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Tissot's Indicatrix
In cartography, a Tissot's indicatrix (Tissot indicatrix, Tissot's ellipse, Tissot ellipse, ellipse of distortion) (plural: "Tissot's indicatrices") is a mathematical contrivance presented by French mathematician Nicolas Auguste Tissot in 1859 and 1871 in order to characterize local distortions due to map projection. It is the geometry that results from Projection (linear algebra), projecting a circle of infinitesimal radius from a curved geometric model, such as a globe, onto a map. Tissot proved that the resulting diagram is an ellipse whose axes indicate the two Principal curvature, principal directions along which scale is maximal and minimal at that point on the map. A single indicatrix describes the distortion at a single point. Because distortion varies across a map, generally Tissot's indicatrices are placed across a map to illustrate the spatial change in distortion. A common scheme places them at each intersection of displayed meridians and parallels. These schematics a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tissot Behrmann
Tissot SA () is a Switzerland, Swiss watchmaker. The company was founded in Le Locle, Switzerland by Charles-Félicien Tissot and his son, Charles-Émile Tissot, in 1853. After several mergers and name changes, the group which Tissot SA belonged to was renamed the Swatch Group in 1998. Tissot is not associated with Mathey-Tissot, another Swiss watchmaking firm. History Independent company Tissot was founded in 1853 by Charles-Félicien Tissot and his son Charles-Émile Tissot in the Swiss city of Le Locle, in the Neuchâtel canton of the Jura Mountains area. The father and son team worked as a casemaker (Charles-Félicien Tissot) and watchmaker (Charles-Emile). His son having expressed an interest in watchmaking from a young age. The two turned their house at the time into a small 'factory'. Charles-Emile Tissot left for Russia in 1858 and succeeded in selling their Pocket watch#Hunter-case watches, savonnette pocket watches across the Russian Empire. In 2021, the company is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parallel (latitude)
A circle of latitude or line of latitude on Earth is an abstract east–west small circle connecting all locations around Earth (ignoring elevation) at a given latitude coordinate line. Circles of latitude are often called parallels because they are parallel to each other; that is, planes that contain any of these circles never intersect each other. A location's position along a circle of latitude is given by its longitude. Circles of latitude are unlike circles of longitude, which are all great circles with the centre of Earth in the middle, as the circles of latitude get smaller as the distance from the Equator increases. Their length can be calculated by a common sine or cosine function. The 60th parallel north or south is half as long as the Equator (disregarding Earth's minor flattening by 0.335%). On the Mercator projection or on the Gall-Peters projection, a circle of latitude is perpendicular to all meridians. On the ellipsoid or on spherical projection, all ci ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stereographic Projection
In mathematics, a stereographic projection is a perspective projection of the sphere, through a specific point on the sphere (the ''pole'' or ''center of projection''), onto a plane (the ''projection plane'') perpendicular to the diameter through the point. It is a smooth, bijective function from the entire sphere except the center of projection to the entire plane. It maps circles on the sphere to circles or lines on the plane, and is conformal, meaning that it preserves angles at which curves meet and thus locally approximately preserves shapes. It is neither isometric (distance preserving) nor equiareal (area preserving). The stereographic projection gives a way to represent a sphere by a plane. The metric induced by the inverse stereographic projection from the plane to the sphere defines a geodesic distance between points in the plane equal to the spherical distance between the spherical points they represent. A two-dimensional coordinate system on the stere ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robinson Projection
The Robinson projection is a map projection of a world map which shows the entire world at once. It was specifically created in an attempt to find a good compromise to the problem of readily showing the whole globe as a flat image. The Robinson projection was devised by Arthur H. Robinson in 1963 in response to an appeal from the Rand McNally company, which has used the projection in general-purpose world maps since that time. Robinson published details of the projection's construction in 1974. The National Geographic Society (NGS) began using the Robinson projection for general-purpose world maps in 1988, replacing the Van der Grinten projection. In 1998 NGS abandoned the Robinson projection for that use in favor of the Winkel tripel projection, as the latter "reduces the distortion of land masses as they near the poles". Strengths and weaknesses The Robinson projection is neither equal-area nor conformal, abandoning both for a compromise. The creator felt that this produc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sinusoidal Projection
