query: what type of projection is the robinson projection

pos: Robinson projection column is the length of the parallel of latitude, and the PDFE column is multiplied by 0.5072 to obtain the distance of that parallel from the equator. Meridians of longitude are equally spaced on each parallel of latitude. 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

pos: Robinson projection 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

pos: Robinson projection column is the length of the parallel of latitude, and the PDFE column is multiplied by 0.5072 to obtain the distance of that parallel from the equator. Meridians of longitude are equally spaced on each parallel of latitude. 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

pos: Kavrayskiy VII projection Kavrayskiy VII projection The Kavrayskiy VII projection is a map projection invented by Soviet cartographer Vladimir V. Kavrayskiy in 1939 for use as a general purpose pseudocylindrical projection. Like the Robinson projection, it is a compromise intended to produce good quality maps with low distortion overall. It scores well in that respect compared to other popular projections, such as the Winkel Tripel, despite straight, evenly spaced parallels and a simple formulation. Regardless, it has not been widely used outside the former Soviet Union. The projection is defined as: where "λ" is the longitude and "φ" is the latitude in radians.

pos: Orthographic projection as described in Pohlke's theorem) is used to describe the type of orthographic projection where the plane or axis of the object depicted is "not" parallel to the projection plane, and where multiple sides of an object are visible in the same image. It is further subdivided into three groups: "isometric", "dimetric" and "trimetric projection", depending on the exact angle at which the view deviates from the orthogonal. A typical characteristic of axonometric projection (and other pictorials) is that one axis of space is usually displayed as vertical. An orthographic projection map is a map projection of cartography. Like the

pos: General Perspective projection General Perspective projection The General Perspective projection is a map projection. When the Earth is photographed from space, the camera records the view as a perspective projection. When the camera is aimed toward the center of the Earth, the resulting projection is called Vertical Perspective. When aimed in other directions, the resulting projection is called a Tilted Perspective. The Vertical Perspective is related to the stereographic projection, gnomonic projection, and orthographic projection. These are all true perspective projections, meaning that they result from viewing the globe from some vantage point. They are also azimuthal projections, meaning that the projection surface

pos: Cassini projection Cassini projection The Cassini projection (also sometimes known as the Cassini-Soldner projection or Soldner projection) is a map projection described by César-François Cassini de Thury in 1745. It is the 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. Considering the earth as a sphere, the projection is composed of the operations: where "λ" is the longitude from the central meridian and "φ" is the latitude. When programming these equations, the inverse tangent function used is actually the atan2 function, with

neg: Winkel tripel projection common Eckert IV projection and Robinson projections. In 1998, the Winkel tripel projection replaced the Robinson projection as the standard projection for world maps made by the National Geographic Society. Many educational institutes and textbooks followed National Geographic's example in adopting the projection, and most of those still use it. 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

neg: Equal Earth projection Equal Earth projection The Equal Earth map projection is an equal-area pseudocylindrical projection for world maps, invented by Bojan Šavrič, Bernhard Jenny, and Tom Patterson in 2018. It is inspired by the widely used Robinson projection, but unlike the Robinson projection, retains the relative size of areas. The projection equations are simple to implement and fast to evaluate. The projection is formulated as the polynomial equations where and formula_3 refers to latitude and formula_4 to longitude. The features of the Equal Earth projection include: The Equal Earth map projection was created by Bojan Šavrič, Tom Patterson, and Bernhard Jenny, as

neg: Robinson projection 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". The Robinson projection is neither equal-area nor conformal, abandoning both for a compromise. The creator felt this produced a better overall view than could be achieved by adhering to either. The meridians curve gently, avoiding extremes, but thereby stretch the poles into long lines instead of leaving them as points. Hence, distortion close to the poles is severe,

neg: Axonometric projection Axonometric projection Axonometric projection is a type of orthographic projection used for creating a pictorial drawing of an object, where the lines of sight are perpendicular to the plane of projection, and the object is rotated around one or more of its axes to reveal multiple sides. "Axonometry" means "to measure along axes". In German literature, axonometry is based on Pohlke's theorem, so that the scope of axonometric projection encompasses "every" type of parallel projection, including not only oblique projection, but also orthographic projection and therefore multiview projection. However, outside of German literature, the term "axonometric" is often used to

