兰勃特投影向高斯投影转换程序编制及难点分析

为了解决兰勃特投影向高斯投影转换中存在的难题,如:如何从兰勃特投影的平面坐标求大地坐标,高斯正算中经度的确定等,更好地促进兰勃特投影地图的应用,本文在对两种投影理论研究的基础之上,采用C#语言进行编程实现兰勃特投影向高斯投影转换.结果表明所编制的程序切实可行,且具有科学性.本研究的程序可以为测绘生产单位提供一种选择.     

The doubly equidistant projection

Résumé Complément à une note de l’auteur parue sous le même titre dans le Bulletin Géodésique d’octobre 1946 (Nouvelle série, n^o 2).

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The doubly equidistant projection

     

兰勃特投影在东西向高速铁路中的应用研究

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。     

兰勃特投影在内蒙古中部地区线路工程的应用

针对目前内蒙古电力工程建设中采用高斯投影带来一些如长度变形、跨越多个投影带问题,为了保证东西方向较长的线路施工精度需要不断地变换高斯抵偿面的问题,提出了使用兰勃特投影来解决这一矛盾,并对实际数据进行分析和评价,以便在内蒙古自治区电力工程建设使用。     

高斯投影公式的机助推导

随着GPS应用的普及,高斯投影在测量中出现的机会越来越多。许多文献上都给出了推导过程,这个推导过程的运算量是非常大的,而且计算精度难于提高。经过研究,一种易于编程的递推公式被发现,虽然这个公式在计算量上没有减少,但是可以较好地解决精度问题。     

地图投影变换网络服务的构建与实现

本文主要从选择地图投影变换方法、地图投影变换功能组件式设计与开发、地图投影变换网络服务的创建及访问入手,深入分析并研究了地图投影网络服务的构建与实现的关键技术,并通过创建桌面和网络两种应用程序进行服务访问与调用,经实验验证了地图投影变换网络服务的发布与共享能快速提高开发效率。     

基于WebGIS Geocoding搜索与Lambert变换的研究与实现

针对项目平台系统开发中遇到的批量POI（PointofInterest）数据与平台地图进行匹配的问题进行分析与研究．通过地理编码对经纬度进行搜索,并建立经纬度与Lambert投影变换的数据模型。运用C#语言进行实现验证,并完成批处理经纬度搜索与投影变换的功能。最终将覆盖全国范围内所有POI坐标数据与平台地图成功匹配,满足了项目的需求,也使平台开发的功能得以进一步加强,为平台支持多分辨率、多尺度、多投影的全球空间数据提供了技术积累。     

The generalized Mollweide projection of the biaxial ellipsoid

Summary The standard Mollweide projection of the sphere S _R ² which is of type pseudocylindrical — equiareal is generalized to the biaxial ellipsoid E _A,B ² .Within the class of pseudocylindrical mapping equations (1.8) of E _A,B ² (semimajor axis A, semiminor axis B) it is shown by solving the general eigenvalue problem (Tissot analysis) that only equiareal mappings, no conformal mappings exist. The mapping equations (2.1) which generalize those from S _R ² to E _A,B ² lead under the equiareal postulate to a generalized Kepler equation (2.21) which is solved by Newton iteration, for instance (Table 1). Two variants of the ellipsoidal Mollweide projection in particular (2.16), (2.17) versus (2.19), (2.20) are presented which guarantee that parallel circles (coordinate lines of constant ellipsoidal latitude) are mapped onto straight lines in the plane while meridians (coordinate lines of constant ellipsoidal longitude) are mapped onto ellipses of variable axes. The theorem collects the basic results. Six computer graphical examples illustrate the first pseudocylindrical map projection of E _A,B ² of generalized Mollweide type.     

