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Conformal Map Projection
In cartography, a conformal map projection is one in which every angle between two curves that cross each other on Earth (a sphere or an ellipsoid) is preserved in the image of the projection; that is, the projection is a conformal map in the mathematical sense. For example, if two roads cross each other at a 39° angle, their images on a map with a conformal projection cross at a 39° angle. Properties A conformal projection can be defined as one that is locally conformal at every point on the map, albeit possibly with Mathematical singularity, singular points where conformality fails. Thus, every small figure is nearly similar to its image on the map. The projection preserves the ratio of two lengths in the small domain. All of the projection's Tissot's indicatrices are circles. Conformal projections preserve only small figures. Large figures are distorted by even conformal projections. In a conformal projection, any small figure is similar to the image, but the ratio of sim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cartography
Cartography (; from , 'papyrus, sheet of paper, map'; and , 'write') is the study and practice of making and using maps. Combining science, aesthetics and technique, cartography builds on the premise that reality (or an imagined reality) can be modeled in ways that communicate spatial information effectively. The fundamental objectives of traditional cartography are to: * Set the map's agenda and select traits of the object to be mapped. This is the concern of map editing. Traits may be physical, such as roads or land masses, or may be abstract, such as toponyms or political boundaries. * Represent the terrain of the mapped object on flat media. This is the concern of map projections. * Eliminate the mapped object's characteristics that are irrelevant to the map's purpose. This is the concern of Cartographic generalization, generalization. * Reduce the complexity of the characteristics that will be mapped. This is also the concern of generalization. * Orchestrate the elements ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gauss–Krüger Coordinate System
The transverse Mercator map projection (TM, TMP) is an adaptation of the standard Mercator projection. The transverse version is widely used in national and international mapping systems around the world, including the Universal Transverse Mercator coordinate system, Universal Transverse Mercator. When paired with a suitable geodetic datum, the transverse Mercator delivers high accuracy in zones less than a few degrees in east-west extent. Standard and transverse aspects The transverse Mercator projection is the map projection#Aspect of the projection, transverse aspect of the standard (or ''Normal'') Mercator projection. They share the same underlying mathematical construction and consequently the transverse Mercator inherits many traits from the normal Mercator: * Both map projection, projections are map projection#Cylindrical, cylindrical: for the normal Mercator, the axis of the cylinder coincides with the polar axis and the line of tangency with the equator. For the transver ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elliptic Function
In the mathematical field of complex analysis, elliptic functions are special kinds of meromorphic functions, that satisfy two periodicity conditions. They are named elliptic functions because they come from elliptic integrals. Those integrals are in turn named elliptic because they first were encountered for the calculation of the arc length of an ellipse. Important elliptic functions are Jacobi elliptic functions and the Weierstrass \wp-function. Further development of this theory led to hyperelliptic functions and modular forms. Definition A meromorphic function is called an elliptic function, if there are two \mathbb- linear independent complex numbers \omega_1,\omega_2\in\mathbb such that : f(z + \omega_1) = f(z) and f(z + \omega_2) = f(z), \quad \forall z\in\mathbb. So elliptic functions have two periods and are therefore doubly periodic functions. Period lattice and fundamental domain If f is an elliptic function with periods \omega_1,\omega_2 it also holds ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Möbius Transformation
In geometry and complex analysis, a Möbius transformation of the complex plane is a rational function of the form f(z) = \frac of one complex number, complex variable ; here the coefficients , , , are complex numbers satisfying . Geometrically, a Möbius transformation can be obtained by first applying the inverse stereographic projection from the plane to the unit sphere, moving and rotating the sphere to a new location and orientation in space, and then applying a stereographic projection to map from the sphere back to the plane. These transformations preserve angles, map every straight line to a line or circle, and map every circle to a line or circle. The Möbius transformations are the projective transformations of the complex projective line. They form a group (mathematics), group called the Möbius group, which is the projective linear group . Together with its subgroups, it has numerous applications in mathematics and physics. Möbius geometry, Möbius geometries and t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Littrow Projection
The Littrow projection is a map projection developed by Joseph Johann von Littrow in 1833. It is the only conformal, retroazimuthal map projection. As a retroazimuthal projection, the Littrow shows directions, or azimuths, correctly from any point to the center of the map. Patrick Weir of the British Merchant Navy independently reinvented the projection in 1890, after which it began to see more frequent use as recognition of its retroazimuthal property spread. Maps based on the Littrow projection are sometimes referred to as Weir Azimuth diagrams. The projection transforms from latitude ''φ'' and longitude ''λ'' to map coordinates ''x'' and ''y'' via the following equations: :\begin x &= R \frac \\ y &= R \cos \left(\lambda - \lambda_0\right) \tan \varphi \end where ''R'' is the radius of the globe to be projected and ''λ''0 is the longitude desired for the center point. See also * List of map projections This is a summary of map projections that have articles of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complex Number
