Projections intergovernmental committee on surveying and. A map projection is defined as a systematic rendering of locations from the curved earth surface onto a flat map surface. Conformal projections in geodesy and cartography united. A projection where the linear distortion is unique the same in every direction at a point. 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.
The transverse mercator projection is a conformal cylindrical projection with the. We will restrict the surface to be mapped to be the ellipsoid as defined in geodesy. Lecture notes that cover all of the mathematics that supports the derivation of conformal map projections. Convert between geodetic and conformal latitudes matlab. We will taker a closer look at the popular mercator projection and examine how the projection.
The term projection here refers to any function defined on the earths surface and with values on the plane, and not necessarily a geometric projection. The department of defense replaced wpg with the conformal utm system in the 1940s. Learn what a map projection is, why they are used and what impact they have on maps gis systems. General principle we now introduce the notion of conformal mapping. Conformal map projections conformality was recognized as an important and desirable property for map projections used.
Number of pages cartography datums projections 170 geodesy coordinates 16. Conformal projections in geodesy and cartography citeseerx. An nga geospatial analysts quickstart guide to arcgis map projections this guide is intended for the generation of custom products such as reference maps, planning maps, graphics that accompany geospatial studies, and digital gis products. One map projection might be used for largescale data in a limited area, while another is used for a smallscale map of the world. Use conformal latitudes when implementing conformal map projections on the ellipsoid.
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. This requires a systematic transformation of the latitudes and longitudes of locations from the surface of the globe into locations on a plane. Geodetic latitude coordinates, specified as a numeric scalar value, vector, matrix, or nd array. Convert authalic, conformal, isometric, or rectifying. Curves that meet at a given angle on the ellipsoid meet at the same angle on the sphere. A guide to the mathematics of map projections rodney e. Projected coordinates maps and gis 90o x y 0,011 11 establish a reference frame identify, through measurements, the locations of important things using this reference frame 10,30 235,78 geodesy science of measuring the size and shape of the earth datuma reference surface e. Conformal conic projection is often used for small scale mapping and aeronautical charting, especially when the area being mapped has a large eastwest extent. The mercator and stereographic projections, and many in between. About map projectionthe classification of map projection.
This conformal projection can be visualized as the projection of the ellipsoid onto a cone with the cones axis. Mathematics and computers are the indispensable allies of map projection. Following is a brief guide to arcgis map projections. Content spherical trigonometry, geodetic coordinate computations in ellipsoidal and rectangular spatial coordinate systems, astronomical coordinates, coordinate system transforma. A map projection is any of many methods used in cartography mapmaking to represent the twodimensional curved surface of the earth or other body on a plane.
These projections include the mercator, the lambert conformal with one. Map projections have their largest and most frequent application in producing maps showing a. For conformal map projections, it is the amount by which a distance or. Special cases include the mercator map and the stereographic. There are two main problem areas in conformal map projections. Without maths and computers, teaching map projections is. Conformal projections in geodesy and cartography ebook. Pdf in this paper, we introduce some known map projections from a. All projections of a sphere on a plane necessarily distort the surface in some way and to some extent. Geodesy the science of determining the size and shape of the earth and the precise location of points on its surface. Coordinate computation and the manual of traverse computation on the. Several dozen of these documents provide the theoretical and practical basis for what ultimately became spcs, including groundbreaking work on conformal projections in the early 1900s. Handbook for transformation of datums, projections, grids. Conformal map projection wikimili, the free encyclopedia.
The purpose of these notes is to give the theory and use of some common conformal map projections. The versions of this projection type used for spcs are the lambert conformal conic, transverse mercator, and oblique mercator. Pdf some equalarea, conformal and conventional map. For example, if two roads cross each other at a 39 angle, then their images on a map. In cartography, a map projection is a way to flatten a globes surface into a plane in order to make a map. The reason why we employ map projections is because globes are not very portable, or practical to use in. Department of geodesy and geomatics engineering, university of new brunswick, 1973. Conformal projections in geodesy and cartography book.
The mercator and stereographic projections, and many in. The degree and kinds of distortion vary with the projection used in making a map of a particular area. The map plane is regarded as a flat two dimensional surface. Conformal projections conformal projections preserve local shape at every point the scale is the same in every direction graticule lines intersect at 90degree angles all angles between intersections of arcs are maintained shapes of very small areas and angles with very short sides are preserved. With the exception of maritime and polar charts, nga maps and charts mainly use the lambert conformal conic lcc and transverse mercator tm projections. Geodesy in mike zero map projection and datum conversion. In the secant case, the standard parallels which lie equidistant north and south of the equator are true to scale and distortion increases with distance from the standard lines.
These projections include the mercator, the lambert conformal with one standard parallel, and the stereographic. State plane coordinate system of 2022 policy geodesy. Map projections are a systematic transformation of longitudes and latitudes of a location on the surface of the sphere. Basic geodesy article 11 october 2006 figure 1 came from the national geospatialintelligence college. Shape conformal map projections preserve shape area equal area map projections preserve area distancescale equidistant map projections preserve distance directionangle azimuthal map projections.
