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property depends largely on the purpose of the map. lines, the parallels are unequally spaced circles centered at the pole (figure below). A conformal projection will have distortion ellipses that vary substantially in size, but are all the same circular shape. to enlarge). used in atlases for maps of the world, and for wall-maps as area distortions are significant towards the polar regions. The graticule refers to longitude and latitude on a three-dimensional globe. Spacing gradually increases away from the pole. All great circles - the shortest routes What professional responsibilities do ECEs, such as those depicted in the case study - The Sara's Confusing Behavior Case, Examine the coordinate system for thestreetsfeature class in theAustingeodatabase. Map scales. Parts of section 3.3 are adapted from DiBiase (1998). displaying the flow of oceanic or atmospheric currents, for instance.

It is equal to Lambert's equal area conic, but has two standard parallels (secant cone). from the central point (tangent plane) or closed line(s) of intersection increases. the equator. projections is however exceptional. All azimuthal projections possess the property of maintaining correct azimuths, or true directions from the centre of the map. A better projection is the Albers equal-area conic projection with two standard parallels, which is The Gall Peters projection is equal area. 5.Lambert azimuthal equal-area projection: The non-perspective Lambert azimuthal equal-area projection preserves areas while simultaneously maintaining a true direction from the center. Mercator projection. The Transverse Mercator The flattening of the ellipses towards the polar regions shows that shape distortions increase towards the polar regions. A subdivision may be made into perspective and non-perspective azimuthal projections. [18]. factor (ratio of the scale at a given point to the true scale). onto cones tangent to each parallel, so the meridians are curved, not The Mercator projection is a cylindrical map projection with a conformal property. Locations on the Earths surface are measured in terms of coordinates, a set of two or more numbers that specifies a location in relation to some reference system. nor equal-area and no point is free of distortion, but the distortions Area, shape, [5]. For beginning mapmakers, understanding the exact mechanics of projections doesnt matter as much as knowing which map properties are maintained or lost with the choice of projection the topic of the next section. Mainly used for educational purposes. Only one hemisphere can be shown. This topographic map has an RF of 1:24,000, which means that one unit on the map represents 24,000 units on the ground. The three possible apects are normal, transverse and oblique. A method to calculate the lines of intersection in a normal conical or cylindrical projection (i.e. Used in several atlases. at the projection centre, but increases moderately with distance equidistance are important properties.

The projection is also known as the Gauss-Krger or Gauss conformal. the Arctic and Antarctic regions. Recommended to the European Commission for statistical analysis and display. area distortions are often reasonably well preserved. by ellipses of distortion. An example is the Mercator projection. Optimal is when the projection centre coincides with centre of the area, or when the projection plane is located depending on the shape of the area, with a secant projection plane located A forward mapping equation transforms the geographic coordinates (f,l) of a point on the curved reference surface to a set of planar Cartesian coordinates (x,y), representing the position of the same point on the map plane: The corresponding inverse mapping equation transforms mathematically the planar Cartesian coordinates (x,y) of a point on the map plane to a set of geographic coordinates (f,l) on the curved reference surface: Following are two examples of mapping equations for the sphere (equations for the ellipsoid are generally more complex). Suppose the same point, located at 60oN and 130oW, is projected on a map that uses the stereographic projection (where the reference surface is a sphere with a radius of 6371000 m., the centre of the projection is located on the North pole and the longitude of the centre (lo) is 0o). equidistance are important properties. Miller. - conformal cylindrical - met a real need,

Projected perspectively from the center of the Earth onto a cylinder tangent to the equator. Georeferencing and Coordinate If an area is approximately circular it is possible to create a map that minimizes distortion for that area on the basis of an azimuthal projection. The selected distortion The projection does not contain the noticeable distortions of the When we use longitude and latitude on a two-dimensional map, we refer to these as geographic coordinates. Shaded in the figure is UTM grid zone 3N which in several countries for topographic mapping purposes. GIS Commons: An Introductory Textbook on Geographic Information Systems, CC BY-NC-SA 4.0. The point at which both x and y equal zero is called the origin of the coordinate system. In the polar cases, the meridians all radiate out from the pole at their correct angular distance apart. This is a bit misleading because no projection can maintain relative distance between all places on the map. The transverse case and occasionally the oblique case of the Mercator projection are used maps, the distortions are not evident to the eye. Lambert projections. With the numerator always set to 1, the denominator represents how much greater the distance is in the world.

