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- Introduction to Coordinate Systems and Projections
- Geographic Information Systems and Geomatics
- Part 2: A Projection Demo:
- Introduction to Coordinate Systems and Projections

Handbook of Satellite Applications pp Cite as. The role of spatial data for decision making has increased the need for geographic information systems. This chapter starts by briefly describing the theory of geographic information systems.

## Introduction to Coordinate Systems and Projections

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.

Indeed, there are thousands of perfectly legitimate coordinate systems in active use. The notion of spatial referenicing systems is one of the most fundamental and interesting ideas that all users of GIS should understand. This document provides an overview of the basic ideas. Latitude and Longitude provide a framework for referencing places on the earth.

It is interesting that an understanding that is thousands of years old continues to be near the cutting edge of our cybernetic culture. To tie this lecture together with the previous lecture on the context of geographic information systems, we will return to our framework for Geographic Models for Decision Support.

Topographic maps are assumed to provide a scale that can be measured in the same units no matter the direction. Latitude and Longitude are a way to distinctly reference any location on the planet. But Latitude and longitude are angular measures. They may be portrayed as if they were cartesian, but in most cases, this will distort sshape and distance such that using a scale to infer distance wil have very substantial errors.

Creating reasonable portrayals of places requires us to understand how latitude and longitude reference a places on the planet, AND how latitude and longitude are transformed into cartesian coordinate systems that uphold the assumption that a map reflects consistent scale, direction, and shape proportion corresponding with the things and relationships being represented. When you gather together data for north america, you will find data registerd to the North American Datum of , The World Geodetic Spheroid of , and occaisionally the North American Datum of Data collected in other parts of the world likely use other local datums.

Mis-specifying the earth model for a dataset can lead to displacements in your ground measurements of as much as 20 meters! One fundamental assumptions about topographic maps of places include the followiong: the map has a scale that can be used to measure distances all over the map, that the shapes that are represented on the map are a reasonable approximation of the shapes the cardinal directions are at right angles to one-another. These assumptions are generally termed the assumption of Planimetric Scale.

They are also the same assumptions of Cartesian coordinate systems that allow us to use plane geometry to infer distances. Furthermore, they seem to be rather instinctive in human beings, in as much as if you show a person a map that violates these assumptions, you are in effect tricking that person into faulty conclusions about your subject.

A very common instance of this sort of trap arises from the fact that datasets we are given often reference locations of points and vertices with decimal degrees of latitude and longitude. And mapping software will graphically portray the geometry so described as if latitude and longitude were coordinates in a cartesian sense. Yet, latitude and longitude are polar coordinates.

A degree of Longitude does not have a constant scale in terms of distances on the earth. At the equator, this distance is approximately km. Near the poles, an entire degree could be spanned by your little toe! The map of Massachusetts in unprojected Decimal Degrees of Longitude and Latitude Note the proportion of the lines and the circle. The circle gives the impression that Worcester is approximately the same distance from Boston as New Hampshire, and that the state is nearly five times longer, east to west, as it is north-to-south.

This misrepresentation of proportion has the same effect no matter how close you are zoomed in. Compare with the same data layers transformed according to the Massachusetts State Plane coordinate system system This shows an image that is much truer relative to distances you would actually experience on the ground.

Worcester is actually much closer than it appeards before. And the state is only 3 times longer than it is tall. The grid on each map is one degree on a side. Using degrees of longitude and latitude as a cartesian coordinate system makes the grids appear square. But ion at the latitude of Massachusetts, the race of one degrees of longitude is much shorter than a degree of latitude.

Transformation of Geographical Coordinates to Cartesian Coordinate Systems While the system of latitude and longitude provides a consistent referencing system for anywhere on the earth, and it is therefore used in geographic databases that are not specific to a particular place.

However, in order to portray our information on maps or for making calculations, we need to transform these angular measures to cartesian coordinates. These transformations amount to a mapping of geometric relationships expessed on the shell of a globe to a flattenable surface -- a mathematical problem that is figurastively refered to as Projection. It turns out that any way you try to do this, you must unavoidably incorporate some distortion into the picture.

Any projection has its area of least distortion. Projections can be shifted around in order to put this area of least distortion over the topographer's area of interest. Thus any projection can have an unlimited number of variations or cases that determined by standard paralells or meridians that adjust the location of the high-accuracy part of the projection.

Projection Cases In the case of the orthographic projection above, the area of least distortion is occurs where the figurative projection plane touches the model of the earth.

To create a projection that works well for a particular area, we can create a case of the orthographic projection that has its point of tangency wherever we want:. Other projection methods are based on more complicated flattenable projection surfaces, and instead of points of tangency, spacial cases of these projections can be made by adjusting their Standard Parallels or Central Meridians. These images are by Erwin Raisz, who worked at the Harvard Institute for Geographical Exploration between and and wrote many fine books on cartography and topography.

