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1.
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
2.
贝赛尔大地主题解算是少数适合长距离大地主题计算的方法之一。文章通过对贝赛尔大地主题解算进行计算分析,发现贝赛尔大地主题反算中的大地线长计算精度受起点方位角的影响很大,误差可达8m。为了消去这一巨大误差,本文提出在大地主题反算时互换大地线起点和终点的方法,计算结果表明该方法可以有效消除方位角对大地线长误差的影响。 相似文献
3.
地形绘制一直是图形学研究的热点问题,尤其是球面地形绘制,其在形状和数据组织方面比平面地形绘制更加复杂。在已有球面地形绘制算法的基础上,提出一种基于Geometry Clipmap的球面地形剖分与绘制方法。该方法以构建正二十面体球面网格为基础,将正二十面体划分为十个菱形区域,采用球面菱形网格的剖分,针对每个菱形区域的周边网格进行重新剖分和组合,形成一个虚拟的3×3的大菱形区域,扩大了Clipmap的活动范围,并在一定程度上解决了Clipmap的跨边界问题。实验结果表明了本文方法的可行性和有效性。 相似文献
4.
Abstract19. Formulae.—In Nos. 6, vol. i, and 9, vol. ii, pp. 259 and 156, there has been described a new method for dealing with long geodesics on the earth's surface. There the so-called “inverse” problem has claimed first attention: given the latitudes and longitudes of the extremities of a geodesic, to find its length and terminal azimuths. It remains to discuss the “direct” problem : a geodesic of given length starts on a given azimuth from a station of known latitude and longitude; to find the latitude and longitude of its extremity and the azimuth thereat. The solution of this direct problem demands a certain recasting of the formulae previously given. In order of working the several expressions now assume the forms below. 相似文献
5.
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
6.
Lars E. Sjöberg 《Journal of Geodesy》2008,82(9):565-567
Through each of two known points on the ellipsoid a geodesic is passing in a known azimuth. We solve the problem of intersection
of the two geodesics. The solution for the latitude is obtained as a closed formula for the sphere plus a small correction,
of the order of the eccentricity of the ellipsoid, which is determined by numerical integration. The solution is iterative.
Once the latitude is obtained, the longitude is determined without iteration. 相似文献
7.
《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
8.
9.
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
10.
椭球面三角形外心到3个相邻顶点的大地线距离都相等。面向椭球面空间的外心大地坐标的求解对于椭球面Voronoi图的生成和椭球面Delaunay三角网的构造具有重要作用。利用基于地图代数理论的矢栅结合方法,首先基于地图代数测地变换建立高精度椭球面空间距离场,再通过边界跟踪配对确定外心所在的栅格范围,最后通过数值计算内插生成初始等距点并不断逼近外心的精确大地坐标。试验结果表明,采用本文方法求解的椭球面三角形外心大地坐标,在103~104 km跨度内其定位误差小于0.001m,且算法非常适用于海量空间数据的高精度快速计算。 相似文献
11.
从球面坐标系的弹性力学基础方程出发，推导出球面上块体的位移与6个位移不变量之间的数学关系，进一步建立了联立方程式的球面坐标形式，为大范围现代地壳运动的非连续形变形下了数学基础。 相似文献
12.
地图扫描数字化中的地图自动定向方法 总被引：1，自引：0，他引：1
提出并实现了二值图像上十字交点的沿线匹配算法，发展了一种根据相关位置自动识别图廓点，进而计算图像坐标系和大地坐标系之间变换参数的方法，实现了地图定向的自动化。实验表明，文中所述的地图定向方法在提高自动化程度的同时，也提高了地图定向的精度。 相似文献
13.
Land cover maps play an integral role in environmental management. However, countries and institutes encounter many challenges with producing timely, efficient, and temporally harmonized updates to their land cover maps. To address these issues we present a modular Regional Land Cover Monitoring System (RLCMS) architecture that is easily customized to create land cover products using primitive map layers. Primitive map layers are a suite of biophysical and end member maps, with land cover primitives representing the raw information needed to make decisions in a dichotomous key for land cover classification. We present best practices to create and assemble primitives from optical satellite using computing technologies, decision tree logic and Monte Carlo simulations to integrate their uncertainties. The concept is presented in the context of a regional land cover map based on a shared regional typology with 18 land cover classes agreed on by stakeholders from Cambodia, Laos PDR, Myanmar, Thailand, and Vietnam. We created annual map and uncertainty layers for the period 2000–2017. We found an overall accuracy of 94% when taking uncertainties into account. RLCMS produces consistent time series products using free long term historical Landsat and MODIS data. The customizable architecture can include a variety of sensors and machine learning algorithms to create primitives and the best suited smoothing can be applied on a primitive level. The system is transferable to all regions around the globe because of its use of publicly available global data (Landsat and MODIS) and easily adaptable architecture that allows for the incorporation of a customizable assembly logic to map different land cover typologies based on the user's landscape monitoring objectives 相似文献
14.
