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Aitoff Projection
The Aitoff projection is a modified azimuthal map projection proposed by David A. Aitoff in 1889. Based on the equatorial form of the azimuthal equidistant projection, Aitoff first halves longitudes, then projects according to the azimuthal equidistant, and then stretches the result horizontally into a 2:1 ellipse to compensate for having halved the longitudes. Expressed simply: :x = 2 \operatorname_x\left(\frac, \varphi\right), \qquad y = \operatorname_y \left(\frac\lambda 2, \varphi \right) where azeq and azeq are the ''x'' and ''y'' components of the equatorial azimuthal equidistant projection. Written out explicitly, the projection is: :x = \frac, \qquad y = \frac where :\alpha = \arccos\left(\cos\varphi\cos\frac\right)\, and sinc ''α'' is the unnormalized sinc function with the discontinuity removed. In all of these formulas, ''λ'' is the longitude from the central meridian and ''φ'' is the latitude. Three years later, Ernst Hermann Heinrich Hammer suggested ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Map Projection
In cartography, map projection is the term used to describe a broad set of transformations employed to represent the two-dimensional curved surface of a globe on a 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 and to some extent. 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, projections are considered in several fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David A
David (; , "beloved one") (traditional spelling), , ''Dāwūd''; grc-koi, Δαυΐδ, Dauíd; la, Davidus, David; gez , ዳዊት, ''Dawit''; xcl, Դաւիթ, ''Dawitʿ''; cu, Давíдъ, ''Davidŭ''; possibly meaning "beloved one". was, according to the Hebrew Bible, the third king of the United Kingdom of Israel. In the Books of Samuel, he is described as a young shepherd and harpist who gains fame by slaying Goliath, a champion of the Philistines, in southern Canaan. David becomes a favourite of Saul, the first king of Israel; he also forges a notably close friendship with Jonathan, a son of Saul. However, under the paranoia that David is seeking to usurp the throne, Saul attempts to kill David, forcing the latter to go into hiding and effectively operate as a fugitive for several years. After Saul and Jonathan are both killed in battle against the Philistines, a 30-year-old David is anointed king over all of Israel and Judah. Following his rise to power, David ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Azimuthal Equidistant Projection
The azimuthal equidistant projection is an azimuthal map projection. It has the useful properties that all points on the map are at proportionally correct distances from the center point, and that all points on the map are at the correct azimuth (direction) from the center point. A useful application for this type of projection is a polar projection which shows all meridians (lines of longitude) as straight, with distances from the pole represented correctly. The flag of the United Nations contains an example of a polar azimuthal equidistant projection. History While it may have been used by ancient Egyptians for star maps in some holy books,, p.29 the earliest text describing the azimuthal equidistant projection is an 11th-century work by al-Biruni. An example of this system is the world map by ‛Ali b. Ahmad al-Sharafi of Sfax in 1571. The projection appears in many Renaissance maps, and Gerardus Mercator used it for an inset of the north polar regions in sheet 13 and le ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sinc Function
In mathematics, physics and engineering, the sinc function, denoted by , has two forms, normalized and unnormalized.. In mathematics, the historical unnormalized sinc function is defined for by \operatornamex = \frac. Alternatively, the unnormalized sinc function is often called the sampling function, indicated as Sa(''x''). In digital signal processing and information theory, the normalized sinc function is commonly defined for by \operatornamex = \frac. In either case, the value at is defined to be the limiting value \operatorname0 := \lim_\frac = 1 for all real . The normalization causes the definite integral of the function over the real numbers to equal 1 (whereas the same integral of the unnormalized sinc function has a value of ). As a further useful property, the zeros of the normalized sinc function are the nonzero integer values of . The normalized sinc function is the Fourier transform of the rectangular function with no scaling. It is used in the concep ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ernst Hammer (cartographer)