The sinusoidal projection is a pseudocylindrical equal-area map projection, sometimes called the Sanson–Flamsteed or the Mercator equal-area projection. Jean Cossin of Dieppe was one of the first mapmakers to use the sinusoidal, appearing in a world map of 1570. The projection represents the poles as points, as they are on the sphere, but the meridians and continents are distorted. The equator and the prime meridian are the most accurate parts of the map, having no distortion at all, and the further away from those that one examines, the greater the distortion. The projection is defined by: :\begin x &= \left(\lambda - \lambda_0\right) \cos \varphi \\ y &= \varphi\,\end where \varphi is the latitude, ''λ'' is the longitude, and ''λ'' is the longitude of the central meridian. Scale is constant along the central meridian, and east–west scale is constant throughout the map. Therefore, the length of each parallel on the map is proportional to the cosine of the latitude, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lambert Cylindrical Equal-area Projection
In cartography, the Lambert cylindrical equal-area projection, or Lambert cylindrical projection, is a cylindrical equal-area projection. This projection is undistorted along the equator, which is its standard parallel, but distortion increases rapidly towards the poles. Like any cylindrical projection, it stretches parallels increasingly away from the equator. The poles accrue infinite distortion, becoming lines instead of points. History The projection was invented by the Swiss mathematician Johann Heinrich Lambert and described in his 1772 treatise, ''Beiträge zum Gebrauche der Mathematik und deren Anwendung'', part III, section 6: ''Anmerkungen und Zusätze zur Entwerfung der Land- und Himmelscharten'', translated as, ''Notes and Comments on the Composition of Terrestrial and Celestial Maps''. Lambert's projection is the basis for the cylindrical equal-area projection family. Lambert chose the equator as the parallel of no distortion. By multiplying the projection's heigh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transverse Mercator Projection
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. 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 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 projections are 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 transverse Mercator, the axis of the cylinder lies in the equatorial plane, and the line of tangency is any chosen meridian, thereby designa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fuller Projection
The Dymaxion map or Fuller map is a projection of a world map onto the surface of an icosahedron, which can be unfolded and flattened to two dimensions. The flat map is heavily interrupted in order to preserve shapes and sizes. The projection was invented by Buckminster Fuller. The March 1, 1943, edition of ''Life'' magazine included a photographic essay titled "Life Presents R. Buckminster Fuller's Dymaxion World". The article included several examples of its use together with a pull-out section that could be assembled as a "three-dimensional approximation of a globe or laid out as a flat map, with which the world may be fitted together and rearranged to illuminate special aspects of its geography." Fuller applied for a patent in the United States in February 1944, showing a projection onto a cuboctahedron, which he called "dymaxion". The patent was issued in January 1946. In 1954, Fuller and cartographer Shoji Sadao produced the Airocean World Map, a version of the Dymaxion m ... [...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 l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Winkel Tripel Projection
The Winkel tripel projection (Winkel III), a modified azimuthal map projection of the world, is one of three projections proposed by German cartographer Oswald Winkel (7 January 1874 – 18 July 1953) in 1921. The projection is the arithmetic mean of the equirectangular projection and the Aitoff projection: The name ( German for 'triple') refers to Winkel's goal of minimizing three kinds of distortion: area, direction, and distance. Algorithm : \begin x &= \frac \left(\lambda \cos \varphi_1 + \frac\right), \\ y &= \frac \left(\varphi + \frac\right), \end where ''λ'' is the longitude relative to the central meridian of the projection, ''φ'' is the latitude, ''φ'' is the standard parallel for the equirectangular projection, sinc is the unnormalized cardinal sine function, and : \alpha = \arccos\left(\cos\varphi \cos \frac \right). In his proposal, Winkel set : \varphi_1 = \arccos \frac. A closed-form inverse mapping does not exist, and computing the inverse numeri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mollweide Projection
file:Mollweide projection SW.jpg, 400px, Mollweide projection of the world file:Mollweide with Tissot's Indicatrices of Distortion.svg, 400px, The Mollweide projection with Tissot's indicatrix of deformation The Mollweide projection is an Equal-area map, equal-area, Map projection#Pseudocylindrical, 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 Mollweide, 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gall–Peters Projection
The Gall–Peters projection is a rectangular, equal-area map projection. Like all equal-area projections, it distorts most shapes. It is a cylindrical equal-area projection with latitudes 45° north and south as the regions on the map that have no distortion. The projection is named after James Gall and Arno Peters. Gall described the projection in 1855 at a science convention and published a paper on it in 1885. Peters brought the projection to a wider audience beginning in the early 1970s through his "Peters World Map". The name "Gall–Peters projection" was first used by Arthur H. Robinson in a pamphlet put out by the American Cartographic Association in 1986.American Cartographic Association's Committee on Map Projections, 1986. ''Which Map is Best'' p. 12. Falls Church: American Congress on Surveying and Mapping. Maps based on the projection are promoted by UNESCO, and they are also widely used by British schools. The U.S. state of Massachusetts and Boston Public Sch ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
