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Hammer Retroazimuthal Projection
The Hammer retroazimuthal projection is a modified azimuthal proposed by Ernst Hermann Heinrich Hammer in 1910. As a retroazimuthal projection, azimuths (directions) are correct from any point to the designated center point. Additionally, all distances from the center of the map are proportional to what they are on the globe. In whole-world presentation, the back and front hemispheres overlap, making the projection a non-injective function. The back hemisphere can be rotated 180° to avoid overlap, but in this case, any azimuths measured from the back hemisphere must be corrected. Given a radius ''R'' for the projecting globe, the projection is defined as: :\beginx &= R K \cos \varphi_1 \sin (\lambda-\lambda_0)\\ y &= -R K \big(\sin \varphi_1 \cos \varphi - \cos \varphi_1 \sin \varphi \cos (\lambda-\lambda_0)\big)\end where :K = \frac and :\cos z = \sin \varphi_1 \sin \varphi + \cos \varphi_1 \cos \varphi \cos (\lambda - \lambda_0) The latitude and longitude of the point ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hammer Retroazimuthal Projection Combined1
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hammer Retroazimuthal 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 (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 elbow, with a small ... [...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] |
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] |
Azimuth
An azimuth (; from ar, اَلسُّمُوت, as-sumūt, the directions) is an angular measurement in a spherical coordinate system. More specifically, it is the horizontal angle from a cardinal direction, most commonly north. Mathematically, the relative position vector from an observer (origin) to a point of interest is projected perpendicularly onto a reference plane (the horizontal plane); the angle between the projected vector and a reference vector on the reference plane is called the azimuth. When used as a celestial coordinate, the azimuth is the horizontal direction of a star or other astronomical object in the sky. The star is the point of interest, the reference plane is the local area (e.g. a circular area with a 5 km radius at sea level) around an observer on Earth's surface, and the reference vector points to true north. The azimuth is the angle between the north vector and the star's vector on the horizontal plane. Azimuth is usually measured in d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Injective
In mathematics, an injective function (also known as injection, or one-to-one function) is a function that maps distinct elements of its domain to distinct elements; that is, implies . (Equivalently, implies in the equivalent contrapositive statement.) In other words, every element of the function's codomain is the image of one element of its domain. The term must not be confused with that refers to bijective functions, which are functions such that each element in the codomain is an image of exactly one element in the domain. A homomorphism between algebraic structures is a function that is compatible with the operations of the structures. For all common algebraic structures, and, in particular for vector spaces, an is also called a . However, in the more general context of category theory, the definition of a monomorphism differs from that of an injective homomorphism. This is thus a theorem that they are equivalent for algebraic structures; see for more details. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Craig Retroazimuthal Projection
The Craig retroazimuthal map projection was created by James Ireland Craig in 1909. It is a modified cylindrical projection. As a retroazimuthal projection, it preserves directions from everywhere to one location of interest that is configured during construction of the projection. The projection is sometimes known as the Mecca projection because Craig, who had worked in Egypt as a cartographer, created it to help Muslims find their qibla. In such maps, Mecca is the configurable location of interest. Given latitude ''φ'' to plot, latitude ''φ'' of the fixed location of interest, longitude ''λ'' to plot, and the longitude ''λ'' of the fixed location of interest, the projection is defined by: :\begin x &= \lambda - \lambda_0\\ y &= \frac\Big(\sin \varphi \cos \left(\lambda - \lambda_0\right) - \tan \varphi_0 \cos \varphi\Big)\end But when ''λ'' − ''λ'' = 0, ''y'' above is undefined, so instead use the ratio's continuous completion: :y = \sin \varphi \cos \lef ... [...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] |
