Coordinate Systems And Map Projections Pdf
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- Map Projections and Coordinate Systems
- Land Management
- Map projection
- Coordinate Systems and Map Projections
The shape of the earth is roughly spherical wheres as maps are two dimensional. Map projection is a set of techniques designed to depict with reasonable accuracy the spherical earth in a two-dimensional i.
For details on it including licensing , click here. This book is licensed under a Creative Commons by-nc-sa 3. See the license for more details, but that basically means you can share this book as long as you credit the author but see below , don't make money from it, and do make it available to everyone else under the same terms. This content was accessible as of December 29, , and it was downloaded then by Andy Schmitz in an effort to preserve the availability of this book.
Map Projections and Coordinate Systems
Conad83 was originally written in to run on the HP computer system. In , Conad83 was rewritten to run on IBM-compatible computers. At that time there was a transcription error, and the south parallel parameter for Beltrami County North Zone was mistakenly set one degree too far south, which results in county coordinate positional errors on the order of one to three meters.
See below in the Lambert Zones table. The erroneous value persisted in the MnCon program that replaced the functionality of the Conad programs in and also appeared in some documentation of the Minnesota County Coordinate System, including this page.
This error was repaired in MnCon Version 1. Beginning with version 1. The uncorrected or bad value appears at the bottom of the lists and is included for the convenience of those who may need to convert from or to the old erroneous county coordinates. Any coordinate projections computed from Beltrami County North Zone coordinates are also suspect and should be examined.
No other counties, zones, or projections are affected. The following tables and examples provide the data needed to perform conversions of coordinates between map projections used in the State of Minnesota. Required parameters, examples of usage and methods of parameter calculation are listed for all projections used in Minnesota. Since different conversion packages give the parameters different names, all known aliases have been noted. For more information, please contact:. Click on the following links to jump to the associated topic:.
When UTM coordinates are used in Minnesota, Zone 15 is usually extended east and west to encompass the entire state within a single zone, which may be denoted as "Zone 15E" or "Zone 15 Extended. The parameters needed to convert to or from UTM Zone 15 are shown below. More detailed examples showing complete conversions are shown in the NAD83 Minnesota County Coordinate System section of this document.
The Semi-major Axis can also be called the Equatorial Radius. It is represented by the letter a in equations. The Semi-minor Axis can also be called the Polar Radius. It is represented by the letter b in equations. The Longitude of Origin may also be called the Central Meridian. A process of trial and error may be necessary to determine the correct terminology.
The parameters needed to convert to or from the Minnesota North State Plane zone are shown below. For the purpose of listing their parameters, they are separated into tables according to their mapping projections.
The Semi-major Axis, or Equatorial Radius, is represented by the letter a in equations. The Semi-minor Axis, or Polar Radius, is represented by the letter b in equations. The following constants apply for all Minnesota counties defined with Lambert projections:. The ellipsoid height must be added to the standard GRS80 semi-major axis.
If you are using a map projection conversion from a commercial software package you will need to create a user defined ellipsoid. This generally requires the lengths of the semi-major axis and the semi-minor axis. Both are available in the table above. The length of the semi-minor axis of the ellipsoid was computed is as follows:. The scale factor is entered typically as PPM, or parts per million, but a trial-and-error process may be necessary, since some programs expect positive values, while others expect negative values.
The correct value of 48 07 00 is now shown above. It uses the same two projection files:. Note: St. Louis County has developed the St. Louis County Transverse Mercator Coordinate System 96 that provides a single map projection for the entire county. Map scaling error is generally limited to less than one part in 40, This projection is included in MnCon , and its parameters are provided below:. When the Minnesota County Coordinate System was designed by University of Minnesota surveying professor Gerald Johnson and some graduate students, the only parameters identified for transverse mercator counties were the central meridian, the latitude of grid origin, and an ellipsoid height.
They used the same false northing They set the grid scale factor at the central meridian to 1. Ellipsoid height is not used in James Stem's manual nor in map projection conversions in commercial software packages. In the Minnesota County Coordinate System the ellipsoid height is used in some extra steps beyond those shown in Stem's equations. Obviously, commercial software packages cannot be changed to handle this.
