File Twopointequidistantprojection SW.jpg 450px thumb Twopointequidistantprojection of Asia . All distances are correct from the two points 45 N, 40 E and 30 N, 110 E . The twopointequidistantprojection is a map projection first described by Hans Maurer in 1919. ref cite web url http www.warnercnr.colostate.edu class info nr502 lg2 projection descriptions twopoint equidistant.html title TwoPointEquidistant Projections accessdate 2007 09 16 Dead link date October 2010 bot H3llBot ref Distances from any point on the map to two control points scale to the geodesic distances of the same points on the sphere. The projection is commonly used in National Geographic Society Atlas atlases for maps of Asia , and it sometimes appears in diagrams of air routes. See also Chamberlin trimetric projection 3D projection References reflist Cartography stub Category Cartographic projections Category Equidistant projections nl Tweepunts equidistante projectie ... more details
File Azimuthal equidistantprojection SW.jpg thumb 300px Geographical pole Polar azimuthal equidistantprojection File Emblem of the United Nations.svg thumb 300px Emblem of the United Nations containing an approximate polar azimuthal equidistantprojection. Compare the relative sizes of Australia and north Africa with those in the previous render. The azimuthal equidistantprojection is a type of map projection . A useful application for this type of projection is a Polar coordinate system polar projection in which all distances measured from the center of the map along any longitudinal line are accurate an example of a polar azimuthal equidistantprojection can be seen on the United Nations flag . This projection is used by the USGS in the http nationalatlas.gov National Atlas of the United ... distances from center point of projection and for seismic and radio work. Distances and directions to all places are true only from the center point of projection. Distances are correct between points ... increases dramatically, the further away one gets from center point. Some types of wide angle camera lenses, known as fisheye lens es produce an azimuthal equidistantprojection of the photographed ... the earth two thousand years of map projections date 1997 , p.29 ref the earliest text describing the azimuthal equidistantprojection is an 11th century work by Abu Rayhan Biruni al Biruni . ref ... deformations of the Azimuthal EquidistantProjection . http geographiclib.sourceforge.net GeographicLib provides a class for performing azimuthal equidistant projections centered at any point on the ellipsoid. http www.globmaritime.com 200903032338 marine navigation azimuthal equidistant projection.html Concept and mathematics of the Azimuthal EquidistantProjection for the marine navigator . Category ... York. ref In some countries this projection is named Postel projection after Guillaume Postel ... http www.wm7d.net azproj.shtml Online Azimuthal Equidistant Map Generator http www.uff.br ... more details
out Image Th 2pts.jpg frame right A famous twopoint conversion in an National Football League NFL ... won on the conversion 36 35. In American football American and Canadian football , a twopoint conversion ... immediately after it scores a touchdown . In a twopoint conversion attempt, the team that just scored ... estimate the success rate of a twopoint conversion to be between 40 and 55 , significantly lower ... is achieved through the twopoint conversion than the extra point. Adoption of rule The twopoint ... article 0,9171,825522,00.html The TwoPoint Conversion, , October 6, 1958. ref and more recently ... football overtime situations in college football, the twopoint conversion is the mandatory method ... the twopoint conversion during its ten seasons from 1960 AFL season 1960 to 1969 AFL season 1969 ... point conversion rule in 1994. ref WiseGeek.com http www.wisegeek.com what is a twopoint conversion.htm ... League of American Football , adopted the twopoint conversion rule for its entire existence from 1991 through 2007. Six man football reverses the extra point and the twopoint conversion because ... are worth one point but successful kicks are worth two. It is also reversed in many high school football ... of this, especially at the youth level, is to allow one point for a running conversion, two points ... the twopoint conversion for its entire existence in both its original 1987 2008 incarnation ... that the NFL did not recognize the twopoint conversion but the AFL did the relatively easy extra ... it a point not to institute a twopoint conversion rule so as to eliminate the easy kick. What would constitute a twopoint conversion in other leagues only counted one point in the AFL NFL games, WFL ... two or even three points by successfully executing a play from a point farther from the opponent ... score from the ten yard line . Defensive twopoint conversion In American college and Canadian football ... twopoint attempt, or one otherwise recovered by the defense, or a blocked extra point kick ... more details
