Page 4 engo 421 map projections lecture notes on map projections engo 421. All map projections distort the surface in some fashion. At present, utm projection is used to compile topographic map by the majority of nations in the world, such as america, japan, canada, france, brazil, switzerland, etc, but gausskruger projection is used by other nations, such as china, vietnam, d. A map projection is a way to flatten a globes surface into a plane in order to make a map. Types of cylindrical map projections you may know include the popular mercator projection, cassini, gausskruger, miller, behrmann, hobodyer, and gallpeters. Gauss conformal projection transverse mercator lantmateriet. In contrast, in the gausskruger projection, distortions increase in the. The latter has positive gauss curvature and therefore contains no lines. Now the focus turns to the gauss conform coordinate system and the definition of the south african coordinate reference system sacrs. Let s be the saddle surface z y2 x2, known as a hyperbolic paraboloid. The central meridian is placed in the center of the region of interest.
Apr 08, 2016 please watch before class on tuesday 44. How universal transverse mercator utm works gis geography. We are measuring to which extent is the map from s to r3 given by p np called the gauss map di. Gauss and utm conformal projections and the plane rectangular. R3 be a parameterization of cby arc length centered at p, i. Mercator projection an overview sciencedirect topics. The following table lists a representative sample of the map projections supported by the ibm. Noaa special publication nos ngs the state plane coordinate system history, policy, and future directions. This conformal projection is the transverse form of the mercator projection and is also known as the gausskrueger projection. A map projection is a geometric function that transforms the earths curved, ellipsoidal surface onto a flat, 2dimensional plane.
Summary of projected epsg geodetic parameters coordinate. Content spherical trigonometry, geodetic coordinate computations in ellipsoidal and rectangu. The definition of the map projection for projected coordinate systems. The most famous transverse mercator map projection is the universal transverse mercator utm developed by the national geospatialinformation agency to provide a worldwide mapping system from 80 south latitude to 80 north latitude. The utm projection flattens the sphere 60 times by shifting the cylinder central meridian 6 for each zone. The vector 000 is called the curvature vector at p. Understanding map projections landing page for kartoweb. Pdf in this paper, we introduce some known map projections from a model of the earth. The transverse mercator projection, also known as the gausskruger projection, is similar to mercator except that the cylinder touches the sphere or ellipsoid along a meridian instead of the equator. Secondly, conic map projections include the equidistant conic projection. Carl friedrich gauss showed that a spheres surface. Aug 06, 2019 types of cylindrical map projections you may know include the popular mercator projection, cassini, gauss kruger, miller, behrmann, hobodyer, and gallpeters.
There are a number of techniques for map projection, yet in all of them distortion occurs in length, angle, shape, area or in a combination of these. Other measurement system properties such as a spheroid of reference, a datum, and projection parameters like one or more standard parallels, a central meridian, and possible shifts in the x and ydirections. Intro to coordinate systems and utm projection youtube. Projected coordinate systems for kazakhstan, kyrgyzstan. Supported linear units, map projections, and projected coordinate systems map projection parameters name sphereonly parameters key below aitoff yes lam0 albers equal area conic lam0 phi1 phi2 phi0 azimuthal equidistant. We will taker a closer look at the popular mercator projection and examine how the projection. The gausskruger projection appears to have two different forms. A map projection is a systematic transformation of the latitudes and longitudes of locations on the surface of a sphere or an ellipsoid into locations on a plane. Because there is no limit to the number of possible map projections, there can be no comprehensive list. Generalized conformal conical gausskruger map projection. Transverse mercatorproperties of maps documentation. Karneykrueger equations these notes 12 pages set out in detail the forward and inverse transformations between geographic coordinates. Learn what a map projection is, why they are used and what impact they have on maps gis systems. Mar 06, 2018 ellipsoidal form following the work of gauss and published projection tables in 1918.
