# projection cylindrique mercator

This map's grid is rectangular and lines of latitude and longitude are parallel throughout. Mercator projection, type of map projection introduced in 1569 by Gerardus Mercator.It is often described as a cylindrical projection, but it must be derived mathematically.The meridians are equally spaced parallel vertical lines, and the parallels of latitude are parallel horizontal straight lines that are spaced farther and farther apart as their distance from the Equator increases. Autor: Dr. Josep Maria Rabella. It became the standard map projection for nautical purposes because of its ability to represent lines of constant course, known as rhumb lines or loxodromes, as straight segments. The Mercator map projection was invented by Gerardus Mercator (1512-1594). Image of: Mercator. Oh yes, I did. For the above model 1 cm corresponds to 1,500 km at a latitude of 60°. On a Mercator projection, for example, the landmass of Greenland appears to be greater than that of the continent of South America; in actual area, Greenland is smaller than the Arabian Peninsula. The graph shows the variation of the scale factor with latitude. For example, the basic transformation equations become. This projection is widely used for navigation charts, because any straight line on a Mercator projection map is a line of constant true bearing that enables a navigator to plot a straight-line course. Often, it is innocent of the crimes it is accused of, and I want to address this as well as what it actually is guilty of. The meridians are equally spaced parallel vertical lines, and the parallels of latitude are parallel horizontal straight lines that are spaced farther and farther apart as their distance from the Equator increases. These circles are rendered on the projected map with extreme variation in size, indicative of Mercator's scale variations. In this case the maximum latitude attained must correspond to y = ±W/2, or equivalently y/R = π. Longer distances require various approaches. In 1569 he created the Mercartor map projection. When α = 0 or π it corresponds to a meridian great circle (if continued around the Earth). The ordinate y of the Mercator projection becomes infinite at the poles and the map must be truncated at some latitude less than ninety degrees. Calling the ruler distances of the end points on the map meridian as measured from the equator y1 and y2, the true distance between these points on the sphere is given by using any one of the inverse Mercator formulæ: where R may be calculated from the width W of the map by R = W/2π. Article 4 : Le système de coordonnées planimétriques est constitué d’un référentiel géodésique et d’une ... - La Projection cartographique BFTM (projection cylindrique transverse de Mercator) ; Did I mention that I’m not a big fan of cylindric projections? Najboljši sosed: prodajna mesta, akcije, ugodnosti, novice, dogodki, recepti in mnogo več. Working from the projected map requires the scale factor in terms of the Mercator ordinate y (unless the map is provided with an explicit latitude scale). For Greenland, taking 73° as a median latitude, hk = 11.7. If the latitudes of the end points cannot be determined with confidence then they can be found instead by calculation on the ruler distance. gd−1(φ). So my first recommendation is: Verify if you reallyneed a rectangular map or if a different shape might fit the purpose of the map better. Mercator projection translation in English-French dictionary. For example, on a map with R = 1 the values of y = 0, 1, 2, 3 correspond to latitudes of φ = 0°, 50°, 75°, 84° and therefore the successive intervals of 1 cm on the map correspond to latitude intervals on the globe of 50°, 25°, 9° and distances of 5,560 km, 2,780 km, and 1,000 km on the Earth. [1913… On peut obtenir ainsi trois types de projections : cylindrique, conique ou azimutale ... Mercator Projection - Duration: 3:12. cylindrical projection. The difference is small for short distances but increases as λ, the longitudinal separation, increases. Les coordonnées des contours résultent d'une simple conversion sur un plan des coordonnées géodésiques. Therefore, the Mercator projection is adequate for mapping countries close to the equator. Français : Limites administratives des départements de la France métropolitaine, Corse incluse. [f], Map projection for navigational use that distorts areas far from the equator. See the discussion on distance formulae below. The projection of Mercator is a cylindrical cartographic projection that represents the whole terrestrial surface. When the Portuguese, under the leadership of Prince Henry the Navigator, ventured farther south along the west coast of Africa, they encountered navigational difficulties by assuming that the charts used in the Mediterranean could simply be extended. Therefore, by construction, the Mercator projection is perfectly accurate, k = 1, along the equator and nowhere else. Only accurate Mercator projections of regions near the equator will necessitate the ellipsoidal corrections. The Mercator projection is a cylindrical map projection presented by the Flemish geographer and cartographer Gerardus Mercator in 1569. Being a cylindrical projection, the deformation experienced by the areas closest to the poles is such that Greenland (2,166,086 km²) is similar in