. In geometry , a two dimensional point group or rosette group is a group mathematics group of geometric symmetry symmetries isometry isometries that keep at least one point fixed in a plane. Every such group ... , U 1 , a group also known as the circle group . The two dimensional point groups are important as a basis for the axial point groups in three dimensions three dimensional point groups , with the addition ... starfish and jellyfish , and organism parts, like flower s. Discrete groups There are two families of discrete two dimensional point groups, and they are specified with parameter n , which is the order ... Center 2.1 Formulas for Symmetries in Cartesian Coordinates two dimensions DEFAULTSORT Point ... limit, these groups become the one dimensional line group s. If a group is a symmetry of a two ... the value of n to 1, 2, 3, 4, and 6 for both families. There are thus 10 two dimensional crystallographic point group s C sub 1 sub , C sub 2 sub , C sub 3 sub , C sub 4 sub , C sub 6 sub , D sub 1 sub ... or commutative, but only two of the dihedral groups are D sub 1 sub Z sub 2 sub and D sub 2 sub ... groups These groups are readily constructed with two dimensional orthogonal matrix orthogonal matrices ... the finite isometry groups and SO 2 and O 2 are closed. These groups fall into two distinct families ... Two dimensions 2D symmetry groups correspond to the isometry groups, except that symmetry according ... called the canonical projection of E 2 onto E 2 T or O 2 . Its kernel algebra kernel is T . For every subgroup of E 2 we can consider its image under p a point group consisting of the cosets to which the elements of the subgroup belong, in other words, the point group obtained by ignoring translational ... theorem , this point group is either C sub n sub or of type D sub n sub for n 1, 2, 3, 4, or 6. C ... to the corresponding C sub n sub also two frieze groups correspond to C sub 1 sub and C sub 2 sub . The isometry groups of p6m are each mapped to one of the point groups of type D sub 6 sub . For the other ... more details
Unreferenced date December 2009 Infobox Automobile image Image Riley TwoPoint Six Saloon 1959.jpg 250px Riley TwoPoint Six Saloon 1959 name Riley TwoPoint Six manufacturer British Motor Corporation BMC production 1957 1959 br 2000 class wheelbase 113 inches 2,855 mm length 185 inches 4700 mm body style 4 door sedan car saloon predecessor Riley Pathfinder successor Riley 4 Riley Four Sixty Eight similar Wolseley Six Ninety engine C.26.R BMC C Series engine C Series Straight 6 The TwoPoint Six replaced the Riley Pathfinder as Riley automobile Riley s top line automobile . While its predecessor retained the Riley twin cam, cross flow motor, the TwoPoint Six was almost identical to the Wolseley 6 90 Wolseley Six Ninety Series III . It featured both monotone and duotone paintwork, as did the last of the Pathfinders. Externally the most obvious difference from the Pathfinder was the bonnet arrangement while the Pathfinder s grille lifted with the bonnet, the TwoPoint Six, in common with the 6 90, had a fixed grille. It used the BMC C Series engine BMC C Series straight 6 , an engine that produced 101 hp 72.3 kW . This was actually less than the 2 Litre Riley Big Four straight 4 engine it replaced. The TwoPoint Six was a commercial failure and was pulled from the market in May, 1959, the last large Riley. Engine 2.6 L 2639 cc BMC C Series engine C Series straight 6 , 97 hp 72.3 kW Category Riley vehicles TwoPoint Six Category Vehicles introduced in 1958 de Riley 2.6 pt Riley TwoPoint Six ... more details
In topology , a branch of mathematics, a discrete twopoint space is the simplest example of a totally disconnected discrete space . The points can be denoted by the symbols 0 and 1. Any disconnected space has a continuous mapping onto the discrete twopoint space. Conversely if a continuous mapping to the discrete twopoint space exists from a topological space, the space is disconnected. ref cite book title Introduction to Topology and Modern Analysis author George F. Simmons publisher McGraw Hill Book Company date 1968 page 144 ref References Reflist Category Topological spaces ... more details
Twopoint discrimination is the ability to discern that two nearby objects touching the skin are truly two distinct points, not one. It is often tested with two sharp points during a neurological examination ref name bates rp 632 ref cite book last Blumenfield first Hal title Neuroanatomy Through Clinical Cases publisher Sinauer year 2002 location Sunderland, MA isbn 0 87893 060 4 ref rp 71 and reflects how finely innervation innervated an area of skin is. Twopoint discrimination is a reliable and widely used technique for determining tactile gnosis . ref cite journal last Shooter first David title Use of twopoint discrimination as a nerve repair assessment tool Preliminary report journal ANZ Journal of Surgery year 2005 volume 75 issue 10 pages 866 868 doi 10.1111 j.1445 2197.2005.03557.x url http onlinelibrary.wiley.com.proxy.queensu.ca doi 10.1111 j.1445 2197.2005.03557.x full accessdate May 14, 2011 ref It relies on the ability and or willingness of the patient to subjectively report what s he is feeling and should be completed with the patient s eyes closed. ref name Blumenfeld cite book last Blumenfeld first Hal title Neuroanatomy through Clinical Cases year 2010 publisher Sinauer Associates, Inc. location Sunderland, MA isbn 978 0 87893 058 6 pages 71 72 ref In order to test for twopoint discrimination, the therapist will use a special pair of calipers or reshaped paperclip . The therapist will alternate randomly between touching the patient with one point or with two points on the area being tested e.g. finger, arm, leg, toe . ref name Blumenfeld The patient will then be asked to report back what s he felt one or two points . The smallest distance between two points at which the patient can still distinguish as two separate stimuli and not one, is recorded. ref ... touch. Therefore, upon damage to this pathway, twopoint discrimination can be impaired. ref ... cortical representation. Normally, a person should be able to recognize two points separated by as little ... more details
