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自定义坐标系的建立及其坐标变换实现

已有 9155 次阅读 2015-8-12 18:26 |个人分类:矿产勘查|系统分类:论文交流| 坐标变换, 自定义坐标系

按:

一、做勘查,尤其在国外,往往第一步就是坐标问题。坐标问题解决不了,就卡主了。其实坐标是个小问题,但是我们地勘行业存在极其普遍。历史原因使然吧,我们搞测绘的前辈别骂我。

这些年发现很多地勘人员不是很了解坐标的含义。老东家单位的有些专家当年还因此指责过我勘查中的坐标问题,一句话两句话也给专家解释不清楚。也难怪,我们大学地质专业的测绘课也没把坐标说清楚(其大地基准的说法就是错误的,如:什么青岛黄海高程大地基准,那个东西就不是大地基准datum)。也遇到过不少同行问过我如何进行坐标变换。经过向/和同行(如合作作者)请教切磋,几年来抽空把此问题进行了一些条理化,写成这一篇拙作以及2013年的《UTM投影和Gauss-Krüger投影及其变换实现》。但愿对大伙有所启发吧。


二、坐标系建立和转换是个小问题,有很多办法可以解决。除了本文说的办法外,还有很多软件(如ENVI,其建立方法类似GeoSoft)都可以实现。就是使用MapInfo也有另外一种办法(先在Mapinfow.txt中加入新坐标系,利用MapInfo的的MapBasic程序的Coordinate Extractor,其效果类似GeoSoft). 使用MapInfo的Discover也可以,但是其修改源文件有些繁琐,修改过程类似GeoSoft)。

这个问题,如果仅仅处理少量数据,也可以用MapSource对付一下来解决。


个人感觉,使用MapInfo修改Mapinfow.txt文件的办法简单一些。


图件加载费劲,愿意看全文的同人看《地质与勘探》网站上的原文吧

http://www.dzykt.com/dzyktcn/ch/reader/view_abstract.aspx?file_no=20150410&flag=1





[摘  要]大地基准(含数学椭球体)和投影方式的组合形成多种投影坐标系。地质勘查人员经常性遇到坐标转换问题和建立自定义坐标问题,尤其是我国北京54坐标系和西安80坐标系地质数据GIS化时。GIS软件已经成为地质勘查的基本工具,而地质数据的GIS化的第一步就是建立坐标系统。本文论述了如何使用MapInfo®Geosoft® Oasis Montaj两种常见地质勘查GIS软件建立自定义坐标,主要是如何在该两个软件中构建自定义大地基准(datum)。并且给出了如何使用它们进行坐标变换的步骤。

[关键词]  坐标; 数学椭球体;大地基准;投影;自定义坐标系; 变换实现;MapInfo®  Geosoft® Oasis Montaj

[中图分类号]   [文献标识码]A    [文章编号]  -

Zhou Chao-xian, Dong Shao-bo, He Zhi-jun, Jiang Gao-zhen, YanDan-chen. Custom coordinate system establishment and coordinate conversion[J]. Geologyand Exploration, 2015,……

[收稿日期]2015-  - [修订日期]    [责任编辑]  

[基金项目] 本文为中央财政国外矿产资源风险勘查基金项目(编号10254B004, 10201B004101001A025)资助的成果。

[第一作者]周朝宪(1970-),男,教授级高级工程师,主要从事矿床地质地球化学研究、矿产勘查和矿山地质等, E-mail: czhou28@126.com


1  引言

从上世纪九十年代以来,地质勘查工作最大的进展就是地理信息系统(GIS)越来越多地渗入并支撑着当今的勘查工作,现在的地质勘查工作要求我们地质人员,尤其勘查人员,应该掌握投影、大地基准(datum)和数学椭球体(ellipsoid)的含义和关系。以免造成错误和不必要的问题。

所谓投影,如周朝宪等(2013)所说,包括2部分内容,一是对地球这个椭球体参数最佳近似的理论化,即构建大地基准;一是把这个理论化的地球大地基准体上的坐标点(大地坐标系的经纬度)转到平面坐标(即方里网)上。大地基准实际也包括两部分内容:首先把实际地球先简单化为数学椭球体。这个数学椭球体由地球半径长轴和扁平率(flattening,扁平率为椭圆率(ellipticity)或者偏心率(eccentricity)的函数)来定义。由于实际地球和数学椭球体还存在比较大的差异(主要是地球质心和数学椭球体并不严格重合),难以满足测绘和各种工程所需,所以datum还包括对数学椭球体ellipsoid进行地球质心的偏移补偿。Ellipsoiddatum和实际地球表面的关系见图1

WeChat Image_20180608165930.png

1 地球实际地形、大地基准和数学椭球体的关系

Fig. 1The relationship among the Earth actual surface, Datum/Geoid and Ellipsoid

地球上任何一点的经纬度是建立在datum基础上,而不是建立在ellipsoid之上。地球上任何一点的经纬度在不同datum体系下的数值基本不相同,相差几十米乃至数百米是很正常的事情。了解这一点十分重要,因为相当多基层的地质人员在其做出的地质图没有给出datum。这是很不严谨的,会给使用图件的人带来很大麻烦。