Presentation of uniform scale is not always the goal when using maps as graphical calculators. A case in point is the Mercator's Cylyndrical Projection , which is unique among projections in terms of portraying lines of constant compass direction rhumb lines as straight lines on the map, as shown on this site by Carlos A Furuti.

In a zone along its standard paralell, the Mercator projection has good scale and shape and direction presentation along with its property that makes a a terriffic tool for aiming missles and artillery!

This is why the Transverse Case of the Mercator projection was invented and is in such common use in broad-scale series of national mapping projects.

And now we can project and unproject massive quantities of coordinates, transforming them backward and forward from Latitude and Longitude assuming this or that earth model to overlay precisely with data that are stored in some other coordinate space. We can be thankful for that. But there are still some details that we have to understand. Automatic transformation of coordinate systems requires that datasets include machine-readable metadata. In about , the makers of ArcMap added one more file to the schema of a shape file.

And this information wil lallow arcmap to do whatever transformation is necessary to get t6hat data to overlay corectly with other data regardless of the projection. There are plenty of datasets that do not include such machine readable metadata. So we should get used to understanding map projections and their properties.

Given that geographic datasets are primarly concerned with spatial references, we really must have metadata data about the data describing the coordinate system that is embedded in the files. Here is an example of the FGDC Content Standards for Geospatial Metadata regarding Coordinate Systems But in actuality, because most datasets make use of special cases of projections, much of this metadata can be generated automatically if we know the following facts about the coordinate system of a dataset:.

Even though the projection method is almost always some sort of very long system of equations, for which the cases plug in several parameters, there are conventions for projections and cases that have handy names, like the State Plane Coordinate System used by most state and local government agencies in the U. Other countries have their National Grid projections. And almost always, systems of quadrangle maps use some variation of the Universal Transverse Mercator system of projectons and cases that divides the world into 60 longitudinal zones.

Situation 1 is when presenting data on a map. The other is when data are encoded for the purposes of spatial analysis or overlaying with other data. For a map with a scale finer than, say ,, the choice of projection establishes whether or not North and East stretch out at right angles and whether the a units of X and Y are nearly equal regardless of what direction of your measurement. The choice of projection establishes whether people can assume that shapes you draw on the map have any actual geometric correspondence with the actual geometry of the place on the ground.

For a person who must judge whether your map is actually useful will get confirmwation of you declare what projection has been applied. A projection declaration should state what projection method and case has been employed to transform the geometry of the earth to a flat screen or sheet of paper.

An example of a projection method, would be "Lamberts Conformal Conic. Units are meters. Some imagery for Martha's Vineyard and Nantucket are also available in the Mass.

Stateplane Island Zone. Another projection you might have chosen for a fine-scale map of Eastern Massachusetts might be declared as Projection: Universal Transverse Mercator Zone When encoding and exchanging data. Geographic data identify the relative location of vertices or pixels -- relative to eachother -- using coordinates. In order for a computer application to overlay data sets having different coordinate systems, each data set must have a very specific declaration that explains how the coordinates used in the data relate to the surface of the planet.

For the purposes of overlaying data in computers much more specific information is required about specific parameters assumed for the shape of the planet Earth Model Examples of Earth Models include: North American Datum of , or World Geodetic Spheroid of Misidentifying the earth model for a dataset can result in apparent shifts in terms of the overlay of one data set on another of up to a couple of meters see the maps on page 17 of NOAA Technical Memorandum NOS NGS Assuming that each data set has its projection identified correctly, then the GIS program can be assumed to be doing an adequate job of overlaying the individual data layers adequately.

In this situation, the cartographer can ask the GIS to reproject all of the data to suit the geometric properties that are desired for the map at hand. The choice of an earth model does not affect the gross geometry of the map in any sense that a person would be able to see.

Credibility is a make-or-break issue for cartographers. Educated map users will attempt to assess the credibility of an analyst by looking for careful choice of words when speaking about data, attribution of source material and declaring the critical transformations that that have been applied. You will gain credibility points by declaring what is necessary to declare and not asking people to dwell on details that are irrelevant, redundant or unfounded. You should definitely avoid using abbreviations that you have not expanded.

The habit of tracking down and expanding abbreviations before you use them will save you from the oblivious embarrassment of using terms that you don't understand. Aside from being a very important and interesting and continuing thread in the history of humanity's struggle to understand their surroundings, the evolving understanding and application of Geodesy and Topography offer a very important lesson for anyone who would attempt to understand the world through representations or models. Understading the logic of one's referencing systems is crucial to understanding the utility of your conclusions.

Choosing a projection means choosing one sort of error over another. This sort of choice comes into play with almost every decision that an educated person makes when creating and evaluating maps and GIS. Our assignment is to make maps of regional and local context. On maps of this scale, we should assume that the assumptions of topographic interpretation will apply, namely:. Our map-making task begins by understanding how ArcGIS transforms the geometry expressed in our data -- which may have their geometry encoded using any number of different coordinate systems that do not have the properties described above.