Target TwoPoint Zero is an interest rate challenge in the UK set by the Bank of England and The Times . The challenge Target Two invites students aged 16 to 18 to take on the role of the Monetary Policy Committee to analyse current economic conditions in the UK and the outlook for inflation . Teams of four students must create a formal presentation that is delivered to a panel of judges from the Bank of England. The presentation must conclude with a recommendation on exactly what interest rate the team would set in order to achieve the UK government s inflation target of 2.0 Consumer Price Index CPI . Following the initial presentation, which lasts a maximum of 15 minutes, the judges have the opportunity to ask questions about what has been said. They might ask the students to justify or clarify certain aspects of their interpretation of the economic conditions. Structure of the competition The Challenge has three identical rounds regional heats, area finals and the national final. There is a sufficient time lapse between rounds to compel teams to change and update their presentation to take into account of new economic statistics, or the Monetary Policy Committee MPC s own interest rate decisions. See also Monetary Policy Interest rate External links http www.bankofengland.co.uk education targettwopointzero index.htm http business.timesonline.co.uk tol business economics target 2 0 Category Bank of England Category Macroeconomics and monetary economics bank stub ... more details
wiktionary projection projector projective tocright Projection , projector , or projective may refer to The display of an image by devices such as Movie projector Video projector Overhead projector Slide projector Camera obscura Projection screen Map projection , reduces a three dimensional planet to a flat map geography Graphical projection , the production of a two dimensional image of a three dimensional object Parallel projection Orthographic projection , including Plan view Plan , or floor plan ... , a view of the interior at a particular cutting plane Axonometric projection , including Isometric projection Dimetric projection Trimetric projection Oblique projection , including Cabinet projection Cavalier projection Perspective projection anchor chemistry Chemistry Fischer projection Haworth projection Newman projection Natta projection Mathematics Projection mathematics , any of several different types of functions, mappings, operations, or transformations 3D projectionProjection relational algebra Projection linear algebra Vector projectionProjection method fluid dynamics Projection ... direction, projective module s and projective object s generalize free modules Other Projection alchemy , process in Alchemy Projection areas , areas of the brain where sensory processing occurs Military power projection , the capacity of a state to implement policy by means of force, or the threat thereof, in an area distant from its own territory Psychological projection , or Freudian projection ..., thoughts, or emotions Projection fibers , in neuroscience, white matter fibers that connect ... developments based on current statistics and trends Projection music , acoustical phenomenon whereby ... and Acoustics Publ. Springer, New York, 2010 See also lookfrom intitle Project disambiguation Projection effect disambiguation disambig de Projektion eo Projekcio fr Projection ko it Proiezione he nl Projectie ja no Projeksjon pl Projekcja pt Proje o ru simple Projection sl Projekcija ... more details
File Equirectangular projection SW.jpg 450px thumb Equirectangular projection of the world the standard parallel is the equator plate carr e projection . Image Tissot indicatrix world map equirectangular proj.svg thumb right 450px The equirectangular projection with Tissot s indicatrix of deformation The equirectangular projection also called the equidistant cylindrical projection , geographic projection , or la carte parall logrammatique projection , and which includes the special case of the plate carr e projection or geographic projection , is a simple map projection attributed to Marinus of Tyre , who Ptolemy claims invented the projection about 100 AD 100 . ref Flattening the Earth Two Thousand Years of Map Projections , John P. Snyder, 1993, pp. 5 8, ISBN 0 226 76747 7. ref The projection ... straight lines of constant spacing for constant intervals of Circle of latitude parallels . The projection is neither equal area nor Conformal map projection conformal . Because of the distortions introduced by this projection, it has little use in navigation or cadastral mapping and finds its ... of the equator where the scale of the projection is true math x math is the horizontal position along the map math y math is the vertical position along the map. The point 0,0 is at the center of the resulting projection. The lang fr plate carr e French language French , for square plate , is the special case where math scriptstyle varphi 1 math is zero. This projection maps math x math to be the value ... called the latitude longitude or lat lon g projection or is said erroneously to be unprojected . See also Portal Atlas Cartography Cassini projection Gall Peters projection with resolution regarding the use of rectangular world maps Mercator projection Panorama References Reflist External links ... Panoramic Equirectangular Projection , PanoTools wiki. Map Projections Category Cartographic projections Category Panorama photography Category Equidistant projections ar ... more details