目前GPS全球定位系统所采用的UTMUniversal Transverse Mercator,通用横轴墨卡托)投影现在采用的datum WGSWorldGeodetic System84椭球体。从理论上讲,投影方法和datum可以自由组合,从而产生众多的坐标系统。另外,由于一些历史原因,在不同的历史时期,许多国家和地区都有建立有各自的基准datumellipsoid。如我国自上个世界五十年代以来,我国使用过与北京54坐标系对应的Krassovsky椭球体,后来的西安80坐标系的IAG 1975椭球体。这就要求我们对GIS坐标有个正确的理解。

我们在实际地质勘查中还遇到过有些中国地质人员不懂这些坐标知识,给工作带来一些麻烦。如某CXB地质队在埃塞俄比亚工作时,由于发现手持式GPS给出的坐标和当地的地形/地质图不相吻合,便按照国内处理北京54坐标系和西安80坐标系的办法,根据当地地形图上的控制点,建立了使用WGS 84为椭球体(手持式GPS接收机坐标所依据的椭球体),并自行修改手持GPSDxDyDz。实际是建立了独特的TM投影。实际上其地形图上标注着其使用的datum和椭球体分别是AdindanClarke_1880。遇到知道已有图件的投影和datum的情况,正确的做法有2种办法:或者把地形图通过坐标变换到WGS 84坐标下,以便和手持式GPS接收机数据套合。因为手持式GPS接收机往往没有AdindanClarke_1880体系。或者把手持式GPS坐标下的地质成果通过GIS软件转换成AdindanClarke_1880坐标系,从而把不同坐标体系下的数据实现套合。

为了使用该地质队自定义坐标体系下的地质成果,我们在GIS软件中,根据其datum采用WGS 84,以及DxDyDz建立了该自定义坐标系,从而利用软件快捷地进行不同坐标体系的转换,从而解决了不同坐标体系下地质数据的套合使用。

周朝宪等(2013)给出了使用MapInfo®UTM投影和Gauss-Krüger投影下方里网坐标和其经纬度的转换过程。其实,对于国内北京54坐标系和西安80坐标系(都采用Gauss-Krüger投影,UTM投影和Gauss-Krüger投影都属于TM横轴墨卡托投影),由于该两种坐标系只有数学椭球体而没有datum,必须先在GIS软件中建立自定义坐标系,即按照自定义坐标系的方式处理即可。否则基本无法利用诸多通用GIS软件对北京54坐标系以及西安80坐标系下的地质数据进行处理。

我国“走出去”战略的实施,也使我们地勘人员经常面临不同坐标体系下的数据。即使是在国内,我们也经常性面临坐标变换问题。如北京54坐标系和西安80坐标系他们之间的相互转换以及和其他投影坐标系(如CGCS2000以及UTM等等)间的变换。建立自定义坐标系以及实现不同坐标系下数据的套合使用已经迫切摆在我们地质勘查人员的面前,成为很多地质勘查人员的经常性的工作。熊忠招(2010)、陈士银(1997)、畅开狮(2008)等从测绘的角度探讨了如何建立个别的自定义坐标系。但是其方法不适合地勘工作。

有些人,如杨启和(1986)、夏兰芳等(2007)、沈本忠(1986)、Osborne2008)、Dozier1980)和Kawase2011等等,给出了就坐标变换给出了严格的数学换算。但是这些运算对绝大多数地质勘查人员而言,不具有可操作性。还有人提出了简易的算法公式,但是因为简易公式做得出的结果,精度太差,以至于这在实际工作中是不可以接受的(见周朝宪等,2013)。也有一些人,如刘健和刘高峰(2005)和王宝军等(2010)等,甚至发展出一些专门的软件程序用以坐标变换。但是这些软件一则普及性很低,广大地勘人员一般无法使用,二则也面临构建datum和投影等问题,并不适用适用于广大地勘人员使用。可以说目前对广大地质人员而言,比较可行的办法就是使用现成的比较通用的GIS软件来进行转换(周朝宪等,2013)。而要进行坐标转换的前提往往就是在在这些软件中建立起我们需要的自定义坐标系。

1990s年代以来,西方地质勘查工作逐步使用各种GIS功能强大的软件。我们现在的地质勘查工作已经离不开GIS软件。没有GIS软件就没有快速勘查。当然GIS的作用远不止其快速性方面,这方面内容在此不予赘述。GIS软件已经成为勘查人员的必备,其重要性如同GPS接收机、锤子、罗盘和放大镜。

常用的GIS软件包括MapInfo®Geosoft® Oasis Montaj™、ArcGIS®以及国内较为通用的MapGIS®MapGIS® 6.7版本(现在最常用的的版本)及其以前版本的软件由于其显示的坐标仅仅是图面坐标。还谈不上是完整的勘查GIS软件,尽管其描图功能较为强大。完整的勘查GIS软件至少应具有三个特点:1)图面显示坐标为该点在所采用的GIS坐标体系中的真实坐标数值。当然,其不随着图面比例尺变化而变化。2)含有目前常见的坐标体系,并可以在相互间进行坐标转换。3)基本可以在其中建立自定义坐标系。MapGIS® 6.7版本及其以前的版本不具备这三个特点。而MapInfo®Geosoft® Oasis Montaj™和ArcGIS®都具备这三个特点。这些软件在非洲等国家地勘人员中的普及程度也远远高于我国。这些都强烈要求我们地质勘查人员尽快熟悉GIS功能强大的勘查软件,如MapInfo®Geosoft® Oasis Montaj™和ArcGIS®等。