Instead you can account for the use of the ellipsoid height by making some minor adjustments to the grid scale factor at the central meridian and the false northing and easting. The method of making these adjustments is shown below. The results from these adjusted parameters give answers that match the original method to the nearest millimeter.
The adjusted parameters were listed in the above table of parameters for transverse mercator zones. False Northing and False Easting were computed on a trial and error basis to give the best results possible for points at the extreme edges of the county using the following procedure. Then, using the map projection conversion from a commercial software package, a transverse mercator projection was defined.
The central meridian and latitude of origin were from the above table. The scale factor was computed as shown in the equation above. The false northing was Next, the same latitudes and longitudes representing the corners of the counties were entered into the map projection conversion from the commercial package.
The difference between the true county coordinates and the commercial software package's results were averaged and added to the false northing and easting. The transverse mercator projection was redefined using the new false northing and easting. Finally, the conversions were re-run on the commercial software package. In all cases, the results were within 1 mm of the true county coordinates. It doesn't require two steps like in the case for the Lambert conformal conic counties because the ellipsoid is not changed.
It uses the same projection file:. The Oblique Mercator parameters for map projection conversions in commercial software packages have not been determined. The following constants apply for all Minnesota county zones defined with the Oblique Mercator projection:. When the Minnesota County Coordinate System was designed by University of Minnesota surveying professor Gerald Johnson and some graduate students, they added some extra steps for oblique mercator formulas to minimize the difference between ground distances and map distances.
As stated above, no one has yet determined how to make them work in map projection conversions in commercial software packages. The state plane coordinates from each datum, however, are different by about , m for Y and , m for X due to the use of different false northings and false eastings.
Another method for computing to or from NAD27 state plane coordinates used the following set of parameters. In order to achieve a coordinate system in which map distances closely matched ground distances, the Minnesota Department of Highways developed the Minnesota Project Coordinate System. In it, the State of Minnesota was divided into a grid of rectangles measuring 15 minutes of latitude by one degree of longitude.
For example zone is bounded by 94 degrees longitude to the west, 45 degrees latitude to the north, 93 degrees longitude to the east and 44 degrees, 45 minutes latitude to the south. Parameters consisting of a combined factor, X constant and Y constant were established for each project coordinate system zone that was defined by one of these rectangles.
More information about this was written by Robert B. Roscoe, P. The portions of these zones that have a National Geodetic Vertical Datum of elevation below feet have been given different parameters than the rest of those zones to provide better results. Some counties have defined project zones that cover different, often larger, areas than the original rectangles.
This enabled all county mapping to be done in one or two or three zones rather than dealing with many of the rectangular one degree by 15 minute zones. The formulas are identical to those used in the Minnesota Project Coordinate System.
The parameters for known project zones created for counties are as follows:. Converting data between the North American Datum of and the North American Datum of is not a simple task, since no direct mathematic relationship exists between them. There are, however, several ways to convert data.
The appropriate method for any situation depends mostly on accuracy requirements. If a high degree of accuracy is required, additional information is necessary.
For example, the coordinates of some points in a data set from both datums will be needed. In addition, best results can be achieved if surveying measurements between data set points are available. The most accurate way to convert data from one datum to the other is not always feasible. It is the case where coordinates are known from both datums for one or more control points that are part of the data set and measurements from those control points s are available to all the other points in the data set.
In this situation, the way to convert the data set to the other datum is by starting with the other datum's coordinates on the control point s and recomputing the coordinates of all the other points based on the measurements from the control points. This method will definitely provide data that is sufficiently accurate for engineering or surveying uses.
The next most accurate method is for the case where coordinates are known from both datums for three or more points in a data set, but measurements are not available. In this situation, a transformation algorithm can be used to compute the relationship between the two datums and apply it to the other points in the data set.
This method may provide data that is sufficiently accurate for engineering or surveying uses, depending on the geographic extent of the data set being converted and the statistical results of the transformation. If accuracy is not as important, there are several tools that can be used to convert between datums. The U. Both of these programs are available from the National Geodetic Survey.
Introduction The following tables and examples provide the data needed to perform conversions of coordinates between map projections used in the State of Minnesota.