Ernst Hammer (20 October 1884 – 2 December 1957) was a German-Austrian officer of four armies since 1 October 1903, entering as a one-year volunteer. He was Oberleutnant of the Common Army, Hauptmann of the k.u.k. Armee, Generalmajor of the Bundesheer (transferred to the German Army 15 March 1938), Generalleutnant of the Wehrmacht during World War II. He was a recipient of the Knight's Cross of the Iron Cross. As commander of the 75th Infantry Division, he ordered his soldiers to shoot female Soviet POWs on the spot. Awards and decorations * Military Merit Cross, 3rd Class with War Decoration and Swords (Austria-Hungary, World War I) * Military Merit Medal, in Silver and in Bronze (Austria-Hungary, World War I) * Karl Troop Cross (World War I) * Gallipoli Star (World War I) * Austrian War Commemorative Medal * Hungarian War Commemorative Medal * Honour Cross of the World War 1914/1918 * Iron Cross (1914) ** 2nd Class ** 1st Class * Clasps to the Iron Cross ** 2nd Class ** 1st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lambert Azimuthal Equal-area Projection
The Lambert azimuthal equal-area projection is a particular mapping from a sphere to a disk. It accurately represents area in all regions of the sphere, but it does not accurately represent angles. It is named for the Swiss mathematician Johann Heinrich Lambert, who announced it in 1772. "Zenithal" being synonymous with "azimuthal", the projection is also known as the Lambert zenithal equal-area projection. The Lambert azimuthal projection is used as a map projection in cartography. For example, the National Atlas of the US uses a Lambert azimuthal equal-area projection to display information in the online Map Maker application, and the European Environment Agency recommends its usage for European mapping for statistical analysis and display. It is also used in scientific disciplines such as geology for plotting the orientations of lines in three-dimensional space. This plotting is aided by a special kind of graph paper called a Schmidt net.Ramsay (1967) Definition To define ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hammer Projection
The Hammer projection is an equal-area map projection described by Ernst Hammer (cartographer), Ernst Hammer in 1892. Using the same 2:1 elliptical outer shape as the Mollweide projection, Hammer intended to reduce distortion in the regions of the outer meridians, where it is extreme in the Mollweide. Development Directly inspired by the Aitoff projection, Hammer suggested the use of the equatorial form of the Lambert azimuthal equal-area projection instead of Aitoff's use of the azimuthal equidistant projection: :\begin x &= \operatorname_x\left(\frac, \varphi\right) \\ y &= \tfrac12 \operatorname_y\left(\frac, \varphi\right) \end where laea and laea are the ''x'' and ''y'' components of the equatorial Lambert azimuthal equal-area projection. Written out explicitly: :\begin x &= \frac \\ y &= \frac \end The inverse is calculated with the intermediate variable :z \equiv \sqrt The longitude and latitudes can then be calculated by :\begin \lambda &= 2 \arctan \frac \\ \varphi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Map Projections
This is a summary of map projections that have articles of their own on Wikipedia or that are otherwise notable Notability is the property of being worthy of notice, having fame, or being considered to be of a high degree of interest, significance, or distinction. It also refers to the capacity to be such. Persons who are notable due to public responsibi .... Because there is no limit to the number of possible map projections, there can be no comprehensive list. Table of projections *The first known popularizer/user and not necessarily the creator. Key Type of projection ; Cylindrical: In standard presentation, these map regularly-spaced meridians to equally spaced vertical lines, and parallels to horizontal lines. ; Pseudocylindrical: In standard presentation, these map the central meridian and parallels as straight lines. Other meridians are curves (or possibly straight from pole to equator), regularly spaced along parallels. ; Conic: In standard presentation, conic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mollweide Projection
400px, Mollweide projection of the world 400px, The Mollweide projection with Tissot's indicatrix of deformation The Mollweide projection is an equal-area, pseudocylindrical map projection generally used for maps of the world or celestial sphere. It is also known as the Babinet projection, homalographic projection, homolographic projection, and elliptical projection. The projection trades accuracy of angle and shape for accuracy of proportions in area, and as such is used where that property is needed, such as maps depicting global distributions. The projection was first published by mathematician and astronomer Karl (or Carl) Brandan Mollweide (1774–1825) of Leipzig in 1805. It was reinvented and popularized in 1857 by Jacques Babinet, who gave it the name homalographic projection. The variation homolographic arose from frequent nineteenth-century usage in star atlases. Properties The Mollweide is a pseudocylindrical projection in which the equator is represented as a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