故此本文使用西方地质勘查应用最广的MapInfo®Geosoft® Oasis Montaj™进行展示,如何建立自定义坐标,即如何在这些软件中建立自定义Datum,以及如何使用它们进行坐标变换。实际上,ArcGIS®也可以定义自定义坐标系。也可以使用其处理我国的北京54坐标系和西安80坐标系下的GIS数据。步骤与MapInfo®Geosoft® Oasis Montaj™类似,其投影信息存储在数据集的PRJ文本文件中,也是通过直接修改该文本文件来建立自定义坐标系。陈悟天(2010)和周朝宪等(2013)说ArcGIS®没有国内现用的Gauss-Krüger投影坐标的说法是不准确的,可以在该软件中建立国内各个地区的Datum,然后就可以进行坐标变换。

2 使用MapInfo建立自定义坐标系及其坐标变换

MapInfo®的坐标参数文件主要是mapinfow.prjmapinfow.prj是个文本文件,可以直接编辑。其结构参见表1

1  MapInfo®中坐标系统各个参数定义格式

Table1  The parameter form of coordinatesystem in MapInfo®

Coordinate System

坐标系统

Projection type

投影类型

Datum 大地基准

Units 单位

Origin, Longitude

原点经度

Origin, Latitude

原点纬度

Standard Parallel 1

标准平行 1

Standard Parallel 2

标准平行 2

Azimuth方位

Scale factor比例因子

False Easting

东伪偏移

False Northing

北伪偏移

Range范围

Transverse Mercator

横轴墨卡托

8

X

X

X

X




X

X

X


注:其中X表示该投影有该项内容。此处仅以横轴墨卡托坐标为例,其他投影的具体参数参见文后注释①和②。

MapInfo®自定义投影参数中,对于横轴墨卡托投影坐标(UTM投影和Gauss-Krüger投影都属于横轴墨卡托投影)而言,主要有如下参数:

投影代号(Type),基准面(Datum),单位(Unit),原点经度(Origin Longitude,对UTMGauss-Krüger投影而言,其原点经度皆为该带的中央经线的经度值),原点纬度(Origin Latitude,为赤道纬度值0),比例因子(Scale Factor,对UTM投影和Gauss-Krüger投影而言,比例因子分别为0.99961,东伪偏移(False Easting),北伪偏移(False Northing)。关于UTMGauss-Krüger投影的上述参数更多内容具体可参见周朝宪等(2013)。

MapInfo®中,横轴墨卡托投影的代号为8,其余各个投影的代号参见MapInfo®的说明书。各个基准面datumMapInfo®代号也参见MapInfo®说明书。如WGS 84 datum的代号是104

例如:对东经34°和北纬8°的点,其UTM投影,选取WGS 84 world作为大地基准(其数学椭球体是WGS 84)的MapInfo®参数为:

"UTMZone 36, Northern Hemisphere (WGS 84)p32636", 8, 104, 7, 33, 0, 0.9996,500000, 0

UTM 36带,投影方法为横轴墨卡托投影,代号为8datumWGS84,代号为104;坐标单位为m,代号为7;该带属于UTM36带,其起始经线(即中央经线)为33°E;其起始纬度为UTM投影的比例因子是0.9996;东伪偏移为500,000m;北伪偏移为0m

如上文所述,北京54坐标系和西安80坐标系没有datum,这就要求我们在datum这一项中予以定义。在MapInfo®中,基准的定义主要有数学椭球体与相应的参数组成(即三参数或七参数)。北京54坐标系采用的是Krassovsky椭球体,其在MapInfo®中的代号是3WGS84数学椭球体的MapInfo®代号是28

以河南新县北部某地的大地坐标(WGS 84)为31°46’06.9’’N114°36’41.6’’E。其北京54坐标系该3度带(带号38,中央经线114°E,三参数)的平移校正Dx= -9.0Dy= -113Dz= -39,那么其datumMapInfo®中格式定义为:(9993-9.0-113-39)。其中999代表自定义datum3代表Krassovsky椭球体。

则可以写出下列语句:

"---Xinxian (Dx: -9.0, Dy: -113, Dz: -39; Beijing_54_Krasovsky) ---", 8 , 999 , 3 , -9 , -113 ,-39 , 7 , 114 , 0 , 1 , 500000 , 0                       ………………. 语句(1

其中:

8代表投影类型为横轴墨卡托投影,这里即为Gauss-Krüger投影;

999表示自定义datum,其后的3代表Krassovsky椭球体,-9.0,-113 , -39分别为 Dx, DyDz

7代表单位为m

114代表起始经线(对横轴墨卡托投影即为该带的中央经线)为114°E

0代表起始纬线为赤道;

1代表比例因子为1

500000代表东伪偏移500,000m

0代表北伪偏移0m

然后打开MapInfo®软件所在的目录下的mapinfow.prj文件,把上述语句(1)写入,保存使用MapInfo®软件调用该投影即可。关于不同坐标系的转换过程步骤可以参见周朝宪等(2013)。

对上文提到的某CXB地质队在埃塞俄比亚西部Abobo地区(其大地坐标(WGS84)为7°39’N34°39’E),其采用的椭球体是WGS84,属于6度带,该区采用三参数格式:Dx=-100Dy=2Dz=-1,该6度带中央经线为33°E。则按照上文所述在mapinfow.prj中加入如下语句即可建立该坐标系。

