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Adams Hemisphere-in-a-square Projection
The Adams hemisphere-in-a-square is a conformal map projection for a hemisphere. It is a transverse version of the Peirce quincuncial projection, and is named after American cartographer Oscar Sherman Adams, who published it in 1925.. When it is used to represent the entire sphere it is known as the Adams doubly periodic projection. Like many conformal projections, conformality fails at certain points, in this case at the four corners. See also * List of map projections * Guyou hemisphere-in-a-square projection * Doubly periodic function In mathematics, a doubly periodic function is a function defined on the complex plane and having two "periods", which are complex numbers ''u'' and ''v'' that are linearly independent as vectors over the field of real numbers. That ''u'' and '' ... References Map projections Conformal projections {{geometry-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adams Hemisphere In A Square
Adams may refer to: * For persons, see Adams (surname) Places United States *Adams, California *Adams, California, former name of Corte Madera, California *Adams, Decatur County, Indiana *Adams, Kentucky *Adams, Massachusetts, a New England town **Adams (CDP), Massachusetts, the central village in the town *Adams, Minnesota * Adams, North Dakota *Adams, Nebraska *Adams, New Jersey * Adams (town), New York **Adams (village), New York, within the town *Adams, Oklahoma *Adams, Oregon * Adams, Pennsylvania, a former community in Armstrong County *Adams, Tennessee *Adams, Wisconsin, city in Adams County *Adams, Adams County, Wisconsin, town *Adams, Green County, Wisconsin, town *Adams, Jackson County, Wisconsin, town *Adams, Walworth County, Wisconsin, unincorporated community *Adams Center, Wisconsin, a ghost town Elsewhere *Adams (lunar crater) *Adams (Martian crater) *Adams Island, New Zealand, one of the Auckland Islands *Adams, Ilocos Norte Transportation ;Vehicles *Adams (1903 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adams Doubly-Periodic With Tissot's Indicatrices Of Distortion
Adams may refer to: * For persons, see Adams (surname) Places United States *Adams, California *Adams, California, former name of Corte Madera, California *Adams, Decatur County, Indiana *Adams, Kentucky *Adams, Massachusetts, a New England town **Adams (CDP), Massachusetts, the central village in the town *Adams, Minnesota * Adams, North Dakota *Adams, Nebraska *Adams, New Jersey * Adams (town), New York **Adams (village), New York, within the town *Adams, Oklahoma *Adams, Oregon * Adams, Pennsylvania, a former community in Armstrong County *Adams, Tennessee *Adams, Wisconsin, city in Adams County *Adams, Adams County, Wisconsin, town *Adams, Green County, Wisconsin, town *Adams, Jackson County, Wisconsin, town *Adams, Walworth County, Wisconsin, unincorporated community *Adams Center, Wisconsin, a ghost town Elsewhere *Adams (lunar crater) *Adams (Martian crater) *Adams Island, New Zealand, one of the Auckland Islands *Adams, Ilocos Norte Transportation ;Vehicles *Adams (1903 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conformal Map
In mathematics, a conformal map is a function that locally preserves angles, but not necessarily lengths. More formally, let U and V be open subsets of \mathbb^n. A function f:U\to V is called conformal (or angle-preserving) at a point u_0\in U if it preserves angles between directed curves through u_0, as well as preserving orientation. Conformal maps preserve both angles and the shapes of infinitesimally small figures, but not necessarily their size or curvature. The conformal property may be described in terms of the Jacobian derivative matrix of a coordinate transformation. The transformation is conformal whenever the Jacobian at each point is a positive scalar times a rotation matrix (orthogonal with determinant one). Some authors define conformality to include orientation-reversing mappings whose Jacobians can be written as any scalar times any orthogonal matrix. For mappings in two dimensions, the (orientation-preserving) conformal mappings are precisely the locally i ... [...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] |
Peirce Quincuncial Projection
The Peirce quincuncial projection is the conformal map projection from the sphere to an unfolded square dihedron, developed by Charles Sanders Peirce in 1879. Each octant projects onto an isosceles right triangle, and these are arranged into a square. The name ''quincuncial'' refers to this arrangement: the north pole at the center and quarters of the south pole in the corners form a quincunx pattern like the pips on the ''five'' face of a traditional die. The projection has the distinctive property that it forms a seamless square tiling of the plane, conformal except at four singular points along the equator. Typically the projection is square and oriented such that the north pole lies at the center, but an oblique aspect in a rectangle was proposed by Émile Guyou in 1887, and a transverse aspect was proposed by Oscar Adams in 1925. The projection has seen use in digital photography for portraying spherical panoramas. History The maturation of complex analysis led to gene ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Doubly Periodic
In the mathematical field of complex analysis, elliptic functions are a special kind of meromorphic functions, that satisfy two periodicity conditions. They are named elliptic functions because they come from elliptic integrals. Originally those integrals occurred at 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 also called ''doubly periodic''. Period lattice and fundamental domain Iff is an elliptic function with periods \omega_1,\omega_2 it also holds that : f(z+\gamma)=f(z) for every linear ... [...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] |
Guyou Hemisphere-in-a-square Projection
The Guyou hemisphere-in-a-square projection is a conformal map projection for the hemisphere. It is an oblique aspect of the Peirce quincuncial projection. History The projection was developed by of France in 1887. Formal description The projection can be computed as an oblique aspect of the Peirce quincuncial projection by rotating the axis 45 degrees. It can also be computed by rotating the coordinates −45 degrees before computing the stereographic projection; this projection is then remapped into a square whose coordinates are then rotated 45 degrees. The projection is conformal except for the four corners of each hemisphere’s square. Like other conformal polygonal projections, the Guyou is a Schwarz–Christoffel mapping. Properties Its properties are very similar to those of the Peirce quincuncial: * Each hemisphere is represented as a square, the sphere as a rectangle of aspect ratio 2:1. * The part where the exaggeration of scale amounts to double that at t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Doubly Periodic Function
In mathematics, a doubly periodic function is a function defined on the complex plane and having two "periods", which are complex numbers ''u'' and ''v'' that are linearly independent as vectors over the field of real numbers. That ''u'' and ''v'' are periods of a function ''ƒ'' means that :f(z + u) = f(z + v) = f(z)\, for all values of the complex number ''z''. The doubly periodic function is thus a two-dimensional extension of the simpler singly periodic function, which repeats itself in a single dimension. Familiar examples of functions with a single period on the real number line include the trigonometric functions like cosine and sine, In the complex plane the exponential function ''e''''z'' is a singly periodic function, with period 2''πi''. Examples As an arbitrary mapping from pairs of reals (or complex numbers) to reals, a doubly periodic function can be constructed with little effort. For example, assume that the periods are 1 and ''i'', so that the repe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Map Projections
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] |