Fourier-series representation and projection of spherical harmonic functions

Computations of Fourier coefficients and related integrals of the associated Legendre functions with a new method along with their application to spherical harmonics analysis and synthesis are presented. The method incorporates a stable three-step recursion equation that can be processed separately for each colatitudinal Fourier wavenumber. Recursion equations for the zonal and sectorial modes are derived in explicit single-term formulas to provide accurate initial condition. Stable computations of the Fourier coefficients as well as the integrals needed for the projection of Legendre functions are demonstrated for the ultra-high degree of 10,800 corresponding to the resolution of one arcmin. Fourier coefficients, computed in double precision, are found to be accurate to 15 significant digits, indicating that the normalized error is close to the machine round-off error. The orthonormality, evaluated with Fourier coefficients and related integrals, is shown to be accurate to O(10^?15) for degrees and orders up to 10,800. The Legendre function of degree 10,800 and order 5,000, synthesized from Fourier coefficients, is accurate to the machine round-off error. Further extension of the method to even higher degrees seems to be realizable without significant deterioration of accuracy. The Fourier series is applied to the projection of Legendre functions to the high-resolution global relief data of the National Geophysical Data Center of the National Oceanic and Atmospheric Administration, and the spherical harmonic degree variance (power spectrum) of global relief data is discussed.     

卫星激光测距系统的异常检测及其稳定性监测

针对卫星激光测距系统(SLR)的稳定性问题,该文分析了北京房山kHz地靶观测数据,根据系统延迟的统计信息构建异常辨识统计量,剔除异常数据。地靶有效数据在一个较小的范围内集中,变化幅度0.25ns左右;分析了单次系统延迟变化在0.2ns左右;通过ARMA时间序列分析方法,确定2018年北京房山SLR系统延迟的变化规律,建立SLR系统延迟变化的预报模型;最后,根据预报模型,对系统延迟进行短期预报,以检测SLR系统异常,实现对SLR系统运行稳定性监测的目的。     

伪距与激光测距法时间比对计算模型及其精度评估

卫星导航定位系统测距的基础是测时,而定轨和定位的前提是各观测量的时间同步,因此,时间同步技术是卫星导航定位系统建设的关键技术基础之一。卫星导航定位系统中时间同步技术包括卫星与地面(星-地)和地面站间(地-地)的时间同步。在本文中,根据伪距与激光测距法时间比对的基本原理,详细推导了地心惯性系中伪距与激光测距法时间比对的基本计算模型,为实现星地之间高精度的时间同步提供了参考。     

卫星图像斜方位投影正反解变换研究

本文针对卫星动态获取的遥感图像,探讨其空间斜方位投影问题。利用空间几何理论建立其斜方位投影的数学模型,得到了该投影的精确表达式。并且利用矢量解法研究该投影模型的正解和反解变换算法以及星下点坐标计算方法,最后给出了算例。根据算例的结果分析表明,该投影的正反解变换均达到较高的精度。     

Event-driven flood management: design and computational modules

Flood management is a set of activities that have to be carried out in collaboration with multiple agencies. Advanced flood information with early warning generated using remote sensing satellite technologies can help the agencies to effectively manage the situation on ground. Various environmental parameters and forecasts provided by different agencies can be analyzed and compared with historical flood events for generating probable flood event alerts. The information (environmental parameters) provided by the agencies are heterogeneous and noncompliant to standards and distributed in nature. Synchronization of data from distributed resources and automation of data analysis process for flood management is a primary prerequisite for faster and efficient decision-making. Web 2.0-based web services enable data creation, sharing, communication, and collaboration on web. Spatial data sharing on web 2.0 for making quality of service using open-source software for efficient flood management is a challenge. Available software architectures proposed for risk and environmental crisis management are too generic in nature and needs lot of modification for flood management. An event-driven model coupled with data standardization procedures using service-oriented architecture provides an effective framework for flood management. In this paper, a framework capable of collecting heterogeneous distributed flood-related information for analyzing and alerting probable flood events is proposed. The framework has been implemented to generate automatic flood extent maps, by analyzing the distributed satellite data (as service). The automation of flood delineation process reduces the overall flood product generation time. Open-source web tools have been utilized in development of spatial information system to visualize and analyze the actual situation on ground facilitating overall decision-making process.     

Enhancing adaptive composite map projections: Wagner transformation between the Lambert azimuthal and the transverse cylindrical equal-area projections

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.     