GIS data differs from other data types, primarily because it contains geographic coordinates describing the location of the data on the earth. Registration Policy. GDC Registration. Skip to main content. Topics Principles of geographic coordinate systems Principles of projections Extracting projection information from datasets Identifying when a layer is missing projection information Deciding how to pick a projection for your project Projecting data from one geographic coordinate system or projection into another Wiki page Introduction to Coordinate Systems Tutorial.
In cartography , a map projection is a way to flatten a globe 's surface into a plane in order to make a map. This requires a systematic transformation of the latitudes and longitudes of locations from the surface of the globe into locations on a plane. Depending on the purpose of the map, some distortions are acceptable and others are not; therefore, different map projections exist in order to preserve some properties of the sphere-like body at the expense of other properties. The study of map projections is the characterization of the distortions. There is no limit to the number of possible map projections. However, "map projection" refers specifically to a cartographic projection.
There are several ways to refer to a coordinate system. Some people casually refer to any coordinate system as a "projection", but this is not strictly true. CRS appears to be the increasingly popular choice, and it's a lot shorter to type than "coordinate system. Unlike local surveys, which treat the Earth as a plane, the precise determination of the latitude and longitude of points over a broad area must take into account the actual shape of the Earth.
The magic of geographic information systems is that they bring together and associate representations from diverse sources and infer relationships based on spatial references. This ability depends on our data sources using well defined coordinate referencing systems. This is not to say that the coordinate systems need to be the same for each data source, only that the relationship between the coordinate references with some shared conception of the surface of the earth needs to be well described.
- Что же это за цикличная функция, над которой три миллиона процессоров бьются уже шестнадцать часов. Он постоял в нерешительности, раздумывая, не следует ли поставить в известность начальника лаборатории безопасности. Да будь они прокляты, эти криптографы. Ничего не понимают в системах безопасности. Присяга, которую Чатрукьян принимал, поступая на службу в АНБ, стала непроизвольно прокручиваться в его голове.
Повернувшись, она увидела, как за стеной, в шифровалке, Чатрукьян что-то говорит Хейлу. Понятно, домой он так и не ушел и теперь в панике пытается что-то внушить Хейлу. Она понимала, что это больше не имеет значения: Хейл и без того знал все, что можно было знать.
Coordinate Systems and Map Projections
Голос Грега Хейла эхом отдавался в ее сознании: Сьюзан, Стратмор меня убьет, коммандер влюблен в. Она подошла к огромному круглому порталу и начала отчаянно нажимать кнопки. Дверь не сдвинулась с места.
Передо мной лежит отчет, из которого следует, что ТРАНСТЕКСТ бьется над каким-то файлом уже восемнадцать часов и до сих пор не вскрыл шифр. Джабба обильно полил приправой кусок пирога на тарелке. - Что-что.
Она показала на экран. Все глаза были устремлены на нее, на руку Танкадо, протянутую к людям, на три пальца, отчаянно двигающихся под севильским солнцем. Джабба замер. - О Боже! - Он внезапно понял, что искалеченный гений все это время давал им ответ. - Три - это простое число! - сказала Соши. - Три - это простое число. Фонтейн пребывал в изумлении.
Сьюзан обшарила весь жесткий диск и в конце концов нашла папку электронной почты, тщательно запрятанную среди других директорий. Открыв ее, она увидела несколько дополнительных папок; создавалось впечатление, что у Хейла было множество почтовых адресов. Один из них, к ее удивлению, был адресом анонимного провайдера. Сьюзан открыла одно из старых входящих сообщений, и у нее тотчас же перехватило дыхание. ТО: NDAKOTAARA.
Действительно хорошая новость. ГЛАВА 54 - Пусти. А потом раздался нечеловеческий крик. Это был протяжный вопль ужаса, издаваемый умирающим зверем. Сьюзан замерла возле вентиляционного люка.
Нет, Мидж. Это абсолютно исключено. - Спасибо. Джабба выдавил из себя смешок и попытался обратить все в шутку. - Если только Стратмор не придумал что-то особенное и не обошел мои фильтры.
Беккер прекрасно помнил все, что произошло, и опустил глаза, думая увидеть перед собой своего убийцу. Но того человека в очках нигде не. Были другие люди. Празднично одетые испанцы выходили из дверей и ворот на улицу, оживленно разговаривая и смеясь.