For axonometricprojection in video games Video games with isometric graphics Mergefrom Isometric projection discuss Talk Axonometricprojection Proposal to merge Dimetric projection and Trimetric projection here date November 2009 Views Axonometricprojection is a type of parallel projection , more specifically a type of orthographic projection , used to create a pictorial drawing of an object, where the object is rotated along one or more of its axes relative to the plane of projection. ref name .... ISBN 0073655988, p.330. ref There are three main types of axonometricprojection isometric , dimetric , and trimetric projection . Axonometric means to measure along axes . Axonometricprojection ... this limitation, axonometricprojection can be useful for purposes of illustration. History The concept ... The three types of axonometric projections are isometric projection , dimetric projection , and trimetric ... projection , the most commonly used form of axonometricprojection in engineering drawing, ref name ... of axonometricprojection Image IsometricFlaw 2.svg thumb right Drawing illustrating the limitations of axonometricprojection See also Impossible object As with all types of parallel projection , objects drawn with axonometricprojection do not appear larger or smaller as they extend closer ... 2009 reflist Further reading Commons category Axonometricprojection Yve Alain Bois, Metamorphosis of Axonometry ... of objects where the axis or plane of the object is parallel with the projection plane, ref name maynard in axonometricprojection the plane or axis of the object is always drawn not parallel to the projection plane. With axonometric projections the scale of distant features is the same as for near ... on a new significance with the advent of visual computing . ref name Kri00 File Graphical projection comparison.png thumb right Comparison of several types of graphical projection gallery widths 300px ... Zeduan 1085 1145 Image Axonometric example.gif Example of a dimetric axonometric drawing from ... 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 view Elevation view Elevation , usually a side view of an exterior Cross section geometry Section , a view of the interior at a particular cutting plane Axonometricprojection , 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 set theory Projective geometry is a non Euclidean geometry that involves projective spaces. In another 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 ... 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 ... more details
6&ved 0CBoQ6AEwBQ v twopage&q axonometric 20orthographic&f false isbn 0801472806 ref It is the projection ... see isometric projection , the most common form of axonometricprojection, ref name godse ...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 projection point , or zoom lens zoom . Within parallel projection there is an ancillary category ... 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 ... books?id 4Y YqOlXoxMC&pg PA22&lpg PA22&dq axonometric orthographic&source bl&ots wqg9m MaKI&sig ... with the projection plane paper on which the Orthographic or parallel projection is drawn. ref name maynard Pictorials AxonometricprojectionAxonometricprojection is a type of orthographic projection where the plane or axis of the object depicted is not parallel to the projection plane, ref name .... pages 232 url http books.google.com books?id WQiIj8ZS0IoC&pg PA231&dq axonometric orthographic v onepage&q axonometric 20orthographic&f false isbn 8120335244 ref ref name godse Cite book title Computer ... YkVp 2ZrmyMC&pg PT224&dq axonometric orthographic v onepage&q axonometric 20orthographic&f false isbn ... 502 url http books.google.com books?id H4eYq7 2YhYC&pg PA502&dq axonometric orthographic v onepage&q axonometric 20orthographic&f false isbn 1558606599 ref such that multiple sides of an object are visible ... books?id JrZoGgQEhKkC&pg PA169&dq axonometric orthographic v onepage&q axonometric 20orthographic ... more details
into multiview orthographic projections and axonometricprojection s . A lens providing an orthographic projection is known as an Telecentric lens Object space telecentric lenses object space telecentric ... as front view, top view and right side view. Pictorials main Axonometricprojection Within orthographic projection there is the subcategory known as pictorials . Axonometric pictorials show an image ... of axonometricprojection to measure along axes . See also commonscat Orthographic projections div ...Views Orthographic projection or orthogonal projection is a means of representing a Three dimensional space three dimensional object in Two dimensional two dimensions . It is a form of parallel projection , where all the projection lines are orthogonal to the projection plane, ref name maynard Cite book ... PA22&dq axonometric orthographic&q axonometric 20orthographic isbn 0801472806 ref resulting in every ... where the axis or plane of the object is also parallel with the projection plane, ref name