Yoshiaki Ohsawa Hirofumi Kagaya Takeshi Koshizuka 《Journal of Geographical Systems》2002,4(3):325-342
When demand points are given as a planar map where projection method is explicitly stated, we usually know the latitudes
and longitudes of these points from the map. Then we can solve the Weber problem on the globe, and we do not suffer from errors.
This paper analyses how cylindrical projections cause distortion in the Weber problem when demands are distributed on the
Northern Hemisphere. First, we demonstrate that planar solutions are always located south of the spherical solution if the
Mercator projection, the equirectangular projections with standard parallels near the demands, or the equal-area projection
with the same characteristic is chosen. Second, we verify that this geographical tendency is inclined to hold when the demand
points, are distributed symmetrically, widely or toward the north.
Received: 15 August 2001 / Accepted: 20 April 2002
This paper was partially written while the first author was visiting the Department of Geography at the Catholic University
of Louvain, Louvain-la-Neuve, Belgium [1993–1994]. He is grateful for the hospitality of this department. An earlier version
of this paper was presented in 1994 at the Seventh Meeting of the European Operational Research Working Group on Locational
Analysis in Brussels, and in 1996 at the Fifth World Congress of the Regional Science Association International in Tokyo.
The authors would also like to thank the participants as well as three anonymous referees for their constructive comments. 相似文献
15.
针对三维虚拟地球中实时GIS数据组织、管理与动态可视化的要求,设计了三维虚拟地球中移动对象的时空数据组织方法。提出了基于HR-tree扩展的时空索引方法,实现了对虚拟地球中移动对象的检索与查询,并基于三维虚拟地球平台对本文方法进行了实验,结果验证了本文方法的有效性和可行性。 相似文献
16.
17.
《International Journal of Digital Earth》2013,6(1):107-118
Abstract The starting point of this paper is the idea that a comprehensive understanding of the earth and its systems calls for consideration of bygone views of the world. Creating facsimiles of antique globes in the form of digital globes provides a new opportunity to make such bygone world views accessible to a wide scientific audience. However, up to now, little practical experience in applying digital technology on globes has been made. Considering these attempts by thorough synopsis, this article deduces a comprehensive approach on virtual representations of antique globes that can be described by the superordinate concept of virtual representation. This concept comprises facilities of data acquisition of the original globe, ways of visualising the digitised globe and its final cartographic preparation. Applications that arise from this procedure are exemplified through both virtual hyperglobes and tactile hyperglobes. New findings on a 16th century earth globe are encouraging results of the presented virtual representation approach, which may offer a sustainable visualisation platform of interdisciplinary research. 相似文献
18.
《制图学和地理信息科学》2013,40(3):147-156
Pointable sensor systems onboard many earth resources satellites today, particularly the higher spatial resolution sensors, provide for a near infinite set of collection opportunities. Satellite orbits of these systems are not systematic repetitive tracks. Predicting future collection opportunities requires predicting where the satellite will be and then computing the potential swath coverage from a pointable sensor along these orbits. While each agency or company models its own satellite-sensor systems, few publicly available sources exist for mapping future satellite ground tracks. Evaluating collection opportunities from multiple satellite-sensor systems from different agencies/companies is problematic. The purpose of the research described in this article was to develop a generic approach for modeling future satellite-sensor collection opportunities. In this article, formulae are developed for computing the potential swath coverage, and an algorithm is designed for constructing the potential swath coverage area. The solution to the swath coverage problem is based on spherical trigonometry, a well known map projection (i.e., azimuthal equidistant map projection) used in an unconventional dynamic form, and a satellite orbital propagation model. We demonstrate how the computation of the swath coverage area can be accomplished using a temporal series of re-centered map projections. 相似文献
19.
《The Cartographic journal》2013,50(3):269-271
AbstractReal 3D objects are typically explored with high efficiency by several fingers. The largest increase in efficiency is obtained between the use of one and two fingers. The aim of the present experiment was to investigate if the efficiency of identifying a country on a 2D tactile map can be increased by the use of two fingers exploration along opposite sides of the map compared with following along the contour. The result was that there was no significant difference between one-finger and two-finger exploration, but there were significant improvements over sessions. The difference between exploration of 2D and 3D objects is discussed. 相似文献
20.
Brian Farelly 《Journal of Geodesy》1991,65(2):92-101
Six sources of error in the use of Fourier methods for the conversion of geoid heights to gravity anomalies are considered. The errors due to spherical approximation are unimportant. The errors due to approximations in Stokes' integral may be eliminated by use of the gravity coating rather than the gravity anomaly. The chord-to-arc error and the truncation error may be reduced by using a reference field. Tapering of the edges of the measurement window reduces the truncation error. The long-wavelength components of the high degree spherical harmonics cause small offsets in the resulting gravity anomalies. The errors due to the plane approximation can be reduced by appropriate choice of map projection and area of integration. 相似文献