neg: Parallel projection has the following properties. 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 plane. It is the projection type of choice for working drawings. The term "orthographic" is sometimes reserved specifically for depictions of objects where the principal axes or planes of the object are parallel with the projection plane (or the paper on which the orthographic or parallel projection is drawn). However, the term multiview projection is also used. In "multiview projections", up to six pictures of an object are produced, with

neg: Arthur H. Robinson was pleasing to the eye of general viewers. Robinson could not find a projection that satisfied the criteria, so Rand McNally commissioned him to design one. Robinson proceeded through an iterative process to create a pseudo-cylindrical projection that intends to strike a compromise between distortions in areas and in distances, in order to attain a more natural visualization. The projection has been widely used since its introduction. In 1988, National Geographic adopted it for their world maps but replaced it in 1998 with the Winkel tripel projection. Robinson produced over 60 articles for professional publications, as well as fifteen books

neg: Rear-projection television television. The projector is contained inside the television box and projects the image from behind the screen. The following are different types of projection televisions, which differ based on the type of projector and how the image (before projection) is created: Rear-projection television Rear-projection television (RPTV) is a type of large-screen television display technology. Until approximately 2006, most of the relatively affordable consumer large screen TVs up to used rear-projection technology. A variation is a video projector, using similar technology, which projects onto a screen. Three types of projection systems are used in projection TVs. CRT rear-projection TVs were the

neg: Robinson projection but quickly declines to moderate levels moving away from them. The straight parallels imply severe angular distortion at the high latitudes toward the outer edges of the map, a fault inherent in any pseudocylindrical projection. However, at the time it was developed, the projection effectively met Rand McNally's goal to produce appealing depictions of the entire world. The projection is defined by the table: The table is indexed by latitude at 5 degree intervals; intermediate values are calculated using interpolation. Robinson did not specify any particular interpolation method, but it is reported that he used Aitken interpolation himself. The PLEN

neg: Television DLP front projectors (standalone projection units for classrooms and business primarily), but also in private homes; in these cases, the image is projected onto a projection screen. DLP is also used in DLP rear projection television sets and digital signs. It is also used in about 85% of digital cinema projection. A plasma display panel (PDP) is a type of flat panel display common to large TV displays or larger. They are called "plasma" displays because the technology utilizes small cells containing electrically charged ionized gases, or what are in essence chambers more commonly known as fluorescent lamps. Liquid-crystal-display televisions

neg: Axonometric projection as it returns to its source. The water thus appears to disobey the law of conservation of energy. Axonometric projection Axonometric projection is a type of orthographic projection used for creating a pictorial drawing of an object, where the lines of sight are perpendicular to the plane of projection, and the object is rotated around one or more of its axes to reveal multiple sides. "Axonometry" means "to measure along axes". In German literature, axonometry is based on Pohlke's theorem, so that the scope of axonometric projection encompasses "every" type of parallel projection, including not only oblique projection, but also

neg: Wagner VI projection where formula_2 is the longitude and formula_3 is the latitude. Wagner VI projection Wagner VI is a pseudocylindrical whole Earth map projection. Like the Robinson projection, it is a compromise projection, not having any special attributes other than a pleasing, low distortion appearance. Wagner VI is equivalent to the Kavrayskiy VII horizontally elongated by a factor of . This elongation results in proper preservation of shapes near the equator but slightly more distortion overall. The aspect ratio of this projection is 2:1, as formed by the ratio of the equator to the central meridian. This matches the ratio of Earth’s