Selected by the National Geographic Society (NGS) for its new reference world map, in place of the Robinson, . (like a source of light rays), is the centre of the Earth. When projected directly onto the mapping plane it produces an azimuthal (or zenithal or planar) map projection. Maps used for the measurement of angles (e.g. The parallel spacing increases that scale distortions remain within certain limits and that map properties Used since 16th century. The distortion property of the map projection is therefore conformal (e.g. CC BY-NC-SA 4.0. Conformal projections should be used if the main purpose of the map involves measuring angles or representing the shapes of features. To represent parts of the surface of the Earth on a flat paper map or on a computer screen, the curved horizontal reference surface must be mapped onto the 2D mapping plane. Most pseudo-cylindrical projections are equal-area (certainly not conformal because the parallels and meridians do not always cross at right angles). The equidistant cylindrical projection (also called Plate Carre projection) is a cylindrical map projection with an equidistant property. Two well known non-perspective azimuthal projections Lambert conformal conic, also called conical orthomorphic (Lambert, 1972). Another descriptor of a map projection might be the name of the inventor (or first publisher) of It is adapted for maps of the United States, for thematic maps and for world atlases. (2012) Mapping our Changing World. similar map. Red lines or dots mark the tangent line or point respectively. along the main axis of the area to be mapped (source: P. H. Dana). The orthographic projection is a perspective projection that views the globe from an infinite distance. It is helpful to think about projections in physical terms. Frequently used for maps of the United States, for thematic maps and for world atlases. A Java tool for the demonstration of map projections with an option to show Tissot's indicatrices is given through the following external link: Demonstration A map can have a representative fraction, graphic scale, or verbal description that all mean the same thing. are suitable for sea, air, and meteorological charts. Scale decreases with distance from the center. Used for topographic maps at scales from 1: 20,000 to 1: 250,000. with distance from the equator (figure below). Put differently, if we were to change the scale of the map with an RF of 1:100,000 so that a section of road was reduced from one unit to, say, 0.1 units in length, we would have created a smaller-scale map whose representative fraction is 1:1,000,000. is a transverse cylindrical conformal projection. Some map projections have rather special properties. plane or cone) with respect to the globe. Interrupted projections such as the interrupted Goode Homolosine projection represent the earth in lobes, reducing the amount of shape and area distortion near the poles. Map projections with a conformal distortion property represent angles and local shapes correctly, but as the region becomes larger, they show considerable area distortions. (also called Plate Carre projection), where the meridians are true to scale map (i.e.

The choice of the aspect of a map projection Equidistant projections, as the name suggests, preserve distance. Mercator's projection - conformal cylindrical - met a real need, The three classes of map projections: cylindrical, conical and azimuthal. Recommended for conformal mapping of regions that are approximately circular in shape; a modified version of the stereographic projection is used in the Netherlands for large-scale and topographic maps.

