Map projection concerns the science of mathematical cartography, the techniques by which the earths dimensions, shape and features are translated in map form, be that twodimensional paper or two or three dimensional electronic representations. Schr o dinger basin in clementine basemap in sinusoidal equalarea projection nasa s pds imaging node, captured in 20. Equal area projections preserve the area of objects. Geodesy and map projections university of missourist. The central focus of this book is on the theory of map projections. In cartography, several named map projections, including the mercator projection and the stereographic projection are conformal. For mapping an area of considerable extent in longitude, a geometrical system based on the notion of an eastwest centre line can be used. Truedirection, or azimuthal, projections maintain some of the great circle arcs, giving the directions or azimuths of all points on the map correctly with respect to the center. Geodesy the science of determining the size and shape of the earth and the precise location of points on its surface.
Mathematical cartography also takes in map scales and their variation, the. Importance of understanding coordinate systems and map projections. Projector software developed by nasa and the goddard institute for spatial studies. These enjoy the property that the distortion of shapes can be made as small as desired by making the diameter of the mapped region small enough. The mercator and stereographic projections, and many in. The family is referred to as the lambert conic conformal projections. We will restrict the surface to be mapped to be the ellipsoid as defined in geodesy. It is extremely important that you gain an understanding of coordinate systems and map projections.
Thomas work can be regarded as the definitive derivation of the tm formulae. Conformal projection definition of conformal projection by. Cartography is distorted the simple point to be made with this slide is that 2d map projections necessarily change shapes in ways that are specific to the type of projection. In a conformal projection, the angles between intersecting lines and curves retain their original form on the map. Special publication on free shipping on qualified orders. Both the stereographic and the mercator projections are conformal, which means that lines intersect at. Specifically, on the basis of two very important properties. Some truedirection projections are also conformal, equal area, or equidistant. Earths surface is divided in rectangular regions, and for each of them a different projection and a different set of geodetical parameters are used. In this final section, we will look at the final concept that connects geodesy to gis. Since gis inherits concepts and ideas previously used to create printed maps, it is mandatory to know them in order to correctly use the tools included in a gis. Any software, documentation, andor data delivered hereunder is subject to the. Matlab software for the leastsquares wavelet and cross wavelet analyses. Without them, it is not possible to understand gis.
Beginning almost two thousand years ago with marinus and ptolemy, map projections have played a very significant role in cartography. In terrestrial geodesy and in a spherical or planetocentric coordinate system. Lamberts conformal conical projection springerlink. In cartography, a conformal map projection is one in which every angle between two curves that cross each other on earth a sphere or an ellipsoid is preserved in the image of the projection, i. Lidar elevation data often capture many manmade features, such as bridges and areas where the ground has been builtup to support road construction, that interfere with correct watershed delineation and flow routing in a gis environment. All projections of a sphere on a plane necessarily distort the surface in some way and to some extent.
Conformal projections in geodesy and cartography citeseerx. Vice versa, an areapreserving projection can not be conformal, resulting in shapes. Projections are also classified in terms of their properties. A sound knowledge of map projections and grids requires an understanding of the mathematical nature of projections and the size and shape of the earth, since in our context.
Refer to the section on projections for more information about distortions generated by projections. Map projection academic dictionaries and encyclopedias. Conformal map projections are the class of projections in which angles on the surface to be mapped are preserved, tnat is, corr esponding angles on the map plane and the surface are equal. One map projection might be used for largescale data in a limited area, while another is used for a smallscale map of the world. Pdf map projections in planetary cartography researchgate. Today the lambert conformal conic projection has become a standard projection for mapping large. In cartography, a map projection is a way to flatten a globes surface into a plane in order to make a map. Handbook for transformation of datums, projections, grids. List of supported map projectionshelp arcgis for desktop. Surveying and geodesy textbooks, with the notable exception of g. Shape conformal map projections preserve shape area equal area map projections preserve area distancescale equidistant map projections preserve distance directionangle azimuthal map projections. Commonly used map projections intergovernmental committee on. Geodesy, coordinate systems, and map projections objectives introduce the main concepts of geodesy coordinate systems, datums, ellipsoids, and geoids describe map projections and coordinate systems we use in gis two key questions what is the shape of the earth, and where are things on the earth. The mercator and stereographic projections, and many in between.
To apply this course to projects in your specific geoscience. Mathematics designating or specifying a mapping of a surface or region upon another surface so that all angles between intersecting curves remain. Map projections designed for smallscale data are usually based on spherical rather than spheroidal geographic coordinate systems. You will need to understand the building blocks of how to define and visualize a location. The usgs has also conceived and designed several new projections, including the space oblique mercator, the first map projection designed to permit mapping of the earth continuously from a. A map projection may do fairly well in terms of one or two attributes but, will always do poorly in the third. Conformal projection definition of conformal projection. A map projection is any method of representing the surface of a sphere or other threedimensional body on a plane.
This introductory textbook introduces students to the different types of map projections, map design, and map production. A compendium of map projections, with derivations is a comprehensive reference. Pdf reference surfaces, coordinate systems and projections are the prerequisites. From basic projecting to advanced transformations, cartographic science. Learn vocabulary, terms, and more with flashcards, games, and other study tools. Oct 28, 2008 4 this process of flattening the earth will cause distortions in one or more of the following spatial properties. Johann heinrich lambert devised and published such a. This projection was developed to provide a conformal map of alaska with less scale distortion than other conformal projections. Geodesy and map projections 1 geodesy and map projections 2 what is a map projection.