maynard ... right 200px Symbols used to define whether a projection is either Third Angle right or First Angle left . Origin The orthographic projection has been known since antiquity, with its cartographic uses being well documented. Hipparchus used the projection in the 2nd century B.C. to determine the places ... the projection to construct sundials and to compute sun positions. ref name Snyder16 Snyder, John ... orthographic from the Greek orthos straight and graph drawing for the projection. However, the name ... maps on the projection appear as woodcut drawings of terrestrial globes of 1509 anonymous , 1533 ... main Multiview orthographic projection With multiview orthographic projections, up to six pictures of an object are produced, with each projection plane parallel to one of the coordinate axes ... first angle or third angle projection. In each, the appearances of views may be thought of as being ... ?id JrZoGgQEhKkC&pg PA169&dq axonometric orthographic v onepage&q axonometric 20orthographic isbn ... more details
, some liberties may be taken for economy of effort and best effect. Orthographic projection The Orthographic projection is derived from the principles of descriptive geometry and is a two dimensional representation of a three dimensional object. It is a parallel projection the lines of projection are parallel both in reality and in the projection plane . It is the projection type of choice for Plans drawings working drawings . Pictorials Axonometricprojection main Axonometricprojection Within ... of axonometricprojection to measure along axes . Image Axonometric projections.png thumb The three Axonometricprojectionaxonometric views . Isometric projection In isometric pictorials for protocols ... . Perspective projection Image Axonometric scheme.jpg left thumb 300px Axonometricprojection of a scheme ...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 ... 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 of graphical projection compared. Parallel projection In parallel projection , the lines of sight from the object to the projection plane are parallel to each other. Within parallel projection there is an ancillary ... more details
for isometric projection in video games Video games with isometric graphics Mergeto Axonometricprojection discuss Talk Axonometricprojection Proposal to merge Dimetric projection and Trimetric projection ... projection. span style color 000000 background fffff Black labels span denote dimensions ... of the 2D projection drawing . Isometric projection is a method for visually representing three dimensional objects in two dimensions in technical drawing technical and engineering drawing s. It is an axonometricprojection in which the three Cartesian coordinate system coordinate axes appear equally ... Greek for equal measure , reflecting that the scale measurement scale along each axis of the projection is the same unlike some other forms of graphical projection . An isometric view of an object can be obtained by choosing the viewing direction in a way that the angles between the projection ... axis. Another way in which isometric projection can be visualized is by considering a view within ... another. The term isometric is often mistakenly used to refer to axonometric projections in general. There are three types of axonometric projections isometric, dimetric and trimetric. Mathematics ... projection, the value of the second may seem counter intuitive and so deserves some ... alpha math . This is then followed by an orthographic projection to the x y plane math begin bmatrix ... edition of the Romance of the Three Kingdoms , China, c. 15th century. main Axonometricprojection First formalized by Professor William Farish professor William Farish 1759 1837 , the concept ... of isometric projection. The height difference between the red and blue balls cannot be determined ... of parallel projection , objects drawn with isometric projection do not appear larger or smaller as they extend ... projection , it is not how our eyes or photography normally work. It also can easily result in situations .... clear See also Graphical projection Isometric graphics in video games and pixel art References refs ... more details
Projection effect may refer to Front projection effect , in camera visual effect Rear projection effect , in camera visual effect Insolation Projection effect , the amount of sunlight onto a portion of the Earth relative to its tilt In astronomy, a type of observational illusion caused by viewing distant objects or phenomenon from a particular perspective. Examples include superluminal motion , the retrograde motion of the planets, and optical double stars. See also Projection disambiguation Effect disambiguation dab ... 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