"---Abobo_ChuanXiBei (Dx:-100, Dy:2, Dz:-1; Local_WGS 84) ---"

"CXB(WGS84)_CM33_Local_WGS 84", 8, 999, 28, -100, 2, -1, 7, 33, 0, 0.9996, 500000,0  …………语句(2  

其中:

8代表横轴墨卡托投影;

999表示自定义datum,其后的28代表MapInfo®WGS84数学椭球体,-100, 2, -1分别为Dx, DyDz

7代表方里网单位为m

33代表起始经线(对横轴墨卡托投影即为中央经线)为33°E

0代表起始纬线为赤道;

0.9996代表比例因子为0.999 6

500000代表东伪偏移500,000m

0代表北伪偏移0m

这里需要说明的是,在写上述坐标参数语句时,语句应该尽可能短,否则MapInfo®在读取这些语句时,往往会读串行,造成坐标错误。

以上是以三参数为例,对七参数的自定义坐标系,其datumMapInfo®中格式定义为:(99993DxDyDzRxRyRzK0)。其中9999代表自定义datum3代表Krassovsky椭球体,RxRyRz为旋转校正,K为比例校正。

经过上述论述,我们可以发现,使用MapInfo®软件设立自定义坐标系就是确立:

1)投影类型及其投影的相关参数(比例因子、起始经纬度和经向和纬向伪偏移量);投影类型的MapInfo®代号参见MapInfo® ProfessionalUser Guide Oasis Montaj v.7.2 mapping and processingsystem tutorials

2)确定datum。确立datum就要确立数学椭球体和datum的相关参数。椭球体的MapInfo®代号参见Geosoft®Oasis Montaj™软件下的ellipsoid.csv文件。

建立自定义坐标系后,便可以使用MapInfo®实现坐标变换。具体过程参见周朝宪等(2013)。也可以使用建立自定义坐标系后的Geosoft®Oasis Montaj™来实现坐标变换。后者用户界面更为友好一些。

3 使用Geosoft®Oasis MontajTM建立自定义坐标系

我们勘查工作一般不会建立全新的投影方法,而是要经常性建立适合于各个地区的datum。建立自定义坐标系的核心就是建立适合于工作区的datum。下面我们简单叙述一下,如何使用Geosoft® Oasis Montaj™软件建立埃塞俄比亚西部Abobo地区的自定义datum

首先修改Geosoft®Oasis Montaj™目录下的“datumtrf.csv”,在其中加入如下内容(参见表2):

2  Geosoft®Oasis Montaj™中datumtrf.csv各个参数定义格式

Table2  The parameter of custom coordinatesystem in datumtrf.csv of Geosoft® Oasis Montaj

Datum_trf

Code

MapInfo

Area_of_use

Datum

Target

Dx

Dy

Dz

Rx

Ry

Rz

Scale

*Abobo special



Abobo_Ethiopia

*Abobo_Local_WGS 84

WGS 84

-100

2

-1

0

0

0

0


然后修改Geosoft® OasisMontaj™目录下的“ldatumtrf.csv”,在其中加入如下语句:

3 Geosoft® Oasis Montaj™中自定义坐标ldatum.csv中各个参数定义格式

Table3 The parameter of custom coordinate system in ldatum.csv of Geosoft® Oasis Montaj

Area_of_use

Datum

Datum_trf

Abobo_Ethiopia

*Abobo_Local_WGS 84

*Abobo special

因为无论MapInfo®还是Geosoft®Oasis Montaj™对datum的命名都遵循EPSGEuropeanPetroleum Survey Group/POSCPetrotechnicalOpen Software Corporation)命名规则。自定义的datum不属于其范围,故此前面加上*以示区别,如埃塞俄比亚西部Abobo地区的自定义datum为“*Abobospecial”,在表2和表3中该名称必须完全一致。

建立自定义坐标系后,可以把坐标数据导入Geosoft® OasisMontaj™。第一步:通过下图(图2)的菜单上的“坐标”选择“坐标系”子菜单,选择我们上文新建的“*Abobo special”,把这些数据设置成以X_CXBY_CXB分别为经向和纬向坐标的“*Abobospecial”坐标系。第二步:通过图2的菜单上的“坐标”选择“新建投影坐标系”子菜单,以X_CXBY_CXB分别为当前的经向和纬向坐标(大地基准为“*Abobo special”),得出WGS84经纬度(即Long_WGS 84Lat_WGS84)。图2中的经纬度单位是度分秒,如图2Point19行对应的经度值34.46.15.837589867034°46’15.8375898670’’。第三步:同第二步类似,以Long_WGS 84Lat_WGS 84为当前坐标数值(大地基准为WGS 84),选择“新建投影坐标系”,新建UTM WGS 84坐标系,即得出图2UTMWGS 84经向(X_UTM)和纬向(Y_UTM)坐标。

2aq.png

2 Geosoft® Oasis Montaj™界面

Fig. 2 Coordinateinterface of Geosoft® Oasis Montaj

X_CXBY_CXB分别代表“*Abobospecial”自定义坐标系的经向和纬向方里网坐标。Long_WGS 84Lat_WGS 84分别代表WGS 84坐标系的经纬度。X_UTMY_UTM分别代表UTM WGS 84坐标系的经向和纬向方里网坐标。

X_CXBand Y_CXB represent the X and Y coordinate values, respectively, of the customcoordinate system, *Abobospecial. Long_WGS84 and Lat_WGS 84 represent the longitude and latitude coordinate values,respectively, with a WGS 84 datum. X_UTM and Y_UTM represent the X and Ycoordinate values, respectively, of the UTM WGS 84 coordinate system.