File Behrmann projection SW.jpg 450px thumb Behrmann projection of the world. Image Tissot indicatrix world map Behrmann equal area proj.svg 450px thumb upright 2.2 right The Behrmann cylindrical equal area projection with Tissot s indicatrix Tissot s indicatrices of deformation The Behrmann projection is a Map projection Cylindrical cylindrical map projection . This is an orthographic projection onto a cylinder secant at the 30 parallels. It is equal area, but distortion of shape increases with distance from the standard parallels. Scale is true along the standard parallels and constant between two parallels equidistant from the Equator. This projection is not equidistant. External links http www.radicalcartography.net ?projectionref Table of examples and properties of all common projections , from radicalcartography.net http www.uff.br mapprojections Behrmann en.html An interactive Java Applet to study the metric deformations of the Berhrmann Projection . Category Cartographic projections cartography stub cs Behrmannovo zobrazen ... more details
Orphan date March 2007 The two dimensional point vortex gas is a discrete particle model used to study turbulence in two dimensional ideal fluid s. The two dimensional guiding center plasma is a completely equivalent model used in plasma physics. General setup The model is a Hamiltonian system of N points in the two dimensional plane executing the motion math k i frac dx i dt frac partial H partial y i , qquad k i frac dy i dt frac partial H partial x i , math In the confined version of the problem, the logarithmic potential is modified. Interpretations In the point vortex gas interpretation, the particles represent either point vortex vortices in a two dimensional fluid, or parallel line vortices in a three dimensional fluid. The constant k sub i sub is the circulation fluid dynamics circulation of the fluid around the i th vortex. The Hamiltonian H is the interaction term of the fluid s integrated kinetic energy it may be either positive or negative. The equations of motion simply reflect the drift of each vortex s position in the velocity field of the other vortices. In the guiding center plasma interpretation, the particles represent long filaments of charge parallel to some external magnetic field. The constant k sub i sub is the linear charge density of the i th filament. The Hamiltonian H is just the two dimensional Coulomb potential between lines. The equations of motion reflect the guiding center drift plasma physics drift of the charge filaments, hence the name. See also List of plasma physics articles Notes reflist References cite journal author Eyink, Gregory and Katepalli Sreenivasan title Onsager and the theory of hydrodynamic turbulence journal Reviews of Modern Physics volume 78 year 2006 month January pages 87 135 doi 10.1103 RevModPhys.78.87 bibcode 2006RvMP...78...87E Category Turbulence models Category Plasma physics fluiddynamics stub ... more details
views Planar projections are the subset of 3D graphical projections constructed by linearly mapping points in three dimensional space to points on a two dimensional projection plane . The projected point on the plane is chosen such that it is Line geometry collinear with the corresponding three dimensional point and the centre of projection . The lines connecting these points are commonly referred to as projectors . The centre of projection can be thought of as the location of the observer while the plane of projection is the surface on which the two dimensional projected image of the scene is recorded or from which it is viewed e.g., photographic negative, photographic print, computer monitor . When the centre of projection is at a finite distance from the projection plane, a Perspective graphical perspective projection is obtained. When the centre of projection is at infinity, all the projectors are parallel, and the corresponding subset of planar projections are referred to as parallel projections . Mathematical formulation Mathematically, planar projections are linear transformations acting on a point in three dimensional space math mathbf a x,y,z math to give a point math mathbf b u,v math on the projection plane. These transformations consist of various function composition compositions of the five transformations orthographic projection , rotation mathematics rotation , Shear mapping shear , Translation geometry translation and Projective transformation perspective . Map uses It is also used in maps to show the planet Earth and other planets or objects in space. This is good for maps of close up areas. Category Graphical projections geometry stub ... more details
File Aitoff projection SW.jpg 450px thumb An Aitoff projection of the world. The Aitoff projection is a modified azimuthal map projection . Proposed by David A. Aitoff in 1889 , it is the equatorial form of the azimuthal equidistantprojection , but stretched into a 2 1 ellipse while halving the longitude from the central meridian math x mathrm azeq x left frac lambda 2, phi right , math math y frac 1 2 mathrm azeq y left frac lambda 2, phi right math where math mathrm azeq x math and math mathrm azeq y math are the x and y components of the equatorial azimuthal equidistantprojection. Written out explicitly, the projection is math x frac 2 cos phi sin left frac lambda 2 right mathrm sinc alpha , math math y frac sin phi mathrm sinc alpha , math where math alpha arccos left cos phi cos left frac lambda 2 right right , math and math mathrm sinc alpha math is the unnormalized sinc function with the discontinuity removed. In all of these formulas, math lambda math is the longitude from the central meridian and math phi math is the latitude. Three years later, Ernst Hermann Heinrich Hammer suggested