disambig There are several projections used in maps carrying the name of Johann Heinrich Lambert Lambert cylindrical equal area projection preserves areas Lambert azimuthal equal area projection preserves areas Lambert conformal conic projection preserves angles, commonly used in aviation navigation maps ... 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 maps meridian geography meridians to vertical straight lines of constant spacing for Meridian geography ... 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 ... 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 ... Equirectangular Projection , PanoTools wiki. Category Cartographic projections Category Panorama ... cs Ekvidistantn v lcov projekce de Plattkarte es Proyecci n cil ndrica equidistante fr Projection ... projection uk ... more details
Population projection , in the field of demography , is an estimate of a future population. In contrast with intercensal estimates and censuses, which usually involve some sort of field data gathering, projections usually involve mathematical models based only on pre existing data. A projection may be made by a governmental organization, or by those unaffiliated with a government. See also Census Unreferenced date November 2010 DEFAULTSORT Population Projection Category Demography statistics stub fr Projection d mographique kk lt Demografin prognoz ru ... more details
File Collignon projection SW.jpg 450px thumb Collignon projection of the world. The Collignon projection is an equal area Map projection Pseudocylindrical pseudocylindrical map projection first known to be published by douard Collignon in 1865 and subsequently cited by A. Tissot in 1881 . For the smallest choices of the parameters chosen for this projection, the sphere may be mapped either to a single diamond, a pair of squares or a triangle. Another projection that maps each hemisphere to a square is the quincuncial map . It is used in the polar areas as part of the HEALPix spherical projection, which is widely used in physical cosmology in making maps of the cosmic microwave background , in particular by the WMAP and future Planck Surveyor space missions. External links http www.progonos.com furuti MapProj Normal ProjPCyl projPCyl.html Collignon Pseudocylindrical Projections Collignon Projection , Carlos A. Furuti http melusine.eu.org syracuse mluque mappemonde doc collignon collignon.html Projection COLLIGNON m ridiens et parall les rectilignes , Manuel Luque, Giuseppe Matarazzo http www.uff.br mapprojections Collignon en.html An interactive Java Applet to study the metric deformations of the Collignon Projection . Category Cartographic projections Category Equal area projections cartography stub ... more details
The Littrow projection is the only conformal retroazimuthal map projection . A retroazimuthal projection is one in which the direction to a fixed location B the bearing at the starting location A of the shortest route corresponds to the direction on the map from A to B. The Littrow projection allows direct measurement of the azimuth from any point on the map. The Littrow projection was created in 1833 by Joseph Johann Littrow 1781 1840 . It is sometimes referred to as a Weir Azimuth diagram . External links http www.csiss.org map projections Azimuthal.html A Gallery of Map Projections Azimuthals & Related http www.csiss.org map projections Azimuthal Littrow.pdf Littrow map http www.uff.br mapprojections Littrow en.html An interactive Java Applet to study the metric deformations of the Littrow Projection . Cartography stub Category Cartographic projections ... 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 Bonne projection SW.jpg 450px thumb Bonne projection of the world, standard parallel at 45 N. A Bonne projection is a pseudoconical equal area map projection , sometimes called a d p t de la guerre or a Sylvanus projection. Although named after Rigobert Bonne 1727 1795 , the projection was in use prior to his birth, in 1511 by Sylvano, Honter in 1561, De l Isle before 1700 and Coronelli in 1696 ref Flattening the Earth Two Thousand Years of Map Projections , John P. Snyder, 1993, pp.60 62, ISBN 0 226 76747 7 ref . The projection is math x rho sin E , math math y cot varphi 1 rho cos E , math where math rho cot varphi 1 varphi 1 varphi , math math E frac lambda cos varphi rho math and &phi is the latitude, &lambda is the longitude from the central meridian, and &phi sub 1 sub is the standard parallel of the projection 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.138 140 ref . Parallels of latitude are concentric circular arcs, and the scale is true along these arcs .... Special cases of the Bonne projection include the sinusoidal projection , when &phi sub 1 sub is zero, and the Werner projection , when &phi sub 1 sub is &pi 2. The Bonne projection can be seen as an intermediate projection in the unwinding of a Werner projection into a Sinusoidal projection an alternative intermediate would be a Bottomley projection ref http www.cybergeo.eu index3977.html Between the Sinusoidal projection and the Werner an alternative to the Bonne , Henry Bottomley 2002 ref References ... manifold manuals 5 userman mfd50Bonne.htm Bonne Map Projection manifold.net http www.radicalcartography.net ... the metric deformations of the Bonne Projection http mathworld.wolfram.com BonneProjection.html Bonne Projection wolfram.com DEFAULTSORT Bonne Projection Category Cartographic projections Category Equal area projections Cartography stub es Proyecci n de Bonne fr Projection de Bonne nl Projectie ... more details