4 结论

投影坐标包括建立大地基准(datum)和把地球椭球体上的坐标点转到平面坐标(即方里网)上。大地基准(datum)包括数学椭球体(ellipsoid)和根据地球质量对该数学椭球体的补偿。数学椭球体、大地基准和投影方式三者可以组合成多种投影坐标系。地质勘查人员要经常性遇到坐标转换问题和建立自定义坐标问题。我国北京54坐标系和西安80坐标系地质数据的GIS化,基本上需要建立自定义坐标。因为其只有数学椭球体,而缺乏大地基准。建立自定义坐标的靠手工不可能实现。必须借助软件实现。而GIS软件已经成为地质勘查的基本工具,而地质数据的GIS化的第一步就是建立坐标系统。

我们论述了如何使用MapInfo®Geosoft® OasisMontaj™两种常见GIS勘查软件建立自定义坐标系,主要是如何在该两个软件中定义自定义大地基准。并且给出了如何使用它们进行坐标变换的步骤,根据这些步骤,都得出了可靠的坐标数值。


[致谢] 在论文的撰写过程中得到中国科学院遥感与数字地球研究所徐新超博士的宝贵建议,在此表示感谢。

注释:

Pitney BowesSoftware Inc. 2010. MapInfo professional user guide (edition v.10.5).

Geosoft Inc. 2010. OasisMontaj v.7.2 mapping and processing system tutorials.

[References]

Chen Wu-tian.2010. Construction survey in countries using UTM projection [J]. Science andTechnology Information, (8):36-37 (in Chinese).

Chen Shi-yin. 1997. Method to establishmentlocal independent coordinate system [J]. Bulletin of Survey and Mapping, (10):5-7(inChinese with English abstract).

Xu Ya-ya, Huang Wen-yuan. 2008. Coordinatesystem method choice for mountain highway surveying [J]. Bulletin of Survey andMapping, (7): 26-28(in Chinese with English abstract).

Chang Kai-shi. 2008. Discussion on problemsrelated with the independent coordinate system establishment [J], City Survey,(1): 86-89(inChinese with English abstract).

Dozier J. 1980. Improved algorithm forcalculation of UTM and geodetic coordinates [R]. NOAA Technical Report NEES81.

Kawase K. 2011. A general formula for calculating meridianarc length and its application to coordinate conversion in the Gauss-Krüger projection[J]. Bulletin of the Geospatial Information Authority of Japan, 59: 1-13.

Liu Jian, Liu Gao-Feng. 2005. Algorithm of CoordinatesConversion in Gauss-Kruger Projection[J]. Computer Emulation: 22(10):119-121(inChinese with English abstract).

Osborne P. 2008. The Mercator Projection [M], Edinburg.

Shen Ben-zhong. 1986. A new calculation for Mercatortransverse projection ellipsoidal coordination [J]. Journal of Xi’anCollege of Geology, 8 (1):71-86. (in Chinese with English abstract).

Xia Lanfang, HuPeng, Huang Meng-long. 2007. A numerical implementation of analytical transformationusing map projection. Science of Surveying and Mapping, 32(3): 69-71 (in Chinesewith English abstract

Xiong Zhong-zhao.2010. Establishment of independentcoordinate systems on the UTM projection [J].Geospatial Information, 8(2): 41-43 (in Chinese with English abstract).

Wang Bao-jun, Song Guo-min, Luo Fen-yong, MaoYu-zhu, Chen Ling-yu. 2010. Map Projection Transformation Interface Technology[J].Journal of Geomatics Science and Technology, 27 (6): 463-466.

Yang Qi-he. 1981. The Gauss-Krüger projectionand the Transverse Mercator projection [J]. Bulletin of Survey and Mapping, (6): 34-37 (inChinese).

Yang Qi-he, 1986.The research of theory and application of map projection transformation [J]. Journalof PLA Institute of Surveying and Mapping, (1): 65-72 (in Chinese).

Zhou Chao-xian,Fang Zhi-feng, Yu Cai-hong, Zhang Yun-guo, Gao Ying-bo, Yan Dan-chen, YangQiang. 2013.UTM projection and Gauss-Krüger projection and their conversion[J]. Geology and Exploration, 49(5): 882-889 (in Chinese with Englishabstract).

[附中文参考文献]

畅开狮. 2008. 建立城市独立坐标系相关问题的探讨[J]. 城市勘测, (1): 86-89.

陈士银. 1997. 建立地方独立坐标系的方法[J]. 测绘通报, (10): 5-7.

陈悟天. 2010. 使用UTM投影坐标系国家的施工测量[J]. 科技资讯, (8):36-37.

刘健, 刘高峰. 2005. 高斯- 克吕格投影下的坐标变换算法研究[J]. 计算机仿真, 22(10):119-121.

沈本忠. 1986. 椭球面横墨卡托投影坐标计算新公式[J]. 西安地质学院学报, 8(1): 71-86.

王宝军, 宋国民, 罗奋勇, 毛玉柱, 陈令羽. 2010. 地图投影变换接口技术[J]. 测绘科学技术学报, 27(6)463-466.

