections can be measured and symbolized much like any other map variable. Methods for symbolizing map projection distortion are reviewed, with each method described and illustrated in graphical form. The symbolization methods are collected under ten separate headings organized from simple to more complex in terms of interpretation. Most of these methods are highly effective at communicating distortion, yet they are rarely used beyond textbooks and technical documentation. Map projections and the distortions they carry need to be better understood by spatial data developers, distributors, and users. Map distortion should be carried along with map data as confidence layers, and the easily accessible distortion displays should be available to help in the selection of map projections. There is a suitably wide array of symbolization methods to match any need from basic education to research. 相似文献
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《测量评论》2013,45(92):263-276
AbstractMost books on the technique of map compilation omit a detailed consideration of projections on the grounds that this subject is adequately treated at length elsewhere. Texts on map projections, however, are largely theoretical and rarely consider the practical problem of the proper choice and use of the graticules which are otherwise so ably described. An investigation of this little explored field has produced the following picture which it is thought may be of wider interest. A study of the fundamental properties which influence the choice of map projections is followed by a survey of projections in use, considered in relation to the fundamental properties. 相似文献
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提出了一种基于带权A*搜索算法的镶嵌线网络优化方法。首先,利用标准Voronoi图生成初始镶嵌线网络;然后,利用测区的数字表面模型（digital surface model,DSM）数据生成对应的高程梯度图（也称为边缘图）;再对初始镶嵌线网络的节点进行自动调整,将位于建筑物上的节点移动至附近的地面;最后,利用一种带权A*搜索算法,结合高程梯度图,对初始镶嵌线网络中的每一条镶嵌线进行智能优化,避开建筑物或者高差变化大的区域,获得最优的镶嵌线网络。利用3组真实的无人机数据对该方法进行实验,初步结果表明,该方法适用于排列不规则的测区,可有效优化镶嵌线网络,镶嵌线可自动避开大部分城区建筑物以及山区的山脊等,对城区以及山区影像都可得到高质量的正射影像。实验结果表明,对于第1组数据,此方法得到的结果在镶嵌线的选取上要优于商业软件OrthoVista。 相似文献
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借助复变函数理论讨论了常用等角投影及其解析变换的复变函数表示;给出了高斯投影、墨卡托投影和等角圆锥投影正反解的复变函数表示模型;在此基础上系统地推导出了高斯投影、墨卡托投影和等角圆锥投影间解析变换的复变函数表达式.这些复数变换公式是含参考椭球第一偏心率的符号形式,可解决不同参考椭球下的变换问题.与传统的实数变换公式相比,其结构更为简单、理论更为严密. 相似文献
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An operational algorithm for computation of terrain correction (or local gravity field modeling) based on application of closed-form solution of the Newton integral in terms of Cartesian coordinates in multi-cylindrical equal-area map projection of the reference ellipsoid is presented. Multi-cylindrical equal-area map projection of the reference ellipsoid has been derived and is described in detail for the first time. Ellipsoidal mass elements with various sizes on the surface of the reference ellipsoid are selected and the gravitational potential and vector of gravitational intensity (i.e. gravitational acceleration) of the mass elements are computed via numerical solution of the Newton integral in terms of geodetic coordinates {,,h}. Four base- edge points of the ellipsoidal mass elements are transformed into a multi-cylindrical equal-area map projection surface to build Cartesian mass elements by associating the height of the corresponding ellipsoidal mass elements to the transformed area elements. Using the closed-form solution of the Newton integral in terms of Cartesian coordinates, the gravitational potential and vector of gravitational intensity of the transformed Cartesian mass elements are computed and compared with those of the numerical solution of the Newton integral for the ellipsoidal mass elements in terms of geodetic coordinates. Numerical tests indicate that the difference between the two computations, i.e. numerical solution of the Newton integral for ellipsoidal mass elements in terms of geodetic coordinates and closed-form solution of the Newton integral in terms of Cartesian coordinates, in a multi-cylindrical equal-area map projection, is less than 1.6×10–8 m2/s2 for a mass element with a cross section area of 10×10 m and a height of 10,000 m. For a mass element with a cross section area of 1×1 km and a height of 10,000 m the difference is less than 1.5×10–4m2/s2. Since 1.5× 10–4 m2/s2 is equivalent to 1.5×10–5m in the vertical direction, it can be concluded that a method for terrain correction (or local gravity field modeling) based on closed-form solution of the Newton integral in terms of Cartesian coordinates of a multi-cylindrical equal-area map projection of the reference ellipsoid has been developed which has the accuracy of terrain correction (or local gravity field modeling) based on the Newton integral in terms of ellipsoidal coordinates.Acknowledgments. This research has been financially supported by the University of Tehran based on grant number 621/4/859. This support is gratefully acknowledged. The authors are also grateful for the comments and corrections made to the initial version of the paper by Dr. S. Petrovic from GFZ Potsdam and the other two anonymous reviewers. Their comments helped to improve the structure of the paper significantly. 相似文献
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The adaptive composite map projection technique changes the projection to minimize distortion for the geographic area shown on a map. This article improves the transition between the Lambert azimuthal projection and the transverse equal-area cylindrical projection that are used by adaptive composite projections for portrait-format maps. Originally, a transverse Albers conic projection was suggested for transforming between these two projections, resulting in graticules that are not symmetric relative to the central meridian. We propose the alternative transverse Wagner transformation between the two projections and provide equations and parameters for the transition. The suggested technique results in a graticule that is symmetric relative to the central meridian, and a map transformation that is visually continuous with changing map scale. 相似文献
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兵棋是对作战过程进行逻辑推演研究和评估的重要工具,是现代作战模拟的一种重要方法和手段。兵棋的三大要素包括棋盘、棋子和规则,棋盘的经典样式就是六角格网兵棋棋盘,计算机兵棋中也常采用六角格网兵棋棋盘描述战场地形环境。推演过程中通常涉及到大量的坐标转换,因此坐标转换效率对于推演效率具有重要影响。针对经纬度坐标和六角格网编码的转换,提出了直接转换和间接转换两种坐标转换方法,分析了各自的基本转换原理,并给出了坐标转换公式,最后通过实验对两种方法的转换效率进行了分析,证实间接坐标转换法具有更高的转换效率。 相似文献
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等面积投影的仿射变换及若干改良等面积投影的探求 总被引：1，自引：0，他引：1
本文探讨了等面积投影仿射变换的理论和方法。包括：仿射变换等面积投影坐标，仿射变换面积元素的一般方法，并对一些常用的等面积投影进行了仿射变换举例。从等面积投影仿射变换中可得到具有很大实用价值的改良等面积投影，其具有很大的概括性和灵活性，在地图设计和计算机屏幕地图设计中有着广阔地应用前景。 相似文献