In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the form a + bi, where and are real numbers. Because no real number satisfies the above equation, was called an imaginary number by René Descartes. For the complex number is called the , and is called the . The set of complex numbers is denoted by either of the symbols \mathbb C or . Despite the historical nomenclature, "imaginary" complex numbers have a mathematical existence as firm as that of the real numbers, and they are fundamental tools in the scientific description of the natural world. Complex numbers allow solutions to all polynomial equations, even those that have no solutions in real numbers. More precisely, the fundamental theorem of algebra asserts that every non-constant polynomial equation with real or complex coefficie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polynomial
In mathematics, a polynomial is a Expression (mathematics), mathematical expression consisting of indeterminate (variable), indeterminates (also called variable (mathematics), variables) and coefficients, that involves only the operations of addition, subtraction, multiplication and exponentiation to nonnegative integer powers, and has a finite number of terms. An example of a polynomial of a single indeterminate is . An example with three indeterminates is . Polynomials appear in many areas of mathematics and science. For example, they are used to form polynomial equations, which encode a wide range of problems, from elementary word problem (mathematics education), word problems to complicated scientific problems; they are used to define polynomial functions, which appear in settings ranging from basic chemistry and physics to economics and social science; and they are used in calculus and numerical analysis to approximate other functions. In advanced mathematics, polynomials are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GS50 Projection
GS50, also hyphenated as GS-50, is a map projection that was developed by John Parr Snyder of the USGS The United States Geological Survey (USGS), founded as the Geological Survey, is an government agency, agency of the United States Department of the Interior, U.S. Department of the Interior whose work spans the disciplines of biology, geograp ... in 1982. The GS50 projection provides a conformal projection suitable only for maps of the 50 United States. Scale varies less than 2% throughout the area covered. Distortion is very low as well. It is not a standard projection in the sense that it uses complex polynomials (of the tenth order) rather than a trigonometric formulation, though it was developed from an oblique stereographic projection. References {{clear Conformal projections ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Europe
Europe is a continent located entirely in the Northern Hemisphere and mostly in the Eastern Hemisphere. It is bordered by the Arctic Ocean to the north, the Atlantic Ocean to the west, the Mediterranean Sea to the south, and Asia to the east. Europe shares the landmass of Eurasia with Asia, and of Afro-Eurasia with both Africa and Asia. Europe is commonly considered to be Boundaries between the continents#Asia and Europe, separated from Asia by the Drainage divide, watershed of the Ural Mountains, the Ural (river), Ural River, the Caspian Sea, the Greater Caucasus, the Black Sea, and the waterway of the Bosporus, Bosporus Strait. "Europe" (pp. 68–69); "Asia" (pp. 90–91): "A commonly accepted division between Asia and Europe ... is formed by the Ural Mountains, Ural River, Caspian Sea, Caucasus Mountains, and the Black Sea with its outlets, the Bosporus and Dardanelles." Europe covers approx. , or 2% of Earth#Surface, Earth's surface (6.8% of Earth's land area), making it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Africa
Africa is the world's second-largest and second-most populous continent after Asia. At about 30.3 million km2 (11.7 million square miles) including adjacent islands, it covers 20% of Earth's land area and 6% of its total surface area.Sayre, April Pulley (1999), ''Africa'', Twenty-First Century Books. . With nearly billion people as of , it accounts for about of the world's human population. Demographics of Africa, Africa's population is the youngest among all the continents; the median age in 2012 was 19.7, when the worldwide median age was 30.4. Based on 2024 projections, Africa's population will exceed 3.8 billion people by 2100. Africa is the least wealthy inhabited continent per capita and second-least wealthy by total wealth, ahead of Oceania. Scholars have attributed this to different factors including Geography of Africa, geography, Climate of Africa, climate, corruption, Scramble for Africa, colonialism, the Cold War, and neocolonialism. Despite this lo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stereographic Map Projection
The stereographic projection, also known as the planisphere projection or the azimuthal conformal projection, is a conformal map projection whose use dates back to antiquity. Like the orthographic projection and gnomonic projection, the stereographic projection is an azimuthal projection, and when on a sphere, also a perspective projection. On an ellipsoid, the perspective definition of the stereographic projection is not conformal, and adjustments must be made to preserve its azimuthal and conformal properties. The universal polar stereographic coordinate system uses one such ellipsoidal implementation. History The stereographic projection was likely known in its polar aspect to the ancient Egyptians, though its invention is often credited to Hipparchus, who was the first Greek to use it. Its oblique aspect was used by Greek Mathematician Theon of Alexandria in the fourth century, and its equatorial aspect was used by Arab astronomer Al-Zarkali in the eleventh century ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Japanese Archipelago
The is an archipelago of list of islands of Japan, 14,125 islands that form the country of Japan. It extends over from the Sea of Okhotsk in the northeast to the East China Sea, East China and Philippine Sea, Philippine seas in the southwest along the Pacific coast of the Eurasian continent, and consists of three island arcs from north to south: the Northeastern Japan Arc, the Southwestern Japan Arc, and the Ryukyu Islands, Ryukyu Island Arc. The Daitō Islands, the Izu–Bonin–Mariana Arc, the Kuril Islands, and the Nanpō Islands neighbor the archipelago. Japan is the largest island country in East Asia and the list of island countries, fourth-largest island country in the world with . It has an Exclusive economic zone of Japan, exclusive economic zone of . Terminology The term "Mainland Japan" is used to distinguish the large islands of the Japanese archipelago from the remote, smaller islands; it refers to the main islands of Hokkaido, Honshu, Kyushu, and Shikoku. From 19 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
