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Collignon Projection
The Collignon projection is an equal-area pseudocylindrical map projection first known to be published by Édouard Collignon in 1865 and subsequently cited by A. Tissot in 1881. For the smallest choices of the parameters chosen for this projection, the sphere may be mapped either to a single diamond, a pair of squares, or a triangle. The projection is used in the polar areas as part of the HEALPix spherical projection, which is widely used in physical cosmology in making maps of the cosmic microwave background, in particular by the WMAP and Planck space missions. Formulae Let ''R'' be the radius of the sphere, ''φ'' the latitude, ''λ'' the longitude, and ''λ0'' the longitude of the central meridian (chosen as desired). Also, define s = \sqrt = \sqrt \sin\left(\frac - \frac\right), where the two forms are equivalent for ''φ'' in the range of possible latitudes. Then the Collignon projection is given by: :\begin x &= \fracR \left( \lambda - \lambda_0 \right) s, \\ y &= ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Collignon Projection SW
Collignon is a surname, and may refer to: * Charles Collignon (fencer), French fencer and 1908 Olympic champion *Charles Collignon (surgeon) (1725–1785), British surgeon and professor of anatomy at Cambridge University * Christophe Collignon (b. 1969), Belgian politician * Claude Boniface Collignon (d. 1819), French proponent of decimal time and metric system * Daphné Collignon (born 1977), French comic book author * Édouard Collignon (1831–1913), French engineer and scientist * François Collignon (c. 1609–1687), French engraver * Frédéric Collignon (b. 1975), Belgian table football player * Giuseppe Collignon (1778–1863), Italian neoclassical painter * Jacques Collignon (b. 1936), French Olympic swimmer * Jean Nicolas Collignon (1762–?1788), French botanist *Maurice Collignon (1893–1978), French geologist and paleontologist *Maxime Collignon (1849–1917), French archaeologist * Médéric Collignon (born 1970), French musician See also * Collignon project ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equal-area Projection
In cartography, an equivalent, authalic, or equal-area projection is a map projection that preserves relative area measure between any and all map regions. Equivalent projections are widely used for thematic maps showing scenario distribution such as population, farmland distribution, forested areas, and so forth, because an equal-area map does not change apparent density of the phenomenon being mapped. By Carl Friedrich Gauss, Gauss's Theorema Egregium, an equal-area projection cannot be conformal map projection, conformal. This implies that an equal-area projection inevitably distorts shapes. Even though a point or points or a path or paths on a map might have no distortion, the greater the area of the region being mapped, the greater and more obvious the distortion of shapes inevitably becomes. Description In order for a map projection of the sphere to be equal-area, its generating formulae must meet this Cauchy-Riemann equations, Cauchy-Riemann-like condition: :\frac \cdo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Map Projection
In cartography, a map projection is any of a broad set of Transformation (function) , transformations employed to represent the curved two-dimensional Surface (mathematics), surface of a globe on a Plane (mathematics), plane. In a map projection, coordinates, often expressed as latitude and longitude, of locations from the surface of the globe are transformed to coordinates on a plane. Projection is a necessary step in creating a two-dimensional map and is one of the essential elements of cartography. All projections of a sphere on a plane necessarily distort the surface in some way. Depending on the purpose of the map, some distortions are acceptable and others are not; therefore, different map projections exist in order to preserve some properties of the sphere-like body at the expense of other properties. The study of map projections is primarily about the characterization of their distortions. There is no limit to the number of possible map projections. More generally, proje ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Édouard Collignon
Édouard Charles Romain Collignon (1831–1913) was a French engineer and scientist, known for the Collignon projection and for his role in building railways in Russia. Career After graduating from the l'École polytechnique in 1849, he became an ingénieur des ponts et chaussées. He became inspecteur des Ponts et chaussées in 1878. In 1857 to 1862 he played an important role in the construction of railways from Saint Petersburg to Warsaw and from Moscow to Nizhny Novgorod Nizhny Novgorod ( ; rus, links=no, Нижний Новгород, a=Ru-Nizhny Novgorod.ogg, p=ˈnʲiʐnʲɪj ˈnovɡərət, t=Lower Newtown; colloquially shortened to Nizhny) is a city and the administrative centre of Nizhny Novgorod Oblast an .... He was a founding member of the ''Association française pour l’avancement des sciences''. He was the author of studies on the Russian railways and of memoirs and treatises on mechanics. External links * Répertoire articles by Collignon in the da ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
HEALPix
HEALPix (sometimes written as Healpix), an acronym for Hierarchical Equal Area isoLatitude Pixelisation of a 2-sphere, is an algorithm for pixelisation of the 2-sphere based on subdivision of a distorted rhombic dodecahedron, and the associated class of map projections. The pixelisation algorithm was devised in 1997 by Krzysztof M. Górski at the Theoretical Astrophysics Center in Copenhagen, Denmark, and first published as a preprint in 1998. Projection and pixelisation The HEALPix projection is a general class of spherical projections, sharing several key properties, which map the 2-sphere to the Euclidean plane. Any of these can be followed by partitioning (pixelising) the resulting region of the 2-plane. In particular, when one of these projections (the H=4, K=3 HEALPix projection) is followed by a pixelisation of the 2-plane, the result is generally known as the HEALPix pixelisation, which is widely used in physical cosmology for maps of the cosmic microwave background. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physical Cosmology