  夏兰芳, 胡鹏, 黄梦龙. 2007.地图投影解析变换的数值实现方法[J]. 测绘科学, 32(3): 69-71.

熊忠招. 2010. 浅谈UTM投影下独立坐标系统建立[J]. 地理空间信息, 8(2): 41-43.

  许娅娅, 黄文元. 2008. 山区公路测量坐标系的选择方法研究[J]. 测绘通报, (7): 26-28.

杨启和. 1981. 高斯-克吕格投影和横墨卡托投影[J]. 测绘通报, (6): 34-37.

杨启和. 1986. 地图投影变换理论和应用研究[J]. 解放军测绘学院学报, (1): 65-72.

周朝宪,房志峰,于彩虹,张云国,高应波,燕丹晨和杨强. 2013. UTM投影和Gauss-Krüger投影及其变换实现[J]. 地质与勘探, 49(5): 882-889.

CustomCoordinate System Establishment and Coordinate Conversion

ZHOU Chao-xian1,2, DONG Shao-bo3HE Zhi-jun3, JIANG Gao-zhen1,4, YAN Dan-chen5

(1. China University of Geosciences, Beijing 100083; 2. Nankai Mining PLC, Beijing 100023; 3. Sinotech Mineral Exploration Company,Limited, Beijing 100012; 4. ChineseAcademy of Geological Sciences, Beijing 100037; 5. National Marine EnvironmentalForecasting Center, Beijing 100081)

AbstractThe differentellipsoid, datum and projection method can combine and result in differentcoordinate system. Exploration geologist often faces to use geological data indifferent coordinate system and to establish the custom coordinate system when he/sheprocesses geological data especially with GIS software, which has been thebasic and important tool for exploration geology, and especially for data inBeijing 54 and / or Xi’an 80 coordinate systems for both of them have nocompleted datum except ellipsoid. So we explain here how to establish thecustom coordinate system with MapInfo® and Geosoft® OasisMontajTM GIS software respectively, especially to establish customdatum and how to convert the coordinate between different systems with them.

Keywords: coordinate;ellipsoid, datum; projection; custom coordinate system; conversion; MapInfo®;Geosoft® Oasis MontajTM




椭球体的MapInfo代号  

Geosoft Oasis Montaj 软件下的ellipsoid.csv文件

(很有意思,该代号表在MapInfo所附的文件中没有,却在GeoSoft文件中附有)


EllipsoidCodeMajor_axisEccentricity1/fMapInfo
*AMMP/SAMMP
6378249.1450*-1
*Clarke 1866 AFT
6378193.6330.082271854294.978698-1
*Clarke 1880 (Jamaica)
6378249.1360.082483216293.4663137
*Clarke 1880 (Merchich)
6378249.20.082483263293.4659816
*Clarke 1880 (Palistine)
6378300.790.082483227293.4662338
*Everest Modified 1969
6377295.6640.081472981300.8017-1
*Fischer 1960
63781660.081813334298.318
*Fischer 1960 (South Asia)
63781550.081813334298.319
*Fischer 1968
63781500.081813334298.320
*Hayford
63783880.081991892975
*Hough 1956
63782700.0819918929723
*IAG 75
63781400.081819191298.25722231
*International 1967 (New)
6378157.50.08182018298.2533
*Merit 83
63781370.081819221298.25732
*South American
63781600.08182018298.2524
*Sphere EMEP
63700000*-1
*Sphere2 (ERM)
63709970*12
*STM1987
63712040*-1
*Venus
60519200*-1
*Walbeck
63768960.081206823302.7834
*WGS 60
63781650.081813334298.326
*WGS 66
63781450.08182018298.2527
*WGS 72
63781350.081818811298.261
Airy 183070016377563.3960.081673374299.3249659
Airy Modified 184970026377340.1890.081673374299.32496513
Australian National Spheroid700363781600.08182018298.252
Average Terrestrial System 1977704163781350.081819221298.25751
Bessel 184170046377397.1550.081696831299.15281310
Bessel Modified70056377492.0180.081696831299.15281335
Bessel Namibia70066377483.8650.081696831299.15281314
Bessel Namibia (GLM)70466377483.8650.081696831299.152813-1
CGCS2000102463781370.081819191298.257222
Clarke 185870076378293.6450.082371998294.26067636
Clarke 186670086378206.40.082271854294.9786987
Clarke 1866 Authalic Sphere705263709970*-1
Clarke 1866 Michigan70096378450.0480.082271854294.9786978
Clarke 188070346378249.1450.082483217293.4663086
Clarke 1880 (Arc)70136378249.1450.082483217293.46630815
Clarke 1880 (Benoit)70106378300.7890.082483215293.46631638
Clarke 1880 (IGN)70116378249.20.082483257293.46602130
Clarke 1880 (international foot)70556378306.370.082483217293.466308-1
Clarke 1880 (RGS)70126378249.1450.0824834293.46516
Clarke 1880 (SGA 1922)70146378249.20.082483263293.4659816
Danish 187670516377019.270.081581588300-1
Everest (1830 Definition)70426377299.3660.081472978300.801726-1
Everest 1830 (1937 Adjustment)70156377276.3450.081472981300.801711
Everest 1830 (1962 Definition)70446377301.2430.081472978300.80172640
Everest 1830 (1967 Definition)70166377298.5560.081472981300.801739
Everest 1830 (1975 Definition)70456377299.1510.081472978300.801726-1
Everest 1830 (RSO 1969)70566377295.6640.081472981300.801748
Everest 1830 Modified70186377304.0630.081472981300.801717
GEM 10C703163781370.081819191298.257224-1
GRS 1967703663781600.081820568298.24716721
GRS 1967 Modified705063781600.08182018298.2521
GRS 1980701963781370.081819191298.2572220
GRS 1980 Authalic Sphere704863710070*-1
Helmert 1906702063782000.081813334298.322
Hough 1960705363782700.0819918929723
Hughes 1980705863782730.081816153298.279411-1
IAG 1975704963781400.081819221298.25733
Indonesian National Spheroid702163781600.081820591298.24741
International 1924702263783880.081991892974
International 1924 Authalic Sphere705763712280*-1
Krassowsky 1940702463782450.081813334298.33
NWL 9D702563781450.08182018298.2542
OSU86F70326378136.20.081819191298.25722444
OSU91A70336378136.30.081819191298.25722445
Plessis 1817702763765230.080433474308.6446
Popular Visualisation Sphere705963781370*
PZ-90705463781360.081819107298.25783952
Sphere703563710000*12
Struve 186070286378298.30.082306499294.7347
War Office702963783000.08213003929625
WGS 72704363781350.081818811298.261
WGS 84703063781370.081819191298.25722428