Bugayevskiy and snyders map projections, a reference manual, is a comprehensive reference of cartographic projections used in mapping the whole earth, continents and smaller areas. Map projection the transformation of a curved earth to a flat map. Geodesy, coordinate systems, objectives and map projections. Gis photogrammetry geodesy equipment total station cartography survey software map projection coordinate systems.
This requires a systematic transformation of the latitudes and longitudes of locations from the surface of the globe into locations on a plane. Mathematical analysis in cartography by means of computer. Buy conformal projections in geodesy and cartography united states. In cartography, a conformal map projection is one in which every angle between two curves that cross each other on earth is preserved in the image of the projection, i. Conformal projections in geodesy and cartography ebook. We publish original articles representing results of completed theory and practice studies, articles by scientists, graduate students, many enterprises experts in the fields of geodesy, cartography, cadastre, navigation, remote sensing, gis technologies, spatial.
Now that we understand what scale is in regards to gis and cartography, we can explore. Any software, documentation, andor data delivered hereunder is subject to the terms of the. Gis works with spatial data, and, with using this data that needs to be placed at locations. A practical guide to map projections because you need geodesy. Coordinate systems any set of numbers, usually in sets of two or three, used to determine location relative to other locations in two or three dimensions. Today the lambert conformal conic projection has become a standard projection for mapping large areas small scale in the midlatitudes such as usa, europe and australia. Mathematical analysis in cartography by means of computer algebra system 5 as the conventional usage in mathematical cartography. Mathematical cartography also takes in map scales and their variation, the division of maps into sets of sheets and nomenclature, and addresses the problems of making measurements and conducting investigations which make use of geodetic measurements and the development of. Understanding map projections american meteorological society. Map projections in which shape is preserved are known as conformal or orthomorphic. This was developed in 1972 by the united states geological survey usgs to publish a map of alaska at 1.
Handbook for transformation of datums, projections, grids and. Awareness of geodetic datums, coordinate reference systems, and map projections is provided via interactive demonstrations and handson workshop exercises using the online epsg geodetic registry. It is how we represent a three dimensional earth on a flat piece of paper however the process of transferring information from the earth to a map causes every projection to distort at least one aspect of the real world either shape, area. Commonly used map projections intergovernmental committee. Equidistant, similar but different then conformal projections, aim to preserve distance, but only from the tangential line or lines. Beginning almost two thousand years ago with marinus and ptolemy, map projections. Pdf in this paper, we introduce some known map projections from a model of. Conformal definition of conformal by the free dictionary. Datums, coordinate systems, coordinate reference systems and datum transformations. A map projection is one of many methods used to represent the 3dimensional surface of the earth or other round body on a 2dimensional plane in cartography mapmaking. For example, if two roads cross each other at a 39 angle, then their images on a map with a conformal projection cross at a 39 angle. All map projections distort the surface in some fashion. Gis works with spatial data, and, with using this data that needs to. A guide to map projections in modern cartography texts, by matthew bazylewskyj.
Depending on the purpose of the map, some distortions are acceptable and others are not. Conformal projections in geodesy and cartography united. On the albers equal area conic projection, the parallels near the northern and southern edges. Special cases include the mercator map and the stereographic. Projector, free software can render many projections nasa giss. The peters map controversy motivated the american cartographic association now cartography and geographic information society to produce a series of booklets including which map is best 6 designed to educate the public about map projections and distortion in maps. Number of pages cartography datums projections 170 geodesy coordinates 16. That is the great circle on which the two points lie. The lambert conformal conic projection with two standard parallels including a comparison of the lambert projection with the bonne and polyconic projections by u. Worked examples conformal mappings and bilinear transfor. It has also become particularly popular with aeronautical charts such as the 1. A conformal projection maintains the shape of small regions, so angles at any point are correct, although sizes will change. Intergovernmental committee on surveying and mapping logo. Gis photogrammetry geodesy equipment total station cartography survey software map projection coordinate systems 1.
While the extremely high vertical and horizontal resolution of aerial lidar provide many advantages, they also add complications. Through the tedious expansion process, yang 1989, 2000 gave a power series of the eccentricity e for the conformal latitude as b b bbb24 6 8sin2 sin4 sin6 sin8. Equations are furnished for map projections and datums commonly used within the army, and references are provided for other, less commonly encountered, map projections and datums. Dec 27, 2002 a map projection is one of many methods used to represent the 3dimensional surface of the earth or other round body on a 2dimensional plane in cartography mapmaking. This tool visualizes any complexvalued function as a conformal map by assigning a color to each point in the complex plane according to the functions value at that point. The mercator and stereographic projections, and many in between daniel daners revised version, july 29, 2011 abstract we consider a family of conformal angle preserving projections of the sphere onto the plane. This is a conformal projection in that shapes are well preserved over the map. This process is typically, but not necessarily, a mathematical procedure some methods are graphically based. Worked examples conformal mappings and bilinear transformations example 1 suppose we wish to. The conformal projections used most in mapping and in geodetic computational work of the u. Map projections a reference manual lev bugayevskiy. This compromise projection was developed in 1889 and used for world maps. The lambert conformal conic projection with two standard parallels including a comparison of the lambert projection with the bonne and polyconic projections.
The oil industry uses conformal projections almost exclusively. The fundamental concepts from cartography and geodesy are the most important ones. Gps remote sensing gis photogrammetry geodesy equipment. Cartography is generally for a sophomore or junior level course for geography majors and many professors are beginning to introduce computer cartography throughout the course. A guide to map projections in modern cartography texts, by. It discusses in depth the main families of projections, their calculations and their most used instances. This system is not just a projection, but a complete system of many of them.
1387 1265 667 726 844 230 425 1334 1393 1136 421 553 53 511 1274 6 732 1495 1255 773 1029 664 1444 1222 517 835 1005 400