Our GIS must transform these data into a map projection that does have these properties. This means we have to choose an appropriate projection method and case for our subject area. Having added this Here we will observe that ArcMap sets the map projection of our Data Frame to adopt the native projection of the datasets that we open. To make this clear, we will begin by opening some world-wide reference layers that will help us choose an appropriate projection for our map.

## Geographic Information Systems and Geomatics

You are viewing an old version of this page. View the current version. Compare with Current View Page History. If you find these tutorials useful and would like to link to them from your own pages,please contact the Drew Spatial Data Center Director, Dr. Catherine Riihimaki via email. You are invited to leave comments or ask questions in any of the Comment areas of each tutorial page.

It also allows the user to define custom coordinate reference systems and supports on-the-fly OTF projection of vector and raster layers. All of these features allow the user to display layers with different CRSs and have them overlay properly. Normally, you do not need to manipulate the database directly. In fact, doing so may cause projection support to fail. Custom CRSs are stored in a user database.

## Part 2: A Projection Demo:

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.

Each polygon would represent an area such as a field, water body or building boundary. For example, your area of interest may be a school campus and all of the buildings, parking lots, sports fields and bike lanes that fall within that area. This information can typically be mapped. These help provide references and added background information to your GeoPortal search and results.

### Introduction to Coordinate Systems and Projections

A geographic coordinate system GCS defines locations on the earth using a three-dimensional spherical surface [1] , it is a reference system that uses latitude and longitude to identify locations on a spheroid or sphere. A datum , prime meridian , and angular unit are parts of a GCS [2]. The Earth is not a sphere , but an irregular shape approximating an ellipsoid ; the challenge is to define a coordinate system that can accurately state each topographical point as an unambiguous tuple of numbers [3]. Latitude abbreviation: Lat.

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.

ArcGIS and ArcGIS Pro Projected Coordinate System Tables. Note: Values may be rounded for display. Area of use values are in decimal degrees.

#### Your Answer

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.

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. Indeed, there are thousands of perfectly legitimate coordinate systems in active use. The notion of spatial referenicing systems is one of the most fundamental and interesting ideas that all users of GIS should understand. This document provides an overview of the basic ideas. Latitude and Longitude provide a framework for referencing places on the earth.

Enroll now! Learn more. On the previous page, you explored the basic concept of a coordinate reference system. You looked at two different types of Coordinate Reference Systems:. As you discussed in the previous lesson, each CRS is optimized to best represent the:. Some CRSs are optimized for shape, some are optimized for distance and some are optimized for area. Geographic coordinate systems which are often but not always in decimal degree units are often optimal when you need to locate places on the Earth.

It only takes a minute to sign up. Can somebody please explain what is the difference between the Coordinate system WGS 84 for example and a Projection Universal Transverse Mercator for example? Both examples are coordinate systems.

Она не могла поверить, что такой алгоритм может быть создан, но ведь доказательство налицо - у нее перед глазами. ТРАНСТЕКСТ не может с ним справиться. Сьюзан подумала о Стратморе, о том, как мужественно он переносит тяжесть этого испытания, делая все необходимое, сохраняя спокойствие во время крушения. Иногда она видела в нем что-то от Дэвида. У них было много общего: настойчивость, увлеченность своим делом, ум.

- Он покачал головой, словно не веря такую удачу. - Чертовское везение, если говорить честно. - Он, казалось, все еще продолжал сомневаться в том, что Хейл оказался вовлечен в планы Танкадо. - Я полагаю, Хейл держит этот пароль, глубоко запрятав его в компьютере, а дома, возможно, хранит копию.

Это звучало вполне логично: Танкадо хотел заставить АНБ рассказать о ТРАНСТЕКСТЕ всему миру. По сути, это был самый настоящий шантаж. Он предоставил АНБ выбор: либо рассказать миру о ТРАНСТЕКСТЕ, либо лишиться главного банка данных. Сьюзан в ужасе смотрела на экран. Внизу угрожающе мигала команда: ВВЕДИТЕ КЛЮЧ Вглядываясь в пульсирующую надпись, она поняла .

Полагаю, Росио и ее гость ушли на вечернюю прогулку. Если вы оставите для нее записку, она получит ее прямо с утра. - Он направился к полке с ячейками для ключей и почты.

*PGP, Lucifer, DSA - не важно. Алгоритм создает шифр, который кажется абсолютно стойким, а ТРАНСТЕКСТ перебирает все варианты, пока не находит ключ. Стратмор ответил ей тоном учителя, терпеливого и умеющего держать себя в руках: - Да, Сьюзан, ТРАНСТЕКСТ всегда найдет шифр, каким бы длинным он ни .*