THE TRANSVERSE MERCATOR PROJECTION

Abstract

I. 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.     

THE TRANSVERSE MERCATOR PROJECTION OF THE SPHEROID

Abstract

In 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.     

THE CONVERSION OF CO-ORDINATES FROM THE CASSINI TO THE TRANSVERSE MERCATOR PROJECTION

Abstract

1. 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.     

MINOR TRIANGULATION ON THE TRANSVERSE MERCATOR PROJECTION

Abstract

1. Computation of a minor triangulation as if it were executed on a plane surface of course ignores spherical excess, an omission not strictly rigorous so far as azimuths are concerned. Further the reduction of such a triangulation to a system of plane coordinates again assumes that the earth's surface is a plane.     

MINOR TRIANGULATION ON THE TRANSVERSE MERCATOR PROJECTION

Abstract

In a previous article in this Review, the writer endeavoured to show that chains of minor triangulation could be adjusted by plane rectangular co-ordinates ignoring the spherical form of the earth with little loss of accuracy, provided that the two ends were held fixed in position. It was demonstrated that the plane co-ordinates produced by the rigorous adjustment between the fixed starting and closing sides, differ by only a comparatively small amount from the projection co-ordinates produced by a rigorous adjustment on the Transverse Mercator projection. The saving in time when computing by plane co-ordinates as opposed to rigorous computation on the projection by any method will be apparent to any computer with experience of both methods.     

THE TRANSVERSE MERCATOR PROJECTION: A CRITICAL EXAMINATION

Abstract

In 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.     

TRANSFORMATION OF RECTANGULAR CO-ORDINATES ON THE TRANSVERSE MERCATOR PROJECTION

Abstract

The necessity of transforming rectangular co-ordinates from one system of projection to another may arise from, various causes, One case, for example, with which the present writer is concerned involves the transformation, to the standard belt now in use, of the co-ordinates of some hundreds of points of a long existing triangulation projected a quarter of a, century ago on a, belt of Transverse Mercator projection, In this case conversion is complicated by the fact that the spheroid used in the original computation differs from that now adopted, and, also, the geodetic datums are not the same, The case in fact approaches the most general that can occur in practice, One step in one solution of this problem, however, is of perhaps wider Interest: that is, the transformation from one belt of Transverse Mercator projection to another when the spheroids and datums are identical. It is this special case which will be discussed here.     

THE FIXATION OF MINOR TRIANGULATION ON THE TRANSVERSE MERCATOR PROJECTION

Abstract

The fixation of Minor Triangulation in a Primary system does not, in general, warrant rigorous adjustments of figures; less laborious methods are desirable. For Secondary work a least square adjustment to approximate coordinates is quite sufficient, while, for Tertiary, graphical solutions are amply accurate. Apart from that, cases may arise to which a figure adjustment is not applicable, as in the small net shown in Fig. 2, p. 464. The line BC cannot be equated to the line AB in the ordinary way since it is not the side of a triangle. In this case an adjustment to approxima te coordina tes will overcome the difficulty.     

空间斜墨卡托投影及其在遥感图象处理中的应用

本文推导了球体、椭球体空间斜墨卡托(SOM)投影公式;指出了空间投影的特点和用途,给出了可实际应用的SOM投影正反解公式计算程序包;分析了真(垂直)卫星地面轨迹投影线附近的变形情况,提出了一种正形多项式快速算法,提高了SOM投影正反解计算速度;最后给出了SOM投影与传统地图投影(例如高斯、等角园锥投影)的转换程序包。     

THE MERCATOR PROJECTION AND THE RHUMB LINE

Abstract

Introductory Remarks.—A line of constant bearing was known as a Rhumb line. Later Snel invented the name Loxodrome for the same line. The drawing of this line on a curvilinear graticule was naturally difficult and attempts at graphical working in the chart-house were not very successfuL Consequently, according to Germain, in 1318 Petrus Vesconte de Janua devised the Plate Carree projection (“Plane” Chart). This had a rectilinear graticule and parallel meridians, and distances on the meridians were made true. The projection gave a rectilinear rhumb line; but the bearing of this rhumb line was in general far from true and the representation of the earth's surface was greatly distorted in high latitudes. For the former reason it offered no real solution of the problem of the navigator, who required a chart on which any straight line would be a line not alone of constant bearing but also of true bearing; the first condition necessarily postulated a chart with rectilinear meridians, since a meridian is itself a rhumb line, and for the same reason it postulated rectilinear parallels. It follows, therefore, that the meridians also must be parallel inter se, like the parallels of latitude. The remaining desideratum—that for a true bearing—was attained in I569 by Gerhard Kramer, usually known by his Latin name of Mercator, in early life a pupil of Gemma Frisius of Louvain, who was the first to teach triangulation as a means for surveying a country. Let us consider, then, that a chart is required to show a straight line as a rhumb line of true bearing and let us consider the Mercator projection from this point of view.     

斜轴墨卡托投影方法在郑西客专中的应用研究

介绍了斜轴墨卡托投影,分析了其具体实现过程,实现了在郑西客运专线精密控制测量的应用,有效地解决了东西走向线路投影差对工程影响较大的问题。     

MARGINAL SCALES OF LATITUDE AND LONGITUDE ON TRANSVERSE MERCATOR MAPS

Abstract

The 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.     

极大验后估计及其在扩建网中的应用

本文基于未知参数具有先验正态分布的广义Ｇ－Ｍ模型，推导了未知参数和方差因子的极大验后估计公式，证明了未知和的极大验后估计是无偏、有效估计量，方差因子的极大验后估计有偏，并推导了方差因子的边缘极大验后估计，证明了它的无偏及有效性，作为应用，本文最后证明了扩建网极大验后平差成果等于新旧网整体平差成果。     

MapGIS到ArcSDE的数据转换方法与实践

 针对省市级地理信息系统开发中普遍存在的数据转换和管理问题，提出从MapGIS到ArcSDE的数据转换方法，通过比较MapGIS与ArcSDE存储结构的异同点，提出点状地物、面状地物转换过程中采用信息筛选的方式进行转换，并论述了分幅数据入库后的数据整合流程和建立地图符号对照表实现符号转化的方法，采用COM 技术编程加以实现,其成果能够满足省市级地理信息系统开发的要求。     

遗传算法在组分温度反演中的应用

介绍了遗传算法的主要内容和工作原理。在连续植被热辐射方向性模型的基础上,从热红外多角度遥感数据中,同时反演混合像元组分温度、土壤比辐射率以及叶面积指数。大量试验表明,利用遗传算法反演组分温度效果非常好。在宽松的先验知识条件下,该方法可以解决不确定性反演问题