extent to Africa (30,221,535 km²), when the actual data show that comparing both territories is simply crazy. A meridian of the map is a great circle on the globe but the continuous scale variation means ruler measurement alone cannot yield the true distance between distant points on the meridian. La projection de Mercator ou projection Mercator est une projection cartographique de la Terre, dite «cylindrique», tangente à l' équateur du globe terrestre sur une carte plane formalisée par le géographe flamand Gerardus Mercator, en 1569. The Mercator map was designed as an aid to navigators with straight lines, loxodromes or rhumb lines—representing lines of constant compass bearing—that are perfect for "true" direction. Mercator projection, type of map projection introduced in 1569 by Gerardus Mercator. The scale is now true at these latitudes whereas parallels between these latitudes are contracted by the projection and their scale factor must be less than one. The difference is 3,338 km so the ruler distance measured from the map is quite misleading even after correcting for the latitude variation of the scale factor. projection.] [18] This section discusses only the last of these cases. This is a standard technique of extending the region over which a map projection has a given accuracy. Since ruler measurements can furnish the map ordinate y and also the width W of the map then y/R = 2πy/W and the scale factor is determined using one of the alternative forms for the forms of the inverse transformation: The variation with latitude is sometimes indicated by multiple bar scales as shown below and, for example, on a Finnish school atlas. The interpretation of such bar scales is non-trivial. Some numerical values are listed below. In a secant (in the sense of cutting) Mercator projection the globe is projected to a cylinder which cuts the sphere at two parallels with latitudes ±φ1. The scale factor is unity on the equator, as it must be since the cylinder is tangential to the ellipsoid at the equator. Since α is constant on the rhumb this expression can be integrated to give, for finite rhumb lines on the Earth: Once again, if Δφ may be read directly from an accurate latitude scale on the map, then the rhumb distance between map points with latitudes φ1 and φ2 is given by the above. The act of throwing or shooting forward. The recommendations below are made by a complete layman! If there is no such scale then the ruler distances between the end points and the equator, y1 and y2, give the result via an inverse formula: These formulæ give rhumb distances on the sphere which may differ greatly from true distances whose determination requires more sophisticated calculations. Le choix d'une projection et la conversion d'une projection à une autre comptent parmi les difficulté que les cartographes ont du … The ellipsoidal correction of the scale factor increases with latitude but it is never greater than e2, a correction of less than 1%. - Les déformations cartographiques - Projection cylindrique, conique, azimutale - Carte Mercator, Peters Erratum : dia 18 - nous sommes "proches" / dia 18 et 19 : territoires et non pays. The northern inflation acutely distorts Russia's shape as well, making it appear much taller north-to-south and greatly stretching its arctic regions compared to its mid latitudes. Mercator's\ projection Mercatori projektsioon. When α = π/2 or 3π/2 the rhumb corresponds to one of the parallels; only one, the equator, is a great circle. [17], There are many alternative expressions for y(φ), all derived by elementary manipulations. The Mercator projection (/ m ər ˈ k eɪ t ər /) is a cylindrical map projection presented by Flemish geographer and cartographer Gerardus Mercator in 1569. cylindrical projection 圆柱投影. When the Earth is modelled by a spheroid (ellipsoid of revolution) the Mercator projection must be modified if it is to remain conformal. [1913 Webster] 2. Scegli tra immagini premium su Mercator Projection della migliore qualità. For all other values it is a spiral from pole to pole on the globe intersecting all meridians at the same angle, and is thus not a great circle. English-Spanish dictionary of Geography . Any of the inverse transformation formulae may be used to calculate the corresponding latitudes: The figure comparing the infinitesimal elements on globe and projection shows that when α=β the triangles PQM and P′Q′M′ are similar so that the scale factor in an arbitrary direction is the same as the parallel and meridian scale factors: This result holds for an arbitrary direction: the definition of isotropy of the point scale factor. More general example of Tissot's indicatrix: the, Fisher, Irving (1943). This need not be done symmetrically. Mercator. It became the standard map projection for nautical purposes because of its ability to represent lines of constant course, known as rhumb lines or loxodromes, as straight segments that conserve the angles with the meridians. Note: I’m no cartographer. It is particularly useful for navigation, though the scale… (The value of e2 is about 0.006 for all reference ellipsoids.) This is not the shortest distance between the chosen endpoints on the parallel because a parallel is not a great circle. Originally, this and other map projections were achieved by a systematic method of drawing… /mɜˌkeɪtəz