Coordinate Systems And Map Projections Pdf

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A revised and expanded new edition of the definitive English work on map projections. The revisions take into account the huge advances in geometrical geodesy which have occurred since the early years of satellite geodesy. Additionally, the chapter on computation of map projections is updated bearing in mind the availability of pocket calculators and microcomputers.

Map Projections and Coordinate Systems

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. Normally, the author and publisher would be credited here. However, the publisher has asked for the customary Creative Commons attribution to the original publisher, authors, title, and book URI to be removed. Additionally, per the publisher's request, their name has been removed in some passages.

More information is available on this project's attribution page. For more information on the source of this book, or why it is available for free, please see the project's home page. You can browse or download additional books there. To download a. All map users and map viewers have certain expectations about what is contained on a map. Such expectations are formed and learned from previous experience by working with maps. It is important to note that such expectations also change with increased exposure to maps.

Understanding and meeting the expectations of map viewers is a challenging but necessary task because such expectations provide a starting point for the creation of any map. The central purpose of a map is to provide relevant and useful information to the map user.

In order for a map to be of value, it must convey information effectively and efficiently. Mapping conventions facilitate the delivery of information in such a manner by recognizing and managing the expectations of map users.

Generally speaking, mapping or cartographic conventions refer to the accepted rules, norms, and practices behind the making of maps. Though this may not always be the case, many map users expect north to be oriented or to coincide with the top edge of a map or viewing device like a computer monitor.

Several other formal and informal mapping conventions and characteristics, many of which are taken for granted, can be identified. Among the most important cartographic considerations are map scale, coordinate systems, and map projections.

Map scale is concerned with reducing geographical features of interest to manageable proportions, coordinate systems help us define the positions of features on the surface of the earth, and map projections are concerned with moving from the three-dimensional world to the two dimensions of a flat map or display, all of which are discussed in greater detail in this chapter.

The world is a big place…really big. One of the challenges behind mapping the world and its resident features, patterns, and processes is reducing it to a manageable size. Nonetheless, all maps reduce or shrink the world and its geographic features of interest by some factor.

Map scale The factor by which phenomena on the surface of the earth are reduced in order to be shown on a map. Map scale can be represented by text, a graphic, or some combination of the two.

Map scale can also be portrayed graphically with what is called a scale bar. Scale bars are usually used on reference maps and allow map users to approximate distances between locations and features on a map, as well as to get an overall idea of the scale of the map.

Figure 2. The representative fraction RF describes scale as a simple ratio. The numerator, which is always set to one i. One of the benefits of using a representative fraction to describe scale is that it is unit neutral. In other words, any unit of measure can be used to interpret the map scale. Consider a map with an RF of , This means that one unit on the map represents 10, units on the ground.

Such units could be inches, centimeters, or even pencil lengths; it really does not matter. For instance, a map with an RF of , is considered a large-scale map when compared to a map with an RF of ,, i. Furthermore, while the large-scale map shows more detail and less area, the small-scale map shows more area but less detail.

Clearly, determining the thresholds for small- or large-scale maps is largely a judgment call. All maps possess a scale, whether it is formally expressed or not.

Understanding map scale and its overall impact on how the earth and its features are represented is a critical part of both map making and GISs. Just as all maps have a map scale, all maps have locations, too. Coordinate systems Frameworks used to determine position on the surface of the earth. For instance, in geometry we use x horizontal and y vertical coordinates to define points on a two-dimensional plane. A spheroid a. Spheres are commonly used as models of the earth for simplicity.

The unit of measure in the GCS is degrees, and locations are defined by their respective latitude and longitude within the GCS. Latitude is measured relative to the equator at zero degrees, with maxima of either ninety degrees north at the North Pole or ninety degrees south at the South Pole.

Longitude is measured relative to the prime meridian at zero degrees, with maxima of degrees west or degrees east. Note that latitude and longitude can be expressed in degrees-minutes-seconds DMS or in decimal degrees DD. When using decimal degrees, latitudes above the equator and longitudes east of the prime meridian are positive, and latitudes below the equator and longitudes west of the prime meridian are negative see the following table for examples.

When we want to map things like mountains, rivers, streets, and buildings, we need to define how the lines of latitude and longitude will be oriented and positioned on the sphere.

A datum serves this purpose and specifies exactly the orientation and origins of the lines of latitude and longitude relative to the center of the earth or spheroid. Depending on the need, situation, and location, there are several datums to choose from.

For locations in the United States and Canada, NAD83 returns relatively accurate positions, but positional accuracy deteriorates when outside of North America. The global WGS84 datum i. Because the datum uses the center of the earth as its origin, locational measurements tend to be more consistent regardless where they are obtained on the earth, though they may be less accurate than those returned by a local datum.