the use of the Lambert azimuthal equal area projection in the same manner as Aitoff, producing the Hammer projection . While Hammer was careful to cite Aitoff, there has been some confusion since, wherein Aitoff has been attributed to Hammer s projection. ref Flattening the Earth Two Thousand Years of Map Projections , John P. Snyder, 1993, pp.130 133, ISBN 0 226 76747 7. ref See also Mollweide projection Hammer projection References references External links http www.radicalcartography.net ?projectionref Table of common projections http www.uff.br mapprojections Aitoff en.html An interactive Java Applet to study the metric deformations of the Aitoff Projection . http map.gsfc.nasa.gov Wilkinson Microwave Anisotropy Probe WMAP Category Cartographic projections ca Projecci d Aitoff de Aitov Projektion es Proyecci n de Aitoff fa ja ... more details
the construction of several large scale nautical charts in the cylindrical equidistantprojection ...ref improve date November 2011 File Mercator projection SW.jpg thumb 450px right Mercator projection ... of the texts The Mercator projection is a Map projection Cylindrical cylindrical map projection ... the standard map projection for nautical purposes because of its ability to represent lines ... the linear scale is equal in all directions around any point, thus preserving the angles and the shapes of small objects which makes the projection conformal projection conformal , the Mercator projection ... projection Cylindrical cylindrical projections , circle of latitude parallel s and meridian geography ... by a corresponding north south stretching, so that at every point location, the east west scale is the same as the north south scale, making the projection conformal map conformal . A Mercator .... Being a conformal projection, angles are preserved around all locations. However scale ... projection is practically unusable. All lines of constant bearing navigation bearing rhumb lines rhumbs ... es are used to indicate geographical directions and to steer the ships. The two properties, conformality and straight rhumb lines, make this projection uniquely suited to marine navigation courses ... transferred from point to point, on the map, with the help of a parallel ruler or a pair of navigational ... projection represented a major breakthrough in the nautical cartography of the 16th century. However ... with its use in navigation. Two main problems prevented its immediate application the impossibility ... was known, could the Mercator projection be fully adopted by navigators. Several authors are associated with the development of Mercator projection German Erhard Etzlaub c. 1460&ndash 1532 , who ... designed a projection identical to Mercator s . Portuguese mathematician and cosmographer Pedro Nunes ... Edward Wright c. 1558&ndash 1615 , who formalized the mathematics of Mercator projection ... more details
File Werner projection SW.jpg 450px thumb Werner projection of the world. The Werner projection is a pseudoconic equal area map projection sometimes called the Stab Werner or Stabius Werner projection. Like other heart symbol heart shaped projections, it is also categorized as cordiform . Stab Werner refers to two originators Johannes Werner 1466&ndash 1528 , a parish priest in Nuremberg , refined and promoted this projection that had been developed earlier by Johannes Stabius Stab of Vienna around 1500. The projection is a limiting form of the Bonne projection , having its standard parallel at one of the poles 90 N S . ref citation title Flattening the Earth Two Thousand Years of Map Projections first John P last Snyder year 1993 pages 60 2 ISBN 0 226 76747 7 . ref ref citation author mask 8 url http pubs.er.usgs.gov usgspubs pp pp1395 contribution Map Projections A Working Manual publisher United States Geological Survey title Professional Paper number 1395 first John P last Snyder year 1987 pages 138 0 . ref Distances along each parallel and along the central meridian are correct, as are all distances from the north pole. References references External links citation url http www.radicalcartography.net ?projectionref title Table of examples and properties of all common projections publisher Radical Cartography . Category Cartographic projections Category Equal area projections Category Equidistant projections es Proyecci n Werner ru ja ... more details
File Sinusoidal projection SW.jpg 450px thumb Sinusoidal projection of the world. Image Tissot indicatrix world map sinusoidal proj.svg thumb right 450px The sinusoidal projection with Tissot s indicatrix of deformation The sinusoidal projection is a pseudocylindrical Map projection Equal area 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 is defined by math x left lambda lambda 0 right cos varphi math math y varphi , math where &phi is the latitude, &lambda is the longitude, and &lambda sub 0 sub is the central meridian. ref http pubs.er.usgs.gov usgspubs pp pp1395 Map Projections A Working Manual , United States Geological Survey USGS Professional Paper 1395, John P. Snyder, 1987, pp. 243 248 ref The north south scale is the same everywhere at the central meridian geography meridian , and the east west scale is throughout the map the same as that correspondingly, on the map, as in reality, the length of each ... earth is the area between two symmetric rotated cosine curves. The true distance between two points on the same meridian corresponds to the distance on the map between the two parallels, which is smaller than the distance between the two points on the map. There is no distortion on the central meridian ... projection shows relative sizes accurately, but distorts shapes and directions. Distortion can be reduced ... projection around the north pole are the Werner projection Werner and the intermediate Bonne projection Bonne and Bottomley projection Bottomley projections. The MODLAND Integerized Sinusoidal Grid, based on the sinusoidal projection, is a geodesic grid developed by the NASA s Moderate Resolution ... projections Category Equal area projections Category Equidistant projections ca Projecci sinuso dal de Sinusoidal Projektion es Proyecci n sinusoidal fr Projection sinuso dale ko it Proiezione ... more details
