Pdf in this paper, we introduce some known map projections from a model of the earth. Gauss kruger projection the gauss kruger coordinate system is implemented as a generalized transverse mercator projection. Content spherical trigonometry, geodetic coordinate computations in ellipsoidal and rectangu. 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. 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. Nov 05, 2016 nepal lies in the utm zone of 44 0 n and 45 0 n. R3 be a parameterization of cby arc length centered at p, i. Generalized conformal conical gausskruger map projection. Projected coordinate systems for kazakhstan, kyrgyzstan. Karneykrueger equations these notes 12 pages set out in detail the forward and inverse transformations between geographic coordinates. 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. Map projections explained a beginners guide youtube.
This chapter, however, is primarily concerned with the two conformal orthomorphic projections used in geodetic survey, i. However, to maintain accuracy for largerscale maps scales of 1. Transform coordinates get position on a map pulkovo 1942 3degree gausskruger zone 24. The utm projection flattens the sphere 60 times by shifting the cylinder central meridian 6 for each zone. The mercator map projection is one of the most well known cylindrical map projections. Commonly, 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. 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.
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. The scale is constant along the central meridian, and increases to the east and west. It generally does not maintain true directions, but angles and shapes are maintained at infinitesimal scale. The specific parameters are set in the geographic defaults dialog box. This projection is also called the gausslambert projection acknowledging the contribution of carl friedrich gauss 17771855 to the development of the transverse mercator. Jan 06, 2017 learn what a map projection is, why they are used and what impact they have on maps gis systems. This booklet provides a conceptual introduction to map projections and geographic reference systems. The gausskruger is one of a family of transverse mercator projections of which the spherical form was originally developed by johann heinrich lambert 17281777. Learn what a map projection is, why they are used and what impact they have on maps gis systems.
Gausskruger gk coordinate system is based on the gausskruger. How universal transverse mercator utm works gis geography. We can recapture the bilinear form, and hence the map dn p itself, by polarizing the quadratic form q, and hence lose no information by focusing on q. Depending on the purpose of the map, some distortions are acceptable and others are not. Summary of projected epsg geodetic parameters coordinate. Aug 06, 2019 types of cylindrical map projections you may know include the popular mercator projection, cassini, gauss kruger, miller, behrmann, hobodyer, and gallpeters. 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. We will taker a closer look at the popular mercator projection and examine how the projection.
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. 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. Distances are accurate along the central meridian if the scale factor is 1. Transverse mercator utm projection and establishes the projection. 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. Although the projection procedure inevitably introduces systematic spatial distortions, particular types of distortion can be minimized to suit the geographic scope and intended use of the map data. Kotsakis objectives in these noteswe develop a body of theory to understand and analyse the distortion. The gauss kruger parameter definition button becomes active once. This projection had constant scale along the central meridian and was known as the gauss conformal or gauss hannover projection. 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. Gausskruger zonation system is very similar to utm, except for a scale factor of. The injectivity of the extended gauss map of general. The first fundamental form and the gaussian fundamental quantities are. Noaa special publication nos ngs the state plane coordinate system history, policy, and future directions.
A sphere is based on a circle, while a spheroid or. Relationship and applications of utm projection and gauss. Understanding map projections landing page for kartoweb. This gives cartographers a map to work with always in meters. This will lead us to the concept of second fundamental form, which is a quadratic form associated to s at the point p. Carl friedrich gauss in theorema egregium proved that a spheres surface cannot be represented on a plane without distortion. Nonconformal plane rectangular coordinates the state plane coordinate system. Code name and aliases source geographic crs map projection projcrs axes units 20353 agd84 amg zone 53 australia south australia between 2e and 8e. There are several techniques to obtain new map projections by combining. We are measuring to which extent is the map from s to r3 given by p np called the gauss map di. The latter has positive gauss curvature and therefore contains no lines. Let x beasmoothndimensionalprojective variety embedded insome projective space pn over the. In contrast, in the gausskruger projection, distortions increase in the. The definition of the map projection for projected coordinate systems.
Gauss conformal projection transverse mercator lantmateriet. Associated with the general projection of x to aspacepn. Now the focus turns to the gauss conform coordinate system and the definition of the south african coordinate reference system sacrs. 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. Apr 08, 2016 please watch before class on tuesday 44. Mar 06, 2018 ellipsoidal form following the work of gauss and published projection tables in 1918. The central meridian is placed in the center of the region of interest.
The vector 000 is called the curvature vector at p. Jacobian, geometric interpretations and examples 1. This conformal projection is the transverse form of the mercator projection and is also known as the gausskrueger projection. Between those scales, choosing to use a sphere or spheroid will depend on the maps purpose and the accuracy of the data. A gauss seidel projection method for micromagnetics. Intro to coordinate systems and utm projection youtube. Let v denote a two dimensional vector space over r. Gauss and utm conformal projections and the plane rectangular. Transverse mercatorproperties of maps documentation.
Supported linear units, map projections, and projected. The gausskruger projection appears to have two different forms. Because there is no limit to the number of possible map projections, there can be no comprehensive list. Carl friedrich gauss showed that a spheres surface. Page 4 engo 421 map projections lecture notes on map projections engo 421. A map projection is a geometric function that transforms the earths curved, ellipsoidal surface onto a flat, 2dimensional plane. This is a summary of map projections that have articles of their own on wikipedia or that are otherwise notable. Types of cylindrical map projections you may know include the popular mercator projection, cassini, gausskruger, miller, behrmann, hobodyer, and gallpeters. Since the earth is roughly the shape of an oblate spheroid, map projections are necessary for creating maps of the earth or parts of the earth that are represented on a plane such as a piece of paper or a computer screen. Mercator projection an overview sciencedirect topics. Secondly, conic map projections include the equidistant conic projection. The following table lists a representative sample of the map projections supported by the ibm.
A map projection is a way to flatten a globes surface into a plane in order to make a map. At the same time, utm projection and gausskruger projection are also. One is a set of equations capable of micrometre accuracy anywhere within 30 of a central meridian of longitude. All map projections distort the surface in some fashion. Let s be the saddle surface z y2 x2, known as a hyperbolic paraboloid. The result is a conformal projection that does not maintain true directions.
Map projection, transverse mercator, gauss krueger, karneykrueger equations. The universal transverse mercator is horrible for smallscale lessdetailed maps like world atlases and perfect for mapping narrow regions. The mercator projection is a cylindrical map projection presented by the flemish geographer and cartographer gerardus mercator in 1569. Pdf the gausskrueger projection rod deakin academia. In many countries, this projection is also known as the gausskru. The injectivity of the extended gauss map of general projections of smooth projective varieties marc coppens abstract.
T he gauss conform coordinate system as used in south africa uses the transverse mercator map projection formulae modified to produce westings y and southings x instead. We are motivated to understand the jacobian of a given function because it will allow us to understand certain. 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. The gauss map can be defined for hypersurfaces in r n as a map from a hypersurface to the unit sphere s n. This requires a systematic transformation of the latitudes and longitudes of locations from the surface of the globe into locations on a plane. 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.
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