补记

2016年8月1日看到如下文章,感觉他的图更形象说明了地球实际地表Terrain、大地基准datum(该文章换用datums),Ellipsoid/Spheroid(数学椭球体)和平均海平面 Mean Sea Level四者的关系。


https://www.icsm.gov.au/education/fundamentals-mapping/datums


Datums 1 – The Basics

Datums are discussed here at two levels:

The content of these two is very similar, but as their titles suggest, they supply different levels of information.  As Datums is a ‘jargon rich’ discipline it is recommended that you read this Section first.

As with all the Modules in this package, ICSM is trying to explain often complex situations using very simple language.  In the case of Datums this is particularly true.  Once you understand the principles being outlined in these two sections it is recommended that you use the hyperlinks to more complex sites if you wish to better understand the intricacies associated with datums.

Contents of both Sections:

Datums 1Datums 2
 » What is a Datum and how is it Different to a Projection?
 » Naming Datums and Projections
 » About the Geometry of Datums
     • The Earth as a Sphere
     • The Earth as an Ellipsoid/Spheroid
     • The Earth as a Geoid
     • The Earth’s True Shape
     • How These Relate to Each Other
 » What is Geodesy?
 » What is a Geocentric Datum?
   » Introduction
   » The Ellipsoid/Spheroid
   » Fitting an Ellipsoid/Spheroid to the Earth
   » Summary to-date
   » Tectonic Plate Movement
   » Common Horizontal Datums of Australia
       • Geocentric Datum of Australia
       • Australian Geodetic Datum
       • WGS84
       • ITRF 2000
   » Projections
   » Height
       • The Geoid
       • Australian Height Datum (1971)
       • Spheroidal Heights
       • Relating AHD and Spheroidal Heights
       • Bathymetric Heights
   » Further Reading



What is a Datum and how is it Different to a Projection?

This confuses many people.  In simple terms:

globe_0.gif

A datum is a system which allows the location of latitudes and longitudes (and heights) to be identified onto the surface of the Earth - ie onto the surface of a ’round’ object.

The basic mathematical/geometric principle which is used is that:

» mathematically a ’round’ surface is created which represents the surface of the Earth

» from here calculations are made to fit this mathematical model to the surface of the Earth - firstly the Equator, then North and South Poles and then lines of latitude and longitude.

Refer to the section on the Earth’s coordinate system.

Because there are different ways to fit the mathematical model to the surface of the Earth, there are many different datums.  Also, in the modern digital era, techniques have vastly improved and many modern datum are very similar to each other.  However, also in this modern digital era, people like to know locations precisely so even a small difference may be significant.


world_0.gif

A projection is a process which uses the latitude and longitude which has already been ‘drawn’ on the surface of the Earth using a datum, to then be ‘drawn’ onto a ‘flat piece of paper’ - called a map.

See the section on Projections for more information about projection methodologies.


Naming Datums and Projections

There are many different datums and projections in existence.  To ensure that these can be easily identified each version of a datum or projection is given a unique name:

For datums this is usually a regional/functional description and a date for when it was last up-dated - eg:

  • the Australian Geodetic Datum which was created in 1966 and updated in1984 is variably described as AGD66, AGD84 or just AGD

  • the International Terrestrial Reference frame is described as ITRF - this has versions which were created in 1994, 1996, 1997, 2000 and 2005

  • the United States Defence Department developed the World Geodetic System 1984 or WGS84 – this is used by GPS satellite navigation systems and on most hydrographic charts

For projections this includes:
   » the person(s) who developed it (eg Mercator); or
   » aspects of the projection (eg Conic); or
   » a combination of the two (eg Lambert Conformal Conic)


About the Geometry of Datums

In order to calculate where latitudes and longitudes occur on the surface of the Earth a number of fundamental geometric concepts and practices need to be applied.  In simple terms these include:


The Earth as a Sphere

In this calculation the Earth is viewed as being an evenly round ‘ball’.  This is called a Sphere.sphere.jpg

From an imaginary centre of the Earth, calculations are made from the centre of the Earth to the surface of the Earth.