Physical cosmology is a branch of cosmology concerned with the study of cosmological models. A cosmological model, or simply cosmology, provides a description of the largest-scale structures and dynamics of the universe and allows study of fundamental questions about its Cosmogony, origin, structure, Chronology of the universe, evolution, and ultimate fate.For an overview, see Cosmology as a science originated with the Copernican principle, which implies that astronomical object, celestial bodies obey identical physical laws to those on Earth, and Newtonian mechanics, which first allowed those physical laws to be understood. Physical cosmology, as it is now understood, began in 1915 with the development of Albert Einstein's general relativity, general theory of relativity, followed by major observational discoveries in the 1920s: first, Edwin Hubble discovered that the universe contains a huge number of external Galaxy, galaxies beyond the Milky Way; then, work by Vesto Sliph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cosmic Microwave Background
The cosmic microwave background (CMB, CMBR), or relic radiation, is microwave radiation that fills all space in the observable universe. With a standard optical telescope, the background space between stars and galaxies is almost completely dark. However, a sufficiently sensitive radio telescope detects a faint background glow that is almost isotropic, uniform and is not associated with any star, galaxy, or other astronomical object, object. This glow is strongest in the microwave region of the electromagnetic spectrum. The accidental Discovery of cosmic microwave background radiation, discovery of the CMB in 1965 by American radio astronomers Arno Allan Penzias and Robert Woodrow Wilson was the culmination of work initiated in the 1940s. The CMB is landmark evidence of the Big Bang scientific theory, theory for the origin of the universe. In the Big Bang cosmological models, during the earliest periods, the universe was filled with an Opacity (optics), opaque fog of dense, hot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
WMAP
The Wilkinson Microwave Anisotropy Probe (WMAP), originally known as the Microwave Anisotropy Probe (MAP and Explorer 80), was a NASA spacecraft operating from 2001 to 2010 which measured temperature differences across the sky in the cosmic microwave background (CMB) – the radiant heat remaining from the Big Bang. Headed by Professor Charles L. Bennett of Johns Hopkins University, the mission was developed in a joint partnership between the NASA Goddard Space Flight Center and Princeton University. The WMAP spacecraft was launched on 30 June 2001 from Florida. The WMAP mission succeeded the COBE space mission and was the second medium-class (MIDEX) spacecraft in the NASA Explorer program. In 2003, MAP was renamed WMAP in honor of cosmologist David Todd Wilkinson (1935–2002), who had been a member of the mission's science team. After nine years of operations, WMAP was switched off in 2010, following the launch of the more advanced Planck spacecraft by European Space Agenc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Planck (spacecraft)
''Planck'' was a space observatory operated by the European Space Agency (ESA) from 2009 to 2013. It was an ambitious project that aimed to map the anisotropies of the cosmic microwave background (CMB) at microwave and infrared frequencies, with high sensitivity and angular resolution. The mission was highly successful and substantially improved upon observations made by the NASA Wilkinson Microwave Anisotropy Probe (WMAP). The Planck observatory was a major source of information relevant to several cosmological and astrophysical issues. One of its key objectives was to test theories of the early Universe and the origin of cosmic structure. The mission provided significant insights into the composition and evolution of the Universe, shedding light on the fundamental physics that governs the cosmos. Planck was initially called COBRAS/SAMBA, which stands for the Cosmic Background Radiation Anisotropy Satellite/Satellite for Measurement of Background Anisotropies. The project sta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Latitude
In geography, latitude is a geographic coordinate system, geographic coordinate that specifies the north-south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from −90° at the south pole to 90° at the north pole, with 0° at the Equator. Parallel (latitude), Lines of constant latitude, or ''parallels'', run east-west as circles parallel to the equator. Latitude and longitude are used together as a coordinate pair to specify a location on the surface of the Earth. On its own, the term "latitude" normally refers to the ''geodetic latitude'' as defined below. Briefly, the geodetic latitude of a point is the angle formed between the vector perpendicular (or ''Normal (geometry), normal'') to the ellipsoidal surface from the point, and the equatorial plane, plane of the equator. Background Two levels of abstraction are employed in the definitions of latitude and longitude. In the first step the physical surface i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Longitude
Longitude (, ) is a geographic coordinate that specifies the east- west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek letter lambda (λ). Meridians are imaginary semicircular lines running from pole to pole that connect points with the same longitude. The prime meridian defines 0° longitude; by convention the International Reference Meridian for the Earth passes near the Royal Observatory in Greenwich, south-east London on the island of Great Britain. Positive longitudes are east of the prime meridian, and negative ones are west. Because of the Earth's rotation, there is a close connection between longitude and time measurement. Scientifically precise local time varies with longitude: a difference of 15° longitude corresponds to a one-hour difference in local time, due to the differing position in relation to the Sun. Comparing local time to an absol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