File Hammer projection SW.jpg 450px thumb Hammer projection of the world. The Hammer projection is an equal area map projection , described by Ernst Hammer cartographer Ernst Hammer in 1892 . 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 equidistantprojection math x mathrm laea x left frac lambda 2, phi right math math y frac 1 2 mathrm laea y left frac lambda 2, phi right math where math mathrm laea x math and math mathrm laea y math are the x and y components of the equatorial Lambert azimuthal equal area projection. Written out explicitly math x frac 2 sqrt 2 cos phi sin left frac lambda 2 right sqrt 1 cos phi cos left frac lambda 2 right math math y frac sqrt 2 sin phi sqrt 1 cos phi cos left frac lambda 2 right math The inverse is calculated with the intermediate variable math z equiv sqrt 1 left frac1 4 x right 2 left frac1 2 y right 2 math The longitude and latitudes can then be calculated by math begin align lambda & 2 arctan left frac zx 2 2z 2 1 right phi & arcsin zy end align math where math lambda math is the longitude from the central meridian and math phi math is the latitude . ref Flattening the Earth Two Thousand Years of Map Projections , John P. Snyder, 1993, pp.130 133, ISBN 0 226 76747 7. ref ref Weisstein, Eric W. http mathworld.wolfram.com Hammer AitoffEqual AreaProjection.html Hammer Aitoff Equal Area Projection. From MathWorld A Wolfram Web Resource ref Visually, the Aitoff and Hammer projections are very similar. The Hammer has seen more use because of its equal area property. The Mollweide projection is another equal area projection of similar aspect, though with straight parallels of latitude, unlike the Hammer s curved parallels. See also Mollweide projection Aitoff projection References references External ... Aitoff Projection . Category Cartographic projections Category Equal area projections ca Projecci ... more details
the two kinds of projections and of defining the image by a central projection of any point different of the center of projection are at the origin of projective geometry . The original notion of projection has been extended or generalized to various mathematical situations, frequently, but not always .... Originally, the notion of projection was introduced in Euclidean geometry to denotes the projection of the Euclidean space of dimension three onto a plane in it. The two main projections of this kind are The projection from a point onto a plane or central projection If C is the point, called center of projection , the projection of a point P different of C is the intersection with the plane of the line CP . The point C and the points P such that the line CP is parallel to the plane do not have any image by the projection. The projection onto a plane parallel to a direction D The image of a point ..., the mapping that takes a point x , y , z in three dimensions to the point x , y , 0 in the plane is a projection ...Image proj map.png thumb right Commutativity of this diagram is the universality of projection , for any map f and set X. Generally speaking, in mathematics , a projection is a mapping of a Set mathematics set or of a structure mathematics mathematical structure which is idempotent , which means that a projection is equal to its Function composition composition with itself. A projection may also refer ... other projections, called projection map s have been defined for the need of cartography. The 3D projection ... sup projection set theory projection map , written proj sub j sub , that takes an element x ... equivalence relation is known as the canonical projection. The evaluation map sends a function f ... product math prod i in X Y i math , and the evaluation map is a projection map from the cartesian ... a canonical projection morphism to each factor. This projection will take many forms in different categories. The projection from the Cartesian product of set mathematics sets , the product topology ... more details
point, twopoint and three point perspective, depending on the orientation of the projection plane ... projection is derived from the principles of descriptive geometry and is a two dimensional ... see dimetric projection , the direction of viewing is such that two of the three axes of space ... is located on the ground plane , and the point of view P.V. is right above it. P.P. is its projection ... are pictured with perspective projection, they appear to converge towards a single point, called ... lines and points, whereby two straight lines determine a point while two points determine a straight line. The orthogonal projection of the eye point onto the picture plane is called the principal vanishing ... of the drawing completes the characterization of the equally distant point of view. Two lines are drawn ... point for 90 . Their new intersection locates the projection of the map. Natural heights are measured ...Other uses Projection disambiguation Views Image Convention placement vues dessin technique.svg thumb right 200px Symbols used to define whether a projection