Note that switching between datums will alter the coordinates i. Previously we noted that the earth is really big. Not only is it big, but it is a big round spherical shape called a spheroid. A globe is a very common and very good representation of the three-dimensional, spheroid earth. One of the problems with globes, however, is that they are not very portable i.

To overcome these issues, it is necessary to transform the three-dimensional shape of the earth to a two-dimensional surface like a flat piece of paper, computer screen, or mobile device display in order to obtain more useful map forms and map scales. Enter the map projection. Map projections The mathematical formulae used to tranform locations from a three-dimensional, spherical coordinate system to a two-dimensional planar system. Specifically, map projections are mathematical formulas that are used to translate latitude and longitude on the surface of the earth to x and y coordinates on a plane.

Since there are an infinite number of ways this translation can be performed, there are an infinite number of map projections. The mathematics behind map projections are beyond the scope of this introductory overview but see Robinson et al.

Map Use. To illustrate the concept of a map projection, imagine that we place a light bulb in the center of a translucent globe. On the globe are outlines of the continents and the lines of longitude and latitude called the graticule. Within the realm of maps and mapping, there are three surfaces used for map projections i. These surfaces are the plane, the cylinder, and the cone. Referring again to the previous example of a light bulb in the center of a globe, note that during the projection process, we can situate each surface in any number of ways.

For example, surfaces can be tangential to the globe along the equator or poles, they can pass through or intersect the surface, and they can be oriented at any number of angles.

In fact, naming conventions for many map projections include the surface as well as its orientation. When moving from the three-dimensional surface of the earth to a two-dimensional plane, distortions are not only introduced but also inevitable. Generally, map projections introduce distortions in distance, angles, and areas. Depending on the purpose of the map, a series of trade-offs will need to be made with respect to such distortions. Map projections that accurately represent distances are referred to as equidistant projections.

Note that distances are only correct in one direction, usually running north—south, and are not correct everywhere across the map. Equidistant maps are frequently used for small-scale maps that cover large areas because they do a good job of preserving the shape of geographic features such as continents. Maps that represent angles between locations, also referred to as bearings, are called conformal.

Conformal map projections are used for navigational purposes due to the importance of maintaining a bearing or heading when traveling great distances.

The cost of preserving bearings is that areas tend to be quite distorted in conformal map projections. Though shapes are more or less preserved over small areas, at small scales areas become wildly distorted. The Mercator projection is an example of a conformal projection and is famous for distorting Greenland. As the name indicates, equal area or equivalent projections preserve the quality of area. Such projections are of particular use when accurate measures or comparisons of geographical distributions are necessary e.

In an effort to maintain true proportions in the surface of the earth, features sometimes become compressed or stretched depending on the orientation of the projection. Moreover, such projections distort distances as well as angular relationships. As noted earlier, there are theoretically an infinite number of map projections to choose from. One of the key considerations behind the choice of map projection is to reduce the amount of distortion.

The geographical object being mapped and the respective scale at which the map will be constructed are also important factors to think about. For instance, maps of the North and South Poles usually use planar or azimuthal projections, and conical projections are best suited for the middle latitude areas of the earth. Features that stretch east—west, such as the country of Russia, are represented well with the standard cylindrical projection, while countries oriented north—south e.

If a map projection is unknown, sometimes it can be identified by working backward and examining closely the nature and orientation of the graticule i.

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. Map projection types are created by an imaginary source of light projected inside the earth. Common Map Projections. Exploring Map Projections Created using D3, Map Projection Transitions provides an excellent way to visualize a wide range of map projections. What is a Map Projection?

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. Normally, the author and publisher would be credited here. However, the publisher has asked for the customary Creative Commons attribution to the original publisher, authors, title, and book URI to be removed.

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.

Map Projections and Coordinate Systems

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.

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.

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.

Map Projections and Coordinate Systems

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.

Тогда они оба подумали, что он где-то допустил ошибку, но сейчас-то она знала, что действовала правильно. Тем не менее информация на экране казалась невероятной: NDAKOTA ETDOSHISHA. EDU - ЕТ? - спросила Сьюзан. У нее кружилась голова.  - Энсей Танкадо и есть Северная Дакота.

 - Нам нужно установить разницу между этими элементами.  - Он повернулся к бригаде своих помощников.  - Кто знает, какая разница между этими элементами. На лицах тех застыло недоумение.

Она окинула его высокомерным взглядом и швырнула отчет на стол. - Я верю этим данным. Чутье подсказывает мне, что здесь все верно. Бринкерхофф нахмурился.

Map projection

Тот поднес его к глазам и рассмотрел, затем надел его на палец, достал из кармана пачку купюр и передал девушке.

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