One of the first maps of the world developed was by Mercator (Carta do Mundo de Mercator, 1569). It represents areas correctly and has reasonable shape distortions in the region between the standard parallels as compared with the noticeable distortions of the. It is for this reason that cylinders are often used for areas near the equator, cones used to map the mid-latitudes, and planes used for polar regions. should be aware of the distortions if he or she computes distances, areas Lambert's cylindrical equal-area projection. Data from SocialExplorer and US Census. Scale bars are graphical representations of distance on a map. Shape and It is best suited for maps of continents or regions that are equally extended in all directions from the centre, such as Asia and the Pacific ocean. The sole projection used for large scale mapping of the United States by the USGS until the 1950's. An example would be the classification conformal conic projection with two standard parallels having the meaning that the projection is a conformal map projection, that the intermediate surface is a cone, and that the cone intersects the ellipsoid (or sphere) along two parallels; i.e. It is used to show great circle paths as straight lines and thus to assist navigators and aviators. and meridians are straight lines intersecting at right angles, a requirement The property of the projection is conformal. Since the projection is conformal, no distortion in East-West direction). Meridians are equally spaced. Map is neither conformal nor equal area, but each parallel is true to scale. Map projection equations have a significant role in projection change By the end of this chapter, you should be able to read map scales and identify common projections along with their basic features and uses. It is recommended for topographic mapping by the United Nations Cartography Committee in 1952. A number of equations are also given at World conformality and reasonable equidistance. map projections (ESRI). The, Suitable equal-area projections for thematic and distribution maps Graticule projected. Scale refers to how map units relate to real-world units. In an equatorial azimuthal or equatorial Parallels It is adaptable for topographic maps, and is earlier used for the International Map of the World, a map series at 1:1,000,000 scale published by a number of countries to common internationally agreed specifications, and also for large-scale mapping of the United States until the 1950's and coastal charts by The parallel spacing increases 1. of the size. Robinson Projection. The extent of the map is national while the resolution is at the state level because they are the finest level of spatial detail that we can see. The Universal Transverse Mercator (UTM) projection is The Earth's reference surface projected on a map wrapped around Lambert Conformal Conic projection (standard parallels 10 and 30 degrees North). Southern California ended up over in China. Areas are, of course, inaccurate in conformal projections. For the gnomonic projection, the perspective point distance and direction distortions are extreme, but all great circles (or orthodromes) - the shortest distances between two places on a sphere - are shown as straight therefore recommended and frequently used for thematic world maps. Distortion of other properties increases away from the center point, but are not very large compared to the distortions of the gnomonic projection. cartographer's task is to ensure that the right type of projection is [4], Locations on the earths surface are measured in terms of coordinates, a set of two or more numbers that specifies a location in relation to some reference system. The shortest air-routes - great circle routes - are shown by a straight line and the directions of the shortest air-routes are true from the centre of the projection. Most projections transform part of the globe to one of three developable surfaces, so called because they are flat or can be made flat: plane, cone, and cylinder. distribution maps. the globe as a cylinder produces a cylindrical map projection. For this reason a 40 kilometre overlap into an adjacent zone is allowed (figure below). the U.S. Coast and Geodetic Survey. therefore recommended and frequently used for thematic world maps. from the centre. distribution maps and do not contain the noticeable distortions of the This equal-area projection is interrupted in the sense that it uses lobes or sections. For quite some time it was thought that our planet was flat, and during those days, a map simply was a miniature representation of a part of the world. along the main axis of the area to be mapped (figure below). Because conformal projections show angles correctly, they each parallel. The most commonly used measure of map scale is the representative fraction (RF), where map scale is shown as a ratio. The Mollweide projection (figure below) is a classic equal-area projection, keeping parallels as straight lines while still preserving areas. Known by Egyptians and Greeks 2000 years ago. or angles on the basis of measurements taken from these maps. Balancing extent and resolution is often one of the most important and difficult decisions a cartographer must make. as Tissot's Indicatrix, shows the shape of an infinite small circle For topographic and large-scale maps, conformality and [11]. Essentials of Geographic Information Systems. There are other possible approaches. This preview shows page 4 - 8 out of 20 pages. The cylindrical projection is best for a rectangular area and a conic projection for a triangular area (figure below). Ghana uses TM projection with the central meridian located at 1W of Greenwich. The most appropriate type of distortion property for a map depends largely on the purpose for which it will be used. It should however not be used for regular geographic maps There are also many projections that are aesthetically pleasing, but not intended for navigation between places or to visualize data. Want to read all 20 pages? on a map. The distortion properties of map are typically classified according to what is not distorted on the map: A particular map projection can have any one of these three properties. After converting from DMS to decimal degrees, the point location for a spot in. Also called Gauss Conformal, or Gauss Krger. nearly conformal. no distortion in north-south direction). Easting value of 500,000m. nearly conformal. navigation. the equidistant cylindrical projection in the figure below).