In this diagram the distances from the centre of the Earth to the Equator and the Geographic/True North Pole (indicated by ‘a’ and ‘b’) are the same value.

The Earth as an Ellipsoid (or Spheroid)

ellipsoid.jpg
However, the Earth is not evenly round - it is in fact wider around the Equator than it is between the North and South Poles.

This is called an Ellipsoid (or a Spheroid)..  All Ellipsoids/Spheroids are ‘wider’ than they are ‘tall’.

In this diagram the length of ‘a’ is greater than the length of ‘b’.

Be warned, the use of the terms Ellipsoid and Spheroid can be very confusing as they are used interchangeably within the geodetic community

A Spheroid is simply an Ellipsoid which is as wide as it is long (ie evenly round and close in shape to that of a sphere).  All other Ellipsoids are longer than they are wide (ie shaped more like an Australian Rules football).

In Australia, most datums refer to the Australian National Spheroid.

The Earth as a Geoid

geoid_0.jpg
However, this is also a very simplistic concept.  The Earth in reality is a very misshapen object.  This is called a Geoid.

The Earth’s Geoid is a surface which is complex to accurately describe mathematically.  But it can be identified by measuring gravity.

The Earth’s Geoid is regarded as being equal to Mean Sea Level.  Over open oceans the Geoid and Mean Sea Level are approximately the same, but in continental areas they can differ significantly.  However, it must be noted that this difference it is not of any practical consequence for most people and and it is considered reasonable that they are regarded as the same.

Because of the Earth’s Geoid’s irregularity Geodesists have chosen to use Ellipsoids (or Spheroids) to calculate the location of latitude and longitude.

The Earth’s True Shape - Its Terrain

terrain_0.jpg
Of course the Earth isn’t just ocean (Mean Sea Level).  Much of the land masses are well above the sea level (eg Mount Everest is over 8,000 metres above Mean Sea Level), while in the ocean it is well below sea level (eg the Mariana Trench is over 10,000 metres below Mean Sea Level.

For more information see the section on Elevation in the sections on Cartographic Considerations andDatums 2.How These Relate to Each Other

In summary - there are four surfaces that geodesists study:
   » the Ellipsoid/Spheroid
   » the Geoid
   » Mean Sea Level
   » the Terrain

It is important to recognise that the relationship between these four surfaces is not always the same.  Rather, as this diagram indicates, they ‘wobble’ around each other.


(Please note that for this diagram the relationship between these four has been exaggerated so that you may better understand the nature of this ’wobbling’.)

cross_section_0.jpg

Four examples (A, B, C and D) have been chosen to describe how these relationships may change.

A and C show the Earths’ terrain as being below Mean Sea Level - this is equivalent to an area of ocean.  Note how the Geoid and Mean Seal Level are very close to the same value, but their relationship to the Ellipsoid/Spheroid varies.

B and D show the Earths’ terrain as being above Mean Sea Level - this is equivalent to an area of land.  It is worth noting that the differences between the Geoid and Mean Seal Level is much greater than in the ocean examples.  And, similarly, their relationship to the Ellipsoid/Spheroid varies.


With an understanding of these four geometric shapes and their relationships to each other it is possible to better understand Datums.


Explaining some Jargon - What is Geodesy

Because people who measure the shape of the Earth generally refer to the Earth as a Geoid, the following terms have been developed:

  • geodesy
    the study of the shape of the Earth and the determination of the exact position of geographical points
    (latitude, longitude and elevation)

  • geodetic
    an activity relating to geodesy

  • geodesist
    a person undertaking geodetic work


A Commonly Asked Question
"What is a geocentric datum and why do we need to use one?"

Because the Earth is so misshapen, when creating a datum to suit their country/region, geodesists have traditionally ’positioned’ the Ellipsoid/Spheroid so that it best matched the Geoid over their country.  These are commonly called Local or Regional Datum.  (AGD was a regional datum for Australia.)

The result of the use of Local Datums was that lines of longitude and latitude between different countries/regions would not connect evenly.  These mismatches were commonly over 100 metres - no big deal in the non-digital era, but with the arrival of the very popular Global Positioning System (GPS) technology this disagreement was no longer acceptable.  World-wide datums which would be used in all countries/regions began to be developed.  These are commonly called Geocentric Datums.

These two diagrams illustrate these two situations:


Local or Regional Datumsregional_0.jpg


This diagram represents the Australian Geodetic Datum which was created in 1984 (AGD84 or AGD).

Note how the Ellipsoid/Spheroid has been ’placed’ over Australia to best identify longitude and latitude.  If you used this datum in the northern hemisphere longitude and latitude would be very poorly identified on the surface of the Earth.

Geocentric Datums

geocentric_0.jpg
This diagram represents the Geodetic Datum of Australia which was created in 1994 (GDA94 or GDA).

This datum is part of a world-wide datum which is compatible with the USA Global Position System (GPS).

Note how the agreement with the Geoid is more even over the whole of the Earth and that the centre of the Earth is also the centre of the Ellipsoid/Spheroid.  This is an essential part of a Geocentric Datum because they are designed for use with Global Position Systems; and their satellites which orbit around the Earth’s central mass.


Further ReadingDatums 2: Datums Explained in More Detailhttp://www.icsm.gov.au/mapping/datums2.html





q1.jpg

q2.png




http://blog.sciencenet.cn/blog-856115-912556.html

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