prəˈdʒɛkʃən/ (say mer.kaytuhz pruh jekshuhn) noun a map projection with rectangular grid which is conformal and on which any rhumb line is represented as a straight line. Cartography of Belgium (history of surveying and creation of maps of, Cartography of the Low Countries (history of surveying and creation of maps of the, This page was last edited on 8 December 2020, at 06:18. ... cylindrical orthomorphic projection; cylindrite The corresponding distances for latitudes 20°, 40°, 60° and 80° are 846 km, 689 km, 450 km and 156 km respectively. geography in cartography, any of numerous map projections of the terrestrial sphere on the surface of a cylinder that is then unrolled as a plane. He stressed that the rhumb line distance is an acceptable approximation for true great circle distance for courses of short or moderate distance, particularly at lower latitudes. A jutting out; also, a part jutting out, as of a building; an extension beyond something else. He even quantifies his statement: "When the great circle distances which are to be measured in the vicinity of the equator do not exceed 20 degrees of a great circle, or 15 degrees near Spain and France, or 8 and even 10 degrees in northern parts it is convenient to use rhumb line distances". Similarly sec 2.56° = 1.001, so a strip of width 5.12° (centred on the equator) is accurate to within 0.1% or 1 part in 1,000. The transformation equations and scale factor for the non-secant version are[20]. The scale on the equator is 0.99; the scale is k = 1 at a latitude of approximately ±8° (the value of φ1); the scale is k = 1.01 at a latitude of approximately ±11.4°. A generator of a cylinder is a straight line on the surface parallel to the axis of the cylinder. Let us know if you have suggestions to improve this article (requires login). In the extreme case where the longitudinal separation is 180°, the distance along the parallel is one half of the circumference of that parallel; i.e., 10,007.5 km. Mercator, Projection de: Source file : RAMEAU: see also : Gerard Mercator (1512-1594) Field : Géographie: Variant subject headings : Mercator, Représentation de Projection de Mercator Représentation cylindrique conforme directe Représentation de Mercator: related to this theme (1 resources in data.bnf.fr) Similar phrases in dictionary English French. English: The Mercator projection is a cylindrical map projection presented by the Flemish geographer and cartographer Gerardus Mercator in 1569. The Mercator Projection is frequently used as a scapegoat by people who are surprised by certain geographical facts, mostly relating to distance or area. in any direction from a point on the equator corresponds to approximately 900 km. 16(3): 222–223. The aspect ratio of his map is 198/120 = 1.65. Abigail Alkire 48,509 views. Even more extreme truncations have been used: a Finnish school atlas was truncated at approximately 76°N and 56°S, an aspect ratio of 1.97. However, if the map is marked with an accurate and finely spaced latitude scale from which the latitude may be read directly—as is the case for the Mercator 1569 world map (sheets 3, 9, 15) and all subsequent nautical charts—the meridian distance between two latitudes φ1 and φ2 is simply. Much Web-based mapping uses a zoomable version of the Mercator projection with an aspect ratio of one. 1989. Converting ruler distance on the Mercator map into true (great circle) distance on the sphere is straightforward along the equator but nowhere else. The classic way of showing the distortion inherent in a projection is to use Tissot's indicatrix. (See Legend 12 on the 1569 map.) This chord subtends an angle at the centre equal to 2arcsin(cos φ sin λ/2) and the great circle distance between A and B is 2a arcsin(cos φ sin λ/2).) English-Estonian dictionary. [18], The above formulae are written in terms of the globe radius R. It is often convenient to work directly with the map width W = 2πR. Mercator or cylindrical map projection The Mercator projection is a cylindrical map projection presented by the Flemish geographer and cartographer Gerardus Mercator in 1569. His name is a latinized version of Gerhard Kramer. It is often described as a cylindrical projection, but it must be derived mathematically. For two points, A and B, separated by 10° of longitude on the parallel at 60° the distance along the parallel is approximately 0.5 km greater than the great circle distance. Narrower strips are better: sec 8° = 1.01, so a strip of width 16° (centred on the equator) is accurate to within 1% or 1 part in 100. The Mercator projection has been used extensively for world maps im which the distortion towards the polar regions grows rather large, thus incorrectly Map Projections Geradus Mercator invented his famous projection in 1569 as an aid to navigators. A straight line on the Mercator map at angle α to the meridians is a rhumb line. Erläuterung Übersetzung For a ruler measurement of a short line, with midpoint at latitude φ, where the scale factor is k = sec φ = 1/cos φ: With radius and great circle circumference equal to 6,371 km and 40,030 km respectively an RF of 1/300M, for which R = 2.12 cm and W = 13.34 cm, implies that a ruler measurement of 3 mm. The map is thereby conformal. Elles correspondent donc à une projection cylindrique équidistante. If α is neither 0 nor π then the above figure