is either Third Angle right or First Angle left . Graphical projection is a protocol by which an image of a Three dimensional space three dimensional ... the focal length and distance of the camera to infinity in a perspective projection results in a parallel projection. The projection is achieved by the use of imaginary projectors . The projected ... drawing, computer aided design, etc. . This is poorly written There are two types of graphical projection, categories each with its own protocol parallel projection Perspective graphical perspective projection gallery widths 100px heights 100px align center style padding 0px Image Isometrie.png Isometric projection . Image Milit rperspektive.PNG Oblique projection . Image Cavalier perspective 45.svg Oblique projection . Image Zentralperspektive.png Vanishing point One point perspective projection . gallery Types of projection File Graphical projection comparison.png thumb right Several types ... more details
angle used in orthographic projection. Mathematically, the parallel projection of the point math x, y ..., see Projection linear algebra . Views Oblique projection is a simple type of graphical projection used for producing pictorial, two dimensional image s of three dimensional objects. Overview Image Oblique projection yz.svg thumb left 240px Oblique projection with foreshortening by half, seen from the side. Oblique projection is a type of parallel projection it projects an image by intersecting parallel rays projectors from the three dimensional source object with the drawing surface projection plane . In both oblique projection and orthographic projection , parallel lines of the source object produce parallel lines in the projected image. The projectors in oblique projection intersect the projection ... b math uniquely specify a parallel projection. When math a b 0 math , the projection is said to be orthographic ... are not necessarily less than 1, and as a consequence lengths measured on an oblique projection may be either larger or shorter than they were in space. In a general oblique projection, spheres of the space ... an orthogonal projection. Oblique drawing is also the crudest 3D drawing method but the easiest ... . One way to draw using an oblique view is to draw the side of the object you are looking at in two ... from the same point may be construed as forming some oblique perspective of three sides of a cube ... overcome by aligning one plane of the image parallel to the plane of projection. Doing so creates .... Cavalier projection is the name of such a projection, where the length along the math z math axis remains ... from PlaneView3D Online ref Cabinet projection , popular in furniture illustrations, is an example ... also two thirds the original Citation needed date September 2008 . Cavalier projections In cavalier projection sometimes cavalier perspective or high view point a point of the object is represented by three coordinates, x , y and z . On the drawing, it is represented by only two coordinates, x and y ... more details
Refimprove date September 2009 Views Parallel projections have lines of projection that are parallel both in reality and in the projection plane. Clarify date November 2009 Parallel projection corresponds to a perspective projection with an infinite focal length the distance from the image plane to the projectionpoint , or zoom lens zoom . Within parallel projection there is an ancillary category ... to perceive. fact date November 2009 Dimetric projection In dimetric pictorials for protocols see dimetric projection , the direction of viewing is such that two of the three axes of space appear ... for economy of effort and best effect. Orthographic projection File Camera focal length distance.gif thumb right Parallel projection corresponds to a perspective projection with a hypothetical viewpoint ... length, or zoom . The orthographic projection is derived from the principles of descriptive geometry , and is a type of parallel projection where the projection rays are perpendicular to the projection ... 6&ved 0CBoQ6AEwBQ v twopage&q axonometric 20orthographic&f false isbn 0801472806 ref It is the projection ... with the projection plane paper on which the Orthographic or parallel projection is drawn. ref name maynard Pictorials Axonometric projection Axonometric projection is a type of orthographic projection where the plane or axis of the object depicted is not parallel to the projection plane, ref name ... projection , depending on the exact angle at which the view deviates from the orthogonal. ref ... of space is usually displayed as vertical. File Graphical projection comparison.png thumb right Comparison of several types of graphical projection . Isometric projection In isometric pictorials for protocols see isometric projection , the most common form of axonometric projection, ref name godse ... are common in dimetric drawings. Trimetric projection In trimetric pictorials for protocols see trimetric projection , the direction of viewing is such that all of the three axes of space ... more details