The mercator map projection is one of the most well known cylindrical map projections. Pdf the gausskrueger projection rod deakin academia. A sphere is based on a circle, while a spheroid or. R n for a general oriented ksubmanifold of r n the gauss map can also be defined, and its target space is the oriented grassmannian, i. This requires a systematic transformation of the latitudes and longitudes of locations from the surface of the globe into locations on a plane. The result is a conformal projection that does not maintain true directions. The first fundamental form and the gaussian fundamental quantities are. This chapter, however, is primarily concerned with the two conformal orthomorphic projections used in geodetic survey, i. At the same time, utm projection and gausskruger projection are also.
This projection is also called the gausslambert projection acknowledging the contribution of carl friedrich gauss 17771855 to the development of the transverse mercator. The scale is constant along the central meridian, and increases to the east and west. Supported linear units, map projections, and projected. Depending on the purpose of the map, some distortions are acceptable and others are not. Kotsakis objectives in these noteswe develop a body of theory to understand and analyse the distortion. Code name and aliases source geographic crs map projection projcrs axes units 20353 agd84 amg zone 53 australia south australia between 2e and 8e. Jacobian, geometric interpretations and examples 1. Carl friedrich gauss in theorema egregium proved that a spheres surface cannot be represented on a plane without distortion. The universal transverse mercator is horrible for smallscale lessdetailed maps like world atlases and perfect for mapping narrow regions. The gauss kruger parameter definition button becomes active once.
Nov 05, 2016 nepal lies in the utm zone of 44 0 n and 45 0 n. Transform coordinates get position on a map pulkovo 1942 3degree gausskruger zone 24. The gausskruger is one of a family of transverse mercator projections of which the spherical form was originally developed by johann heinrich lambert 17281777. This gives cartographers a map to work with always in meters. This projection had constant scale along the central meridian and was known as the gauss conformal or gauss hannover projection. The injectivity of the extended gauss map of general projections of smooth projective varieties marc coppens abstract. Distances are accurate along the central meridian if the scale factor is 1. Gausskruger zonation system is very similar to utm, except for a scale factor of. One is a set of equations capable of micrometre accuracy anywhere within 30 of a central meridian of longitude. In many countries, this projection is also known as the gausskru. This is a summary of map projections that have articles of their own on wikipedia or that are otherwise notable. This will lead us to the concept of second fundamental form, which is a quadratic form associated to s at the point p. There are several techniques to obtain new map projections by combining.
This map projection is practical for nautical applications due to its ability to represent lines of constant course, known as rhumb lines, as straight segments that conserve the angles with the meridians. Relationship and applications of utm projection and gauss. Map projection, transverse mercator, gauss krueger, karneykrueger equations. Between those scales, choosing to use a sphere or spheroid will depend on the maps purpose and the accuracy of the data. Map projections explained a beginners guide youtube. This booklet provides a conceptual introduction to map projections and geographic reference systems. The mercator projection is a cylindrical map projection presented by the flemish geographer and cartographer gerardus mercator in 1569. A gauss seidel projection method for micromagnetics. Associated with the general projection of x to aspacepn. The specific parameters are set in the geographic defaults dialog box. Let x beasmoothndimensionalprojective variety embedded insome projective space pn over the.
Gauss kruger projection the gauss kruger coordinate system is implemented as a generalized transverse mercator projection. Otherwise, g is meromorphic in the entire plane, so by picards theorem it takes on all values with at most two exceptions or is constant. Jan 06, 2017 learn what a map projection is, why they are used and what impact they have on maps gis systems. Biography of author rod deakin started work in 1968 age 17 as a surveyors assistant with john horne of frankston, victoria and fell in the kananook creek on his first day. Gausskruger gk coordinate system is based on the gausskruger. Nonconformal plane rectangular coordinates the state plane coordinate system. It generally does not maintain true directions, but angles and shapes are maintained at infinitesimal scale. Kotsakis objectives in these noteswe develop a body of theory to understand and analyse the distortion properties of maps that underlie different map projection algorithms. We are motivated to understand the jacobian of a given function because it will allow us to understand certain. Let v denote a two dimensional vector space over r. The gauss map can be defined for hypersurfaces in r n as a map from a hypersurface to the unit sphere s n. The injectivity of the extended gauss map of general.
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