of the infinitesimal elements shows that the length of an infinitesimal rhumb line on the sphere between latitudes φ; and φ + δφ is a sec α δφ. "A World Map on a Regular Icosahedron by Gnomonic Projection.". Projection Pro*jec tion, n. [L. projectio: cf. On any other parallel the scale factor is sec φ so that. Omissions? It was developed by Gerardus Mercator in the sixteenth century, in the year 1569. projection de Mercator transverse [ projection cylindrique conforme de Lambert | projection de Gauss | projection de Mercator transversale ] Below is what it looked like: The length of the chord AB is 2(a cos φ) sin λ/2. F. La projection cartographique est un ensemble de techniques permettant de représenter la surface de la Terre dans son ensemble ou en partie sur la surface plane d'une carte. Without a doubt, the most famous map projection is the Mercator projection. Corrections? (The distance AB along the parallel is (a cos φ) λ. This is his famous world map of 1569. Specified in [square brackets]: Actual size of the projection (minus the black or white background). For cylindrical projections, the axes of the ellipse are aligned to the meridians and parallels. On the other hand, the geodesic between these points is a great circle arc through the pole subtending an angle of 60° at the center: the length of this arc is one sixth of the great circle circumference, about 6,672 km. For Great Britain, taking 55° as a median latitude, hk = 3.04. assurée par un modèle mathématique appelé système de projection. Today, the use of the Mercator projection is not justified except by specific interests. cylindrical projection. The result is that deviation of the scale from unity is reduced over a wider range of latitudes. English-Chinese geology dictionary (英汉地质大词典). projection cylindrique oblique. In fact, the Mercator projection was the first projection regularly identified in atlases. The Mercator projection is a transformation of a cylindrical projection used for navigation. [16][19][e] For the Mercator projection, h = k, so the ellipses degenerate into circles with radius proportional to the value of the scale factor for that latitude. It is a cylindrical map projection that is a product of its time. magnetic directions, instead of geographical directions, Universal Transverse Mercator coordinate system, "Mercator Projection vs. Peters Projection, part 2", "Mercator Projection vs. Peters Projection, part 1", Table of examples and properties of all common projections, An interactive Java Applet to study the metric deformations of the Mercator Projection, Web Mercator: Non-Conformal, Non-Mercator (Noel Zinn, Hydrometronics LLC), Mercator's Projection at University of British Columbia, Map projection of the tri-axial ellipsoid, Early modern Netherlandish cartography, geography and cosmography, Dutch celestial cartography in the Age of Discovery, Dutch celestial and lunar cartography in the Age of Exploration, Dutch systematic mapping of the far southern sky, c. 1595–1599, Dutch commercial cartography in the Age of Discovery, Dutch corporate cartography in the Age of Discovery, Dutch maritime/nautical cartography in the Age of Discovery, Golden Age of Dutch exploration and discovery, Constellations created and listed by Dutch celestial cartographers, Dutch discovery, exploration and mapping of Svalbard, Dutch discovery, exploration and mapping of Jan Mayen, European exploration and mapping of Southern Africa, Great Southern Land/Great Unknown South Land, European maritime exploration of Australia, Dutch discovery, exploration and mapping of Australasia, Dutch discovery, exploration and mapping of Nova Hollandia, Dutch discovery, exploration and mapping of Tasmania/Van Diemen's Land, Dutch discovery, exploration and mapping of the Australian continent, Dutch discovery, exploration and mapping of the Australian mainland, Dutch discovery, exploration and mapping of Nova Zeelandia, Dutch exploration and mapping of Formosa/Taiwan, Dutch exploration and mapping of the East Indies, Dutch exploration and mapping of Southern Africa, Dutch exploration and mapping of South Africa, Dutch exploration and mapping of the Americas, Dutch exploration and mapping of the Pacific, Dutch discovery and exploration of Easter Island, Science and technology in the Dutch Republic, Golden Age of Dutch science and technology, Early modern Iberian (Spanish and Portuguese) cartography, First undisputed non-Indigenous discovery, exploration and mapping of Australasia, First published systematic uses of the triangulation method in modern surveying and mapmaking, First published use of the Mercator projection for maritime navigation, First printed nautical atlas in the modern sense, History of selenography / lunar cartography, First published scientific map of the Moon with a topographical nomenclature, History of uranography / celestial cartography, https://en.wikipedia.org/w/index.php?title=Mercator_projection&oldid=992995821, Short description is different from Wikidata, Articles with unsourced statements from July 2020, Articles with unsourced statements from February 2017, Wikipedia articles with SUDOC identifiers, Creative Commons Attribution-ShareAlike License, Greenland's real area is comparable to the, Africa appears to be roughly the same size as.

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