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《制图学和地理信息科学》2013,40(4):341-356
A series of new equal-area map projections has been devised. Called Oblated Equal-Area, its lines of constant distortion follow approximately oval or rectangular paths instead of the circles of the Lambert Azimuthal Equal-Area projection or the straight lines of the Cylindrical Equal-Area projection. The projection series permits design of equal-area maps of oblong regions with less overall distortion of shape and scale than equal-area maps on other projections. 相似文献
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AbstractI. Introduction.—Map projection is a branch of applied mathematics which owes much to J. H. Lambert (v. this Review, i, 2, 91). In his “Beyträge zum Gebrauche der Mathematik und deren Anwendung” (Berlin, 1772) he arrived at a form of projection whereof the Transverse Mercator is a special case, and pointed out that this special case is adapted to a country of great extent in latitude but of small longitudinal width. Germain (“Traité des Projections”, Paris, 1865) described it as the Projection cylindrique orthomorphe de Lambert, but he also introduced the name Projection de Mercator transverse or renversée; he shows that Lambert's treatment of the projection was remarkably simple. 相似文献
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《测量评论》2013,45(58):142-152
AbstractIn January 1940, in a paper entitled “The Transverse Mercator Projection: A Critical Examination” (E.S.R., v, 35, 285), the late Captain G. T. McCaw obtained expressions for the co-ordinates of a point on the Transverse Mercator projection of the spheroid which appeared to cast suspicion on the results originally derived by Gauss. McCaw considered, in fact, that his expressions gave the true measures of the co-ordinates, and that the Gauss method contained some invalidity. He requested readers to report any flaw that might be discovered in his work, but apparently no such flaw had been detected at the time of his death. It can be shown, however, that the invalidities are in McCaw's methods, and there seems no reason for doubting the results derived by the Gauss method. 相似文献
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Richard Barnes 《International Journal of Digital Earth》2020,13(7):803-816
ABSTRACT Spatial analyses involving binning often require that every bin have the same area, but this is impossible using a rectangular grid laid over the Earth or over any projection of the Earth. Discrete global grids use hexagons, triangles, and diamonds to overcome this issue, overlaying the Earth with equally-sized bins. Such discrete global grids are formed by tiling the faces of a polyhedron. Previously, the orientations of these polyhedra have been chosen to satisfy only simple criteria such as equatorial symmetry or minimizing the number of vertices intersecting landmasses. However, projection distortion and singularities in discrete global grids mean that such simple orientations may not be sufficient for all use cases. Here, I present an algorithm for finding suitable orientations; this involves solving a nonconvex optimization problem. As a side-effect of this study I show that Fuller's Dymaxion map corresponds closely to one of the optimal orientations I find. I also give new high-accuracy calculations of the Poles of Inaccessibility, which show that Point Nemo, the Oceanic Pole of Inaccessibility, is 15?km farther from land than previously recognized. 相似文献
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《测量评论》2013,45(15):16-23
AbstractTHE formula for the projection is based upon the spherical assumption. To calculate it for the spheroid might be very complicated and would not be worth while. The projection is suitable for very large areas as a compromise between the Zenithal Equal-area projection on the one hand and the Zenithal Equidistant or Zenithal Orthomorphic on the other. Its application to an area as small as the British Isles would not serve any useful purpose. An analysis of its errors in the general case reveals some unexpected simplicities. This analysis is given below, followed by its application to the particular case of the British Isles on the ten-mile scale. This is done merely to find out what changes would have occurred if the supposed drawing of that map on Airy's projection had been real. 相似文献
