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