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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 ...
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Hammer Projection SW
A hammer is a tool, most often a hand tool, consisting of a weighted "head" fixed to a long handle that is swung to deliver an impact to a small area of an object. This can be, for example, to drive nail (fastener), nails into wood, to shape metal (as with a forge), or to crush Rock (geology), rock. Hammers are used for a wide range of driving, shaping, breaking and non-destructive striking applications. Traditional disciplines include carpentry, blacksmithing, war hammer, warfare, and mallet percussion, percussive musicianship (as with a gong). Hammering is use of a hammer in its strike capacity, as opposed to pry bar, prying with a secondary claw or grappling with a secondary hook. Carpentry and blacksmithing hammers are generally wielded from a stationary stance against a stationary target as gripped and propelled with one arm, in a lengthy downward plane (geometry), planar arc—downward to add kinetic energy to the impact—pivoting mainly around the shoulder and elbo ...
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Hammer With Tissot's Indicatrices Of Distortion
A hammer is a tool, most often a hand tool, consisting of a weighted "head" fixed to a long handle that is swung to deliver an impact to a small area of an object. This can be, for example, to drive nails into wood, to shape metal (as with a forge), or to crush rock. Hammers are used for a wide range of driving, shaping, breaking and non-destructive striking applications. Traditional disciplines include carpentry, blacksmithing, warfare, and percussive musicianship (as with a gong). Hammering is use of a hammer in its strike capacity, as opposed to prying with a secondary claw or grappling with a secondary hook. Carpentry and blacksmithing hammers are generally wielded from a stationary stance against a stationary target as gripped and propelled with one arm, in a lengthy downward planar arc—downward to add kinetic energy to the impact—pivoting mainly around the shoulder and elbow, with a small but brisk wrist rotation shortly before impact; for extreme impact, conc ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 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, England 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 absolute measure of time allows ...
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Latitude
In geography, latitude is a 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. 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'') to the ellipsoidal surface from the point, and the 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 is modeled by the geoid, a surface which approximates the mean sea level over the ocean ...
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United States Geological Survey
The United States Geological Survey (USGS), formerly simply known as the Geological Survey, is a scientific agency of the United States government. The scientists of the USGS study the landscape of the United States, its natural resources, and the natural hazards that threaten it. The organization's work spans the disciplines of biology, geography, geology, and hydrology. The USGS is a fact-finding research organization with no regulatory responsibility. The agency was founded on March 3, 1879. The USGS is a bureau of the United States Department of the Interior; it is that department's sole scientific agency. The USGS employs approximately 8,670 people and is headquartered in Reston, Virginia. The USGS also has major offices near Lakewood, Colorado, at the Denver Federal Center, and Menlo Park, California. The current motto of the USGS, in use since August 1997, is "science for a changing world". The agency's previous slogan, adopted on the occasion of its hundredt ...
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John (Ian) Bartholomew
John Bartholomew, generally known as Ian Bartholomew (12 February 1890 – 9 February 1962) was a Scottish cartographer and geographer. Life John was the son of John George Bartholomew and Janet MacDonald. He was educated at Merchiston Castle School. Bartholomew studied cartography in Leipzig, Paris and at the University of Edinburgh and took over the family business John Bartholomew and Son Ltd. on the death of his father John George Bartholomew. He inherited the task from his father of completing the ''Times Survey Atlas of the World'' (1921), which was expanded into the Times Mid-Century Edition (issued in five volumes between 1955 and 1960). He introduced new cartographic techniques, modern printing and expanded the company significantly. He was awarded the Military Cross in 1915 after serving with the Gordon Highlanders and General Staff during the 1914—18 War. He was also Mentioned in Dispatches. He served as Honorary Secretary and President of the Royal Scottish G ...
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