It divides the world into 60 narrow longitudinal zones of 6 degrees. You are mapping soils of the world and want to show which soils cover the most of, the earth's surface. have been selected, the distortion property of the map projection The distortion properties of map are typically classified according to what is not distorted on the map: Based on these discussions, a particular map projection can be classified. The gnomonic projection is a useful projection for defining routes of navigation for sea and air travel, because great circles - the The Mercator projection is conformal because it preserves shape and angle but strongly distorts area. It is possible to preserve any one of the three properties using any of the developable surfaces. distortion). The central meridian is located at 117 degrees west of Greenwich. Only a limited amount are frequently used. A part of the world mapped on a transverse cylinder in the Transverse Mercator for Both shape and area are reasonably well preserved with the exception of the polar regions. Suppose a point, located at 60oN and 130oW, is projected on a map that uses the Mercator projection (where the reference surface is a sphere with a radius of 6371000 m. and the central meridian (lo) is 0o, equal to the Greenwich meridian). locations, helping the map-reader to become aware of the distortions. Non-published This is called the aspect of a map projection. Transverse and oblique aspects of many projections can be used for most parts of the world, though they are usually more difficult to construct. Lambert projections. Some projections, including the Robinson projection, strike a balance between the different map properties. and the equidistant projections of the same class will provide a very The projection plane of the UTM projection is a secant cylinder these names are not very helpful because sometimes one person developed several projections, or several people have developed similar projections. Distances measured from the centre of the map to any point are correct and the bearing of any point from the center is correct (this applies to all azimuthal maps). The general pattern of distortion is radial. Adapted from Michael Schmandt (nd). We can think of the earth as a sphere. parallels; Lambert cylindrical equal-area projection with When we visually represent a region of the world on a map, we must reduce its size to fit within the boundaries of the map. Mercator distortion. This type of projection would be useful for a general purpose world map. Lambert projections. Of these three problems, tearing is seen as the worst because you would be making maps with all sorts of holes in them! Any straight line drawn on this projection represents an actual compass bearing. It represents areas correctly and has reasonable shape distortions in the region between the standard parallels as compared with the noticeable distortions of the Lambert's equal-area conic projection with one standard parallel. projection). The geographic coordinate system is designed specifically to define positions on the Earths roughly-spherical surface. are wrongly sized or out of shape and the meridians and parallels do not Excellent for mid-latitude CC BY-NC-ND 3.0. For example, Greenland is only 7-percent the land area of Africa, but it appears to be just as large! The central meridian is the only meridian that is straight. The ellipses of distortion appear as circles (indicating What are the map units? In the polar aspect, meridians are straight lines radiating from the center, and the lines of latitude are projected as concentric circles that become closer toward the edge of the globe. The scale is constant along any circle having its centre They are grouped into cylindrical, conical and azimuthal projections. The ellipse of distortion, also known in several countries for topographic mapping purposes. The indicatrices on the map in the figure below have a varying degrees of flattening, but the areas of the indicatrices everywhere on the map are the same, which means that areas are represented correctly on the map. The figure below shows a topographic map with an RF of 1:24,000, which means that one unit on the map represents 24,000 units on the ground. The representative fraction is accurate regardless of which units are used; the RF can be measured as 1 centimeter to 24,000 centimeters, one inch to 24,000 inches, or any other unit. Goode homolosine projection of the world. More examples of map projections are given through the following links: Demonstration of great transoceanic voyaging, there was a need for conformal navigation The field of map projections concerns itself with the ways of translating the curved surface of the Earth into a flat map. Gall-Peters projection. On a secant map projection - the application of a scale factor of less than 1.0000 to the central point or the central meridian has the effect of making the projection secant - the overall distortions are less than on one that uses a tangent map surface. For the, is a conformal projection. The equidistant cylindrical projection (also called Plate Carre projection). conformal conic projection, the simple conic projection, the Albers equal-area projection ii.) This disadvantage makes the projection unsuitable for large areas on a single sheet. All circular parallels are spaced evenly along the meridians, which creates a true scale along all meridians (i.e. In the 15th, 16th and 17th centuries, during the time