Main Conformational isomerism style border 1px solid AAA float right margin left 10px colspan 2 Molecule of butane in syn clinal sc conformation align center Image Sawhorse projection butane sc.png 120px align center Image Newman projection butane sc.png align center Sawhorse br projection align center Newman br projection A Newman projection , useful in alkane stereochemistry , visualizes chemical conformation s of a carbon carbon chemical bond from front to back, with the front carbon represented by a dot and the back carbon as a circle see below . The front carbon atom is called proximal , while the back atom is called distal . This type of representation is useful for assessing the torsional angle between bonds. A Sawhorse representation , on the other hand, views a carbon carbon bond from an oblique angle. This type of representation makes it easy to visualize the molecule as a whole in 3 D. Other methods for depicting molecules are the Fischer projection , the Haworth projection and the Natta projection . This projection is named after Melvin Spencer Newman , an American chemist of Ohio State University who introduced it in 1952. References Newman, M. S. Record. Chem. Progr. Kresge Hooker Sci. Lib. 1952 , 13 , 111. Newman, M. S. A notation for the study of certain stereochemical problems. J. Chem. Educ. 1955 , 32 , 344 347. See also commons category Newman projection Haworth projection Fischer projection Natta projection Category Stereochemistry ar de Newman Projektion es Proyecci n de Newman fr Projection de Newman it Proiezione di Newman he hu Newman projekci nl Newmanprojectie ja pl Projekcja Newmana ru zh ... 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 equidistant projection , 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 equidistant projection. 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 ja ... more details
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 ... i is idempotenT. 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 ... do not have any image by the projection. The projection onto a plane parallel to a direction D ... P . Various other projections, called projection map s have been defined for the need of cartography. The 3D projection s are also at the basis of the theory of perspective graphical perspective . The need of unifying 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 ... sup th sup projection set theory projection map , written proj sub j sub , that takes an element ... under a given equivalence relation is known as the canonical projection. The evaluation map sends a function ... product math prod i in X Y i math , and the evaluation map is a projection map from ... objects has 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 ... is a projection. This type of projection naturally generalizes to any number of dimensions ... more details
Refimprove date February 2012 A projection clock also called ceiling clock is an analog signal analog or digital clock equipped with a Image projector projector that creates an enlarged image of the clock face on any suitable projection screen , most often the ceiling. The advantage of a projection clock is that the clock can be placed almost anywhere. Depending on the projector used, the image can be in monochrome or color. The image generated by most projection clocks is large enough that a nearsightedness nearsighted person can see it from distance without glasses or contact lenses. Projection clocks are also used in advertising and merchandising . High brightness analog projection clocks can superimpose a business logo on top of the clock face, while there are low brightness projection clocks designed for home use that project for example a logo in addition to the time. Projection clocks may be connected to and synchronize with an Atomic clock to self adjust their time accurately. History Projection clocks were patented at least twice once in 1909, and another time in 1940. ref http www.roger russell.com project project.htm Dead link date February 2012 ref Both patents have expired by now. Early projection clocks were universally analog but with the widespread adoption of digital clocks, digital projection clocks became the standard. Technology A projection clock usually needs a backlight like an incandescent light bulb incandescent bulbs or light emitting diode LEDs . There are low brightness and high brightness clocks. While the projection created by low brightness clocks ... indoor places. Low brightness projection clocks Most modern projection clocks use a red ... reading there is too much light for the projection to be seen. They are often integrated into alarm clocks. High brightness projection clocks Modern high brightness projection clocks are in most cases ... analog and digital information on the projected image. Projectors used in projection clocks are similar ... more details