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《测量评论》2013,45(21):417-422
AbstractThe Transverse Mercator Projection is also called the Conformal of Gauss since it was devised by him in the early part of the nineteenth century in connexion with the Triangulation of Hanover. It belongs to the class of cylindrical orthomorphic projections. That is to say, the Earth's surface, or part thereof, is developed on the surface of a cylinder, and there is practically no angular distortion, an angle on the surface of the Earth being represented on the map by almost precisely the same angle. The representation of meridians and parallels, for instance, shows them intersecting at right angles as they actually do on the Earth's surface; but this orthotomic condition, though essential, is not in itself sufficient for orthomorphism. 相似文献
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Steven E. Greco 《地球空间信息科学学报》2013,16(4):288-293
ABSTRACTConceptually, the theory and implementation of “map projection” in geographic information system (GIS) technology is difficult to comprehend for most introductory students and novice users. Compounding this difficulty is the concept of a “map projection file” that defines map projection parameters of geo-spatial data. The problem of the “missing projection file” appears ubiquitous for all users, especially in practice where data is widely shared. Another common problem is inadvertent misapplication of the “Define Projection” tool that can result in a GIS dataset with an incorrectly defined map projection file. GIS education should provide more guidance in differentiating the concepts of map projection versus projection files by increasing understanding and minimizing common errors. A novel pedagogical device is introduced in this paper: the seven possible states of GIS data with respect to map projection and definition. The seven possible states are: (1) a projected coordinate system (PCS) that is correctly defined, (2) a PCS that is incorrectly defined, (3) a PCS that is undefined, (4) a geographic coordinate system (GCS) that is correctly defined, (5) a GCS that is incorrectly defined, (6) a GCS that is undefined, and (7) a non-GCS. Recently created automated troubleshooting tools to determine a missing map projection file are discussed. 相似文献
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《测量评论》2013,45(62):311-314
AbstractIn E.S.R., viii, 56, 70, Brigadier K. M. Papworth has given expressions for the angular corrections, known as (t – t) corrections, in the Lambert NO.2 Projection, derived from empirical considerations based on actual detailed calculations. Apparently some difficulty has been experienced in offering a proof. In view of the widespread use of the Lambert Projection in World War II, it is hoped that the following proof will be found to be of more than academic interest. 相似文献
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《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
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刘家臣 《测绘与空间地理信息》2011,(6):215-218
高速铁路轨道控制测量采用精密控制测量技术,采用斜轴墨卡托投影可以避免高斯投影投影带可控范围小,坐标转换和分带计算的问题,对于东西走向的线路能很好地控制投影长度变形。文章以长吉高铁控制测量数据,实现斜轴墨卡托投影,经过其投影精度的探讨,确定斜轴墨卡托投影能满足高铁精密控制测量的精度要求。 相似文献
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《The Cartographic journal》2013,50(2):109-116
AbstractIn this paper the cartographic grids engraved on two antique instruments from Iran for finding the sacred direction and distance to Mecca are discussed. It appears that these grids can be well explained in terms of the Mecca-centred retro-azimuthal orthographic projection described in 1968 by J. E. Jackson. In this projection the lines of constant latitude reduce to a set of ellipses with their major axes parallel to the equator and the lines of the constant longitudes reduce to a set of non-equidistant straight lines parallel to the north-south direction. It is shown that the curves actually engraved on the instrument conform to this projection and can be fairly easily constructed. This interpretation of the grid on the Iranian instruments stands in contrast with another explanation, recently proposed by King (1999), which is based on medieval Arabic concepts such as the so-called 'methods of the zijes'. Insufficiently accurate workmanship makes it impossible to distinguish between the two explanations through the study of the instruments themselves. The newly gained insight into the projection itself, however, shows that a direct relation between the Iranian maps and Islamic mappings insight knows from the ninth century, as suggested by King, does not exit. Thus, it is concluded that it is as yet completely unknown when and where the very idea behind the Iranian cartographic grid was first conceived, and that the quest for their historical background is still open. 相似文献