Handbook for transformation of datums, projections, grids and. These projections are only applicable to limited areas on the model of the earth for any one map. Therefore, as a general rule of thumb, use tm or utm for largescale small area maps, and lcc for smallscale largearea maps. Map projection the transformation of a curved earth to a flat map. An nga geospatial analysts quickstart guide to arcgis map. Download full version here if you are searching for the ebook by paul d. The conformal projections used most in mapping and in geodetic. A projection that preserves the shape of features across the map is called conformal. 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. 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. Pdf in australia, largescale topographic mapping and survey coordination is. In this paper, we introduce some known map projections from a model of the earth to a flat sheet of paper or map and derive the plotting equations for these projections.
Figure 2 is a slightly modified diagram from dma tm defense mapping agency technical manual 8358. Search for library items search for lists search for contacts search for a library. Unbs department of geodesy and geomatics engineering is a world class centre for the study of computer mapping, spatial information management and gis, land management systems, remote sensing, geodesy, hydrography, ocean mapping, navigation, and precision engineering surveys. Indeed it would be beyond the abilities of todays geospatial professionals to produce a map projection without a computer. This projection had constant scale along the central meridian and was known as the gauss conformal or gauss hannover projection. Conformal projections are important because, unlike other projections, local areas retain their true shape.
The family is referred to as the lambert conic conformal projections. The projection is conformal, so angles are preserved but distances are distorted. Commonly used map projections intergovernmental committee. Some equalarea, conformal and conventional map projections. The two corresponding sets of coordinates for any point are the geodetic latitude cp and longitude a. Lecture 2 map projections and gis coordinate systems. And embedded in the software will be mathematical algorithms. Special publication on free shipping on qualified orders. Map projection wikipedia, the free encyclopedia the azimuthal conformal projection, also known as the stereographic projection, geodetic datum. Some projections are suited for mapping large areas that are mainly northsouth in. Esriscanada lambert conformal conic is a customized map projection package that includes the datum nad 1983 and is designed with parameters that suit the geographic extent of canada. Apr 25, 2017 there are many different ways of display the geography of the world, with the robinson and mercator projections amongst the most popular. To compare maps in a gis, both maps must be in the same.
The stereographic map projection is another ancient projection, dating back to the second century b. Distortion patterns on common conformal map projections. In order to produce the map of a region, it is necessary to make a geodetic survey of that region and then to visualise the results of such a survey. Geodesy map projections, datums, and coordinate systems. 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. Projector, free software can render many projections nasa giss. Thomas conformal projections in geodesy and cartography special publication no.
The conformal latitude maps an ellipsoid oblate spheroid to a sphere while preserving shapes and angles locally. The main reason is that there is no one projection best overall see section 4. It begins with the basics of differential geometry and conformal mapping. Reference systems of maps and geographic information systems of. These projections maintain the shape of an area during transformation from the earth to a map. The stereographic map projection is most useful for maps of polar regions for navigation purposes or large continentsized areas of similar extent in all directions. A projection that preserves the area of a feature across the map is called equal area or equivalent. Surveying and geodesy textbooks, with the notable exception of g. As its name implies, this map projection uses a cone as its developable surface. Introduction to geodesy and map projections geodesy is a 21st century science making use of the most advanced geodesy and map projections conformal. Basic geodesy national geospatialintelligence agency. Conformal projections in geodesy and cartography special. It begins with the basics of differential geometry and conformal. It should not be used as guidance for nga standard products or any other.
The stereographic map projection is conformal but not. Having developed a coordinate system and measurement techniques for the earth, the next problem map makers faced was how to transfer the information from the surface of a 3 dimensional 3d or spherical, irregularly shaped sphere the earth to a 2dimensional 2d or flat piece of paper. Conic map projection the lambert conformal conic map projection was introduced by johann lambert in 1772. Then, given the conditions for a particular map projection, the particular conformal mapping equations are derived. 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. 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. The angle between any intersecting curves is preserved under conformal mapping. A map projection is a systematic representation of all or part of the surface of a round body, especially the earth, on a flat surface. Geodesy, coordinate systems, objectives and map projections. Buy conformal projections in geodesy and cartography special publication no. The question may arise here why are there so many map projections. Otherwise, values of phi are consistent with the units of angleunit.
A cornucopia of map projections, a visualization of distortion on a vast array of map projections in a single image. Map projections explained a beginners guide youtube. Because earth has a curving, notquite sphericial shape, planar maps. Map projections are important in creating maps with map. It has also become particularly popular with aeronautical charts such as the 1. This allows us to flatten the curved surface onto a flat surface such as a piece of paper, or computer screen. This representation usually includes lines delineating meridians of longitude and parallels of latitude, but they may be omitted, depending on the purpose of the map. Map projections page 3 introduction to map projections although earth images and map data that you use are typically rendered onto flat surfaces such as your computer screen or a sheet of paper, the earths surface obviously is not flat.
Buy conformal projections in geodesy and cartography united states. Understanding map projections landing page for kartoweb. Datums, coordinate systems, coordinate reference systems and datum transformations dean c. Oct 28, 2008 4 this process of flattening the earth will cause distortions in one or more of the following spatial properties. Jan 06, 2017 learn what a map projection is, why they are used and what impact they have on maps gis systems. You can read conformal projections in geodesy and cartography. We present full variation of this ebook in epub, djvu, pdf, doc, txt forms. Map projections designed for smallscale data are usually based on spherical rather than spheroidal geographic coordinate systems. Deakin school of mathematical and geospatial sciences rmit. Laufs geodesy and map projections lauf 1983, often have only an outline of the mathematics of the tm projection and a statement of formula if there is any mention of the 2.
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