Image Usgs map albers equal area conic.PNG frame right An Albers projection shows areas accurately, but distorts shapes. File Albers projection SW.jpg 450px thumb Albers projection the world, standard parallels 20 N and 50 N. The Albers equal area conic projection , or Albers projection named after Heinrich C. Albers , is a Map projection Conical conic , Map projection Equal area equal area map projection that uses two standard parallels. Although scale and shape are not preserved, distortion is minimal between the standard parallels. The Albers projection is the standard projection for British Columbia . ref cite web title British Columbia Map Projection Standard publisher BC Integrated Land Management Bureau url http www.ilmb.gov.bc.ca risc pubs other mappro map.htm accessdate 2010 08 05 ref It is also used by the United States Geological Survey and the United States Census Bureau . ref cite web title Projection Reference publisher Bill Rankin url http www.radicalcartography.net ?projectionref accessdate 2009 03 31 ref Snyder ref name snyder Cite book author Snyder, John P. title Map Projections &ndash A Working Manual. U.S. Geological Survey Professional Paper 1395 publisher United States Government Printing Office, Washington, D.C. year 1987 This paper can be downloaded from http pubs.er.usgs.gov pubs pp pp1395 USGS pages. ref Section 14 describes generating formul for the projection, as well as the projection s characteristics. Formul also appear at http mathworld.wolfram.com AlbersEqual AreaConicProjection.html Mathworld s page on the Albers projection . References ... s page on the Albers projection http www.radicalcartography.net ?projectionref Table of examples and properties ... geomatics techweb yt albers projection.html Yukon Albers Projection http www.uff.br mapprojections Albers en.html An interactive Java Applet to study the metric deformations of the Albers Projection ... fr Projection d Albers nl Projectie van Albers pt Proje o de Albers ru ... more details
Image Bottomley projection.gif thumb 250px right A Bottomley projection A Bottomley projection is an equal area map projection . The projection is math x frac rho sin E sin phi 1 , math math y tfrac pi 2 rho cos E , math where math rho tfrac pi 2 phi , math math E frac lambda sin phi 1 sin rho rho math and &phi is the latitude, &lambda is the longitude from the central meridian, and &phi sub 1 sub is the given parallel of the projection which determines its shape, all in radians. Parallels i.e. lines of latitude are concentric ellipse elliptical arcs of constant eccentricity mathematics eccentricity , centred on the north pole . On the central meridian geography meridian , shapes are not distorted, but elsewhere they are. Different projections can be produced by altering the eccentricity of the arcs, making it vary between the sinusoidal projection and the Werner projection . It was introduced by Henry Bottomley as an alternative to the Bonne projection to reduce the extent of extreme distortion at the edges and give a more satisfying overall shape. External links http www.cybergeo.eu index3977.html Cybergeo article Category Cartographic projections Category Equal area projections Cartography stub ... more details
Projection pursuit is a type of statistical technique which involves finding the most interesting possible projections in multidimensional data. Often, projections which deviate more from a Normal distribution are considered to be more interesting. As each projection is found, the data are reduced by removing the component along that projection, and the process is repeated to find new projections this is the pursuit aspect that motivated the technique known as matching pursuit . The projection pursuit concept was developed by Jerome H. Friedman and John Tukey in 1974. See also Projection pursuit regression Targeted projection pursuit References cite journal title A Projection Pursuit Algorithm for Exploratory Data Analysis author J. H. Friedman and J. W. Tukey journal IEEE Transactions on Computers month Sep. year 1974 volume C 23 issue 9 pages 881 890 issn 0018 9340 url http www.slac.stanford.edu cgi wrap getdoc slac pub 1312.pdf doi 10.1109 T C.1974.224051 cite journal title Projection pursuit author P. J. Huber journal The Annuals of Statistics month Jun. year 1985 volume 13 issue 2 pages 435 475 url http www.stat.rutgers.edu rebecka Stat687 huber.pdf doi 10.1214 aos 1176349519 cite journal doi 10.2307 2981662 author M. C. Jones and R. Sibson title What is Projection Pursuit? journal Journal of the Royal Statistical Society, Series A General year 1987 volume 150 issue 1 pages 1 37 jstor 2981662 Category Exploratory data analysis Category Multivariate statistics stat stub de Projection Pursuit fr Poursuite de projection ru ... more details