sphere. See also Twopointequidistantprojection References reflist External links http 909ers.apl.washington.edu ... 2 ref The Chamberlin trimetric projection is not Map projectionEquidistantequidistant , not Map projection Conformal conformal , Map projection Equal area inequivalent , and not Map projection Azimuthal projections onto a plane azimuthal . Rather, the projection strikes a balanced compromise between ...Image Africa ChamberlinTrimetric.png thumb alt A map of Africa in the Chamberlin Trimetric Projection A map of Africa using the Chamberlin trimetric projection. The three red dots indicate the selected ... trimetric projection is a map projection where three points are fixed on the globe and the points ... Flattening the earth two thousand years of map projections publisher University of Chicago Press year 1997 isbn 9780226767475 ref The projection s principal feature is that it compromises between ... Christensen title The Chamberlin Trimetric Projection year 1992 publisher Cartography and Geographic ... Society maps have often used this projection for representations of many of the continents . ref name JPS As originally implemented, the projection algorithm begins with the selection of three points ... to a point on the mapping area are calculated. The distances from each of the three base points are then drawn ... circles will intersect at a unique point, the compass circles from a sphere do not intersect precisely at a point. A small triangle is generated from the intersections, and the center of this triangle is calculated as the mapped point. ref name WC Deleted image removed Image SouthAmerica NGS 1992a.png ... projection A 1992 National Geographic Society map of South America in the Chamberlin trimetric projection. A Chamberlin trimetric projection map was originally obtained by graphically mapping points ... by interpolation. Based on the principles of the projection, precise, but lengthy, mathematical formulas were later developed for calculating this projection by computer for a spherical earth . ref name ... more details
mathematics Complex analysis Although any stereographic projection misses one point on the sphere the projectionpoint , the entire sphere can be mapped using two projections from distinct projection ... mathematics plane . The projection is defined on the entire sphere, except at one point &mdash the projection ... intersects the plane z 0 in exactly one point P nowiki nowiki . Define the stereographic projection ... is not defined at the projectionpoint N 0, 0, 1 . Small neighborhoods of this point are sent ... properties. Circles on the sphere that do not pass through the point of projection are projected to circles on the plane. Circles on the sphere that do pass through the point of projection are projected ... The stereographic projection relates to the plane inversion in a simple way. Let P and Q be two ... Antipodal point antipode , the south pole S, P is the image of P in a stereographic projection with the projectionpoint N and P is the image of P in a stereographic projection with the projection ... with the bottom net. The point marked in step 3 is then the projection that we wanted. To plot ... StereographicGeneric.svg thumb right Stereographic projection of a sphere from a point Q onto ... s defined everywhere except at the projectionpoint. They are conformal and not area preserving ... a hyperplane in E sup n 1 sup , then the stereographic projection of a point P S sup ... Q . Then the stereographic projection of a point P in S &minus Q is the unique point of intersection of math scriptstyle overline QP math with E . As before, the stereographic projection ... or two dimensional manifold . This construction has special significance in complex analysis. The point ... lines intersect the southern hemisphere in two antipodal point s along the equator, either of which ... projection is the point math left frac 2mn n 2 m 2 , frac n 2 m 2 n 2 m 2 right math which ...Deleted image removed Image Stereographic Projection Northern Hemisphere.png thumb right Stereographic ... more details
Image Gnomonic.png thumb right 300px Great circles transform to lines via gnomonic projection Image Usgs map gnomic.PNG frame right Examples of gnomonic projections A gnomonic map projection displays all great circle s as straight lines. Thus the shortest route between two locations in reality corresponds to that on the map . This is achieved by projecting, with respect to the center of the Earth hence perpendicular to the surface , the Earth s surface onto a tangent plane. The least distortion occurs at the tangent point. Less than half of the sphere can be projected onto a finite map. As a corollary, a rectilinear photographic lens cannot encompass more than 180 degrees for the same reason. Since Meridian 28geography 29 meridians and the equator are great circles, they are always shown as straight lines. If the tangent point is one of the Poles then the meridians are radial and equally ... s. If the tangent point is on the equator then the meridians are parallel but not equally spaced ... that the projection is not conformal map conformal . br style clear both File Gnomonic projection SW.jpg 450px thumb Gnomonic projection of the world centered on the geographic North Pole As for all azimuth al projections, angles from the tangent point are preserved. The map distance from that point is a function r d of the true distance d , given by math r d R , tan d R math where R is the radius ... scale even more. The gnomonic projection is said to be the oldest map projection, developed by Thales .... History In 1946 Buckminster Fuller patented a projection method similar to the Gnomonic Projection ... referred to today. Gnomonic projection is used extensively in photography , where it is called rectilinear projection . See also Beltrami Klein model , the analogous mapping of the hyperbolic geometry ... pp pp1395 USGS pages External links http www.bfi.org node 25 Description of the Fuller Projection ... Projektion es Proyecci n gnom nica fr Projection gnomonique ko it Proiezione gnomonica nl ... more details
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