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《测量评论》2013,45(10):226-238
AbstractThe Stereographic Projection, owing to the ease and accuracy with which it can be drawn on a small scale, offers natural attractiveness for the treatment of spherical geometry upon a plane surface. It would therefore be rash for a present-day writer to claim as novel what may well be an infringement of patent rights morally belonging to Hipparchus, who possibly knew most of what is worth knowing about the matter 2,000 years ago. However, since a fairly extensive delving into writings upon the subject has not brought to light anything quite on the lines here put forward, it may be worth while to systematize in this paper some processes which the present writer has found practically useful for some time past. 相似文献
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AbstractIn chain and traverse surveys areas are frequently required between chain lines and crooked fences. Commonly these areas are computed from offsets measured at equal intervals, which are so much the shorter according as the sinuosity is the greater. Most frequently Simson's Rules are employed for this computation; for (2m+1) offset ordinates, Simson's First Rule may be used; for (3m+1) ordinates, Simson's Second Rule. The First Rule assumes that the fence is made up of arcs of ordinary parabolae; the Second Rule, of arcs of cubic parabolae. 相似文献
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双等距离投影及其应用 总被引：1，自引：0，他引：1
双等距离投影是指自图上两定点出发至图上任意点间的距离都与实地等长的投影。本文先从球面极坐标出发，讨论了双等距离投影公式的建立，继而给出了在地理坐标下的正轴和斜轴投影计算方法。本文证明了该投影的性质属任意投影，其计算方法是可行的，有实用价值。双等距离投影在测量上可用于圆圆系统定位，在军事上可用于敌情监测等。 相似文献
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公元1430年前中国测绘美洲——《坤舆万国全图》探秘 总被引：1，自引：0，他引：1
定性与定量分析《坤舆万国全图》和同时期的欧洲绘世界地图:墨卡托(1569)、奥特里乌斯(1570)、墨卡托(1595)北极圈地图和普兰修斯(1594)地图,揭示《坤舆万国全图》内容并非采自欧洲地图.《坤舆万国全图》显示文艺复兴前的欧洲,而美洲一半的地名在同时期的欧洲绘地图上没有出现,部分是利玛窦去世至少200年后欧洲人才知道的地理.《坤舆万国全图》准确标示今日的加利福尼亚、雷尼尔山(雪山)、阿拉斯加的冰川峡湾(美湾)、安克拉治附近的水潮与北美最高峰迪纳利(水潮峰)纬度与地理特征完全符合,南美智利与秘鲁的经度比较正确.普兰修斯与墨卡托的地图严重错误和不确定.《坤舆万国全图》的中国地名地理不是利玛窦年代的,是公元1430年以前的,比哥伦布到达美洲早60年以上.传教士卫匡国1655年出版的《中国新地图集》不可能是他测绘,只能翻译中国原数据,说明明代中国有能力测绘大面积有准确经纬度和球形投影的地图.这两种地图证实中国的世界地理知识和地图学并非来自西方.《坤舆万国全图》证明中国明代大航海是世界地理大发现与地图学的先行者. 相似文献
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《测量评论》2013,45(98):177-184
Abstract1. The Secondary and Tertiary Triangulations of the six counties of Northern Ireland which were observed about 1900 were computed county by county each on its own meridian on a Cassini projection using Airy's figure of the earth. Although a number of points common to two or more counties were fixed no attempt was made to bring the separate counties into sympathy either with each other or even with the old Primary triangulation as adjusted by Clarke in 1856. 相似文献
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AbstractIn January 1938 the writer decided against holding up for more years some work on the Transverse Mercator Projection (E.S.R., 27, 275). The extension to the spheroid was not then complete, nor is the present paper to be regarded as a logical continuance. It is first proposed to show the results of “transplanting” orthomorphically upon the spheroid a spherical configuration forming a graticule. 相似文献
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《The Cartographic journal》2013,50(2):138-140
AbstractThe readjustment of a major geodetic control network results in a new set of spheroidal coordinates for the network stations. Those new coordinates followed by an appropriate control densification serve as input for computing new plane coordinates. There are many surveying and mapping products which are based on the existing 'old' plane coordinates system. This paper deals with considerations and procedures aiming at the introduction of a new projection defined in such a way as to minimise the detrimental consequences of readjustment through the use of a synthetic point of origin for the new projection. 相似文献