File Cassini projection SW.jpg thumb Cassini projection of the world. The Cassini projection is a map projection described by C sar Fran ois Cassini de Thury in 1745 . ref Flattening the Earth Two Thousand Years of Map Projections , John P. Snyder, 1993, pp. 74 76, ISBN 0 226 76747 7. ref It is the Transversality transverse aspect of the equirectangular projection , in that the globe is first rotated so the central meridian becomes the equator , and then the normal equirectangular projection is applied. Composing these operations math x arcsin cos phi sin lambda , math math y arctan left frac tan phi cos lambda right math where math lambda math is the longitude from the central meridian and math phi math is the latitude. When programming these equations, the inverse tangent function used is actually the atan2 function, with the first argument math sin phi math and the second math cos phi cos lambda math . The use of the Cassini projection has largely been superseded by the Transverse Mercator projection, at least with central mapping agencies. Distortions Things along the central meridian, and at right angles to it, are not distorted. Elsewhere, the distortion is largely in a north south direction, and varies by the square of the central meridian. As such, the greater the longitudinal extent of the area, the worse the distortion becomes. Due to this, the Cassini projection works best on long, narrow areas, and worst on wide areas. References references External links http www.radicalcartography.net ?projectionref Table of examples and properties of all common projections , from radicalcartography.net http www.ordnancesurvey.co.uk oswebsite freefun geofacts geo1164.html Ordnance Survey GeoFacts on the Cassini Projection DEFAULTSORT Cassini Projection Category Cartographic projections Cartography stub ... more details
, see Projection linear algebra . Views Oblique projection is a simple type of graphical projection used ... 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 ... angle used in orthographic projection. Mathematically, the parallel projection of the point math x, y ... 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 ... 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 ... projection sometimes cavalier perspective or high view point a point of the object is represented by three ... are drawn with a 1 1 scale it is thus similar to the dimetric projection s, although it is not an orthographic projection , as the third axis, here y , is drawn in diagonal, making an arbitrary angle ... Cabinet projection The term cabinet projection sometimes cabinet perspective stems from its use in illustrations ... as going off in an angle typical 30 or 45 . Unlike cavalier projection, where the third axis keeps its length, with cabinet projection the length of the receding lines is cut in half. Mathematical formula ... more details
File Mollweide projection SW.jpg 450px thumb Mollweide projection of the world. Image Tissot indicatrix world map Mollweide proj.svg thumb 450px The Mollweide projection with Tissot s indicatrix of deformation The Mollweide projection is a Map projection pseudocylindrical map projection generally used for global maps of the world or sky . Also known as the Babinet projection , homalographic projection , homolographic projection , and elliptical projection . As its more explicit name Mollweide equal area projection indicates, it sacrifices accuracy of angle and shape in favor of accurate depiction ... small maps depicting global distributions. The projection was first published by mathematician .... It was popularized by Jacques Babinet in 1857, giving it the name homalographic projection . The variation ... as seen by the Wilkinson Microwave Anisotropy Probe . Projected using the Mollweide projection. Image ... Data Analysis Project . Projected using the Mollweide projection. The projection is math x frac 2 ... be bypassed otherwise, division by zero may result. Properties The Mollweide is a Map projection Pseudocylindrical pseudocylindrical projection in which the equator is represented as a straight horizontal ..., although not as severe as in the sinusoidal projection . Shape distortion may be diminished by using an interrupted version. A sinusoidal interrupted Mollweide projection discards the central ... projection uses multiple disjoint central meridians, giving the effect of multiple ellipses joined ... inspired the creation of several other projections, including the Goode homolosine projection Goode s homolosine , van der Grinten projection van der Grinten and the Boggs eumorphic projection Boggs ... ref See also Aitoff projection Hammer projection References reflist External links http www.uff.br ... of the Mollweide Map Projection http mathworld.wolfram.com MollweideProjection.html Mollweide Projection at Mathworld Category Cartographic projections Category Equal area projections ca Projecci ... more details
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