Coordinate Systems And Map Projections Making Pdf

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In the latest GeoJSON specification , the coordinate reference system for all coordinates is a geographic coordinate reference system—using the World Geodetic System WGS 84 datum—with longitude and latitude units of decimal degrees. The previous specification allowed for the use of alternative coordinates systems, but this was removed because of interoperability issues. Occasionally, this may cause a problem of improperly formatted files that contain projected coordinates but have no specified coordinate system.

Various software for Geographical Information Systems GISs have been developed and used in many different engineering projects. In GIS applications, map coverage is important in terms of performing reliable and meaningful queries. Map projections can be conformal, equal-area and equidistant. The goal of an application plays an important role in choosing one of those projections. Choosing the equal-area projection for an application in which area information is used forestry, agriculture, ecosystem etc reduces the amount of distortion on the area, but many users using GIS ignore this fact and continue to use applications with present map sheets no matter in what map projection it is.

Part 2: A Projection Demo:

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.

Selecting Map Projections in Minimizing Area Distortions in GIS Applications

This is not a simple as it sounds. These seven images are viewed over the Equator. In each of these views the central area is clear, but at the edges shapes are distorted. Beyond the Equator you need to twist your point of view to look directly at the area you are interested in. By way of example, note the way that Arctic, Antarctica and Australia appear on these views compared to when you look at them from the Equator see above images.

Accurately describing locations on Earth is essential to exploration geophysics. The interpretation of fault zones, the surface and bottom locations of a well, and the position and orientation of seismic ground control points and receivers are all dependent on being able to accurately describe where they are. Unfortunately the latitude and longitude of a location and the height are not enough to describe where on Earth it is. There are numerous datums and projections to which the coordinates are referenced, and using the correct one can make the difference between successful exploration and expensive legal fees. There are also numerous applications for analyzing and interpreting spatial data, all of which have different methods for representing a three-dimensional position in two-dimensional space.

Elizabeth Borneman October 2, January 5, Maps. The ways in which we visualize the world are varied- we have pictures, maps, globes, satellite imagery, hand drawn creations and more. For centuries mankind has been making maps of the world around them, from their immediate area to the greater world as they understood it at the time. These maps depict everything from hunting grounds to religious beliefs and speculations of the broader, unexplored world around them. Maps have been made of the local waterways, trade routes, and the stars to help navigators on land and sea make their way to different locations. How we visualize the world not only has practical implications, but can also help shape our perspectives of the Earth we live in.

PDF | MSc Student Assignment Nr. 6 'Coordinates and Map Projections' on module 'Geographical Information Systems: Advanced Course (GISA02)' a set of mathematical equations allowing making this transformation.

Types of Map Projections

A map projection is a geometric function that transforms the earth's curved, ellipsoidal surface onto a flat, 2-dimensional plane. A map projection is an essential component of any modern map, and there are an infinite number of possible map projections. Since Gerardus Mercator presented his Mercator global map projection in , numerous map projections have been developed and scores of projections are currently used by cartographers today. Carl Friedrich Gauss's Theorema Egregium [2] proved that a sphere cannot be represented on a plane without distortion.

Datums, 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.

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.

This book offers a much-needed critical approach to the intelligent use of the wide variety of map projections that are rapidly and inexpensively available today. It also discusses the distortions that are immanent in any map projection. A well-chosen map projection is one in which extreme distortions are smaller than those in any other projection used to map the same area and in which the map properties match its purpose. Written by leading experts in the field, including W. Tobler, F. Kessler, S.

Nearly all projections are applied via exact or iterated mathematical formulas that convert between geographic latitude and longitude and projected X an Y .

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Map projections try to portray the surface of the earth or a portion of the earth on a flat piece of paper or computer screen. A coordinate reference system CRS then defines, with the help of coordinates, how the two-dimensional, projected map in your GIS is related to real places on the earth. The decision as to which map projection and coordinate reference system to use, depends on the regional extent of the area you want to work in, on the analysis you want to do and often on the availability of data. There is, however, a problem with this approach. They are also only convenient to use at extremely small scales e. Most of the thematic map data commonly used in GIS applications are of considerably larger scale. Typical GIS datasets have scales of or greater, depending on the level of detail.

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