The oblique Mercator projection of the ellipsoid of revolution IE a 2 ,b

While the standardMercator projection / transverse Mercator projecton maps the equator / the transverse metaequator equivalent to the meridian of referenceequidistantly, theoblique Mercator projection aims at aconformal mapping of the ellipsoid of revolution constraint to anequidistant mapping of an oblique metaequator. Obliqueness is determined by the extension of the area to be mapped, e.g. determined by the inclination of satellite orbits: Satellite cameras map the area just under the orbit geometry. Here we derive themapping equations of theoblique Mercator projection being characterized to beconformal andequidistant on the oblique metaequator extending results ofM. Hotine (1946, 1947).     

基于球面投影的散乱点云三维建模算法实现与效果分析

介绍基于球面投影的散乱点云三维建模算法步骤,运用VC++编程语言结合OpenGL图形接口实现该算法,并结合实例说明球面投影法相对于圆柱面投影法、椭球面投影法在三维建模中的优势.     

抛物线拟合的高斯投影长度比计算方法

针对传统的高斯投影长度比计算公式存在的次数高、参数多、计算过程复杂等不足,该文提出利用抛物线拟合法计算高斯投影长度比。首先,对高斯投影规律进行全面分析,得出高斯投影长度比与距离中央子午线横坐标值的变化成抛物线关系。然后,以点在高斯平面直角坐标系中距离中央子午线的横坐标值为参数计算高斯投影长度比。实验结果表明,采用该文方法计算高斯投影长度比运算简便、精度高,与传统公式计算的长度比差值在整个高斯投影带均达百万分之一量级,对完善高斯投影长度变形规律的研究以及实际计算均具有一定的参考价值。     

The oblique azimuthal projection of geodesic type for the biaxial ellipsoid: Riemann polar and normal coordinates

Summary Riemann polar/normal coordinates are the constituents to generate the oblique azimuthal projection of geodesic type, here applied to the reference ellipsoid of revolution (biaxial ellipsoid).Firstly we constitute a minimal atlas of the biaxial ellipsoid built on {ellipsoidal longitude, ellipsoidal latitude} and {metalongitude, metalatitude}. TheDarboux equations of a 1-dimensional submanifold (curve) in a 2-dimensional manifold (biaxial ellipsoid) are reviewed, in particular to represent geodetic curvature, geodetic torsion and normal curvature in terms of elements of the first and second fundamental form as well as theChristoffel symbols. The notion of ageodesic anda geodesic circle is given and illustrated by two examples. The system of twosecond order ordinary differential equations of ageodesic (Lagrange portrait) is presented in contrast to the system of twothird order ordinary differential equations of ageodesic circle (Proofs are collected inAppendix A andB). A precise definition of theRiemann mapping/mapping of geodesics into the local tangent space/tangent plane has been found.Secondly we computeRiemann polar/normal coordinates for the biaxial ellipsoid, both in theLagrange portrait (Legendre series) and in theHamilton portrait (Lie series).Thirdly we have succeeded in a detailed deformation analysis/Tissot distortion analysis of theRiemann mapping. The eigenvalues — the eigenvectors of the Cauchy-Green deformation tensor by means of ageneral eigenvalue-eigenvector problem have been computed inTable 3.1 andTable 3.2 (₁, ₂ = 1) illustrated inFigures 3.1, 3.2 and3.3. Table 3.3 contains the representation ofmaximum angular distortion of theRiemann mapping. Fourthly an elaborate global distortion analysis with respect toconformal Gau-Krüger, parallel Soldner andgeodesic Riemann coordinates based upon theAiry total deformation (energy) measure is presented in a corollary and numerically tested inTable 4.1. In a local strip [-l _E,l _E] = [-2°, +2°], [b _S,b _N] = [-2°, +2°]Riemann normal coordinates generate the smallest distortion, next are theparallel Soldner coordinates; the largest distortion by far is met by theconformal Gau-Krüger coordinates. Thus it can be concluded that for mapping of local areas of the biaxial ellipsoid surface the oblique azimuthal projection of geodesic type/Riemann polar/normal coordinates has to be favored with respect to others.     

在GIS技术条件下地图投影的应用和发展

论文介绍了地图投影的基本原理和进展,总结了地图投影在GIS中的应用;讨论了在GIS的技术条件下地图投影出现的新问题,并针对这一问题简要介绍了椭球面制图模型。