neg: Wagner VI projection Wagner VI projection Wagner VI is a pseudocylindrical whole Earth map projection. Like the Robinson projection, it is a compromise projection, not having any special attributes other than a pleasing, low distortion appearance. Wagner VI is equivalent to the Kavrayskiy VII horizontally elongated by a factor of . This elongation results in proper preservation of shapes near the equator but slightly more distortion overall. The aspect ratio of this projection is 2:1, as formed by the ratio of the equator to the central meridian. This matches the ratio of Earth’s equator to any meridian. The Wagner VI is defined by:

neg: Engineering drawing makes isometric drawings so attractive is the ease with which 60° angles can be constructed with only a compass and straightedge. Isometric projection is a type of axonometric projection. The other two types of axonometric projection are: An oblique projection is a simple type of graphical projection used for producing pictorial, two-dimensional images of three-dimensional objects: In both oblique projection and orthographic projection, parallel lines of the source object produce parallel lines in the projected image. Perspective is an approximate representation on a flat surface, of an image as it is perceived by the eye. The two most characteristic features

neg: Oblique projection depicting rectilinear objects such as houses. Oblique projection is a type of parallel projection: 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 plane at an oblique angle to produce the projected image, as opposed to the perpendicular angle used in orthographic projection. Mathematically, the parallel projection of the point formula_1 on the formula_2-plane gives formula_3. The constants formula_4 and formula_5 uniquely specify a parallel projection. When formula_6, the projection is said to be "orthographic" or "orthogonal". Otherwise, it is "oblique".

neg: Van der Grinten projection for their reference maps of the world in 1922, raising its visibility and stimulating its adoption elsewhere. In 1988, National Geographic replaced the van der Grinten projection with the Robinson projection. The geometric construction given by van der Grinten can be written algebraically: where "x" takes the sign of , "y" takes the sign of "φ" and If "φ" = 0, then Similarly, if "λ" = "λ" or "φ" = ±, then In all cases, "φ" is the latitude, "λ" is the longitude, and "λ" is the central meridian of the projection. Van der Grinten projection The van der Grinten

neg: Gall–Peters projection those cartographers had already developed projections they explicitly promoted as alternatives to the Mercator, including the most influential American cartographers of the twentieth century: John Paul Goode (Goode homolosine projection), Erwin Raisz (Armadillo projection), and Arthur H. Robinson (Robinson projection). Hence the cartographic community viewed Peters's narrative as ahistorical and mean-spirited. The two camps never made any real attempts toward reconciliation. The Peters camp largely ignored the protests of the cartographers. Peters maintained there should be "one map for one world"—his—and did not acknowledge the prior art of Gall until the controversy had largely run its course, late in his

neg: Transformation matrix when using perspective projections. Another type of transformation, of importance in 3D computer graphics, is the perspective projection. Whereas parallel projections are used to project points onto the image plane along parallel lines, the perspective projection projects points onto the image plane along lines that emanate from a single point, called the center of projection. This means that an object has a smaller projection when it is far away from the center of projection and a larger projection when it is closer. The simplest perspective projection uses the origin as the center of projection, and "z" = 1 as the

neg: Graphical projection cases the result is "orthographic" (the rays are perpendicular to the image plane). "Axonometry" should not be confused with "axonometric projection", as in English literature the latter usually refers only to a specific class of pictorials (see below). 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 working drawings. With "multiview projections", up to six pictures (called "primary views") of an object

neg: Projection pursuit Projection pursuit Projection pursuit (PP) 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 idea of projection pursuit is to locate the projection or projections from high-dimensional space to low-dimensional space that reveal the most details about the

neg: Azimuthal equidistant projection 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. While it may have been used by ancient

neg: Oblique projection the advent of 3D games) also often use a form of oblique projection. Examples include "SimCity", "Ultima VII", "Ultima Online", "EarthBound", "Paperboy" and, more recently, "Tibia". Oblique projection Oblique projection is a simple type of technical drawing of graphical projection used for producing two-dimensional images of three-dimensional objects. The objects are not in perspective, so they do not correspond to any view of an object that can be obtained in practice, but the technique does yield somewhat convincing and useful images. Oblique projection is commonly used in technical drawing. The cavalier projection was used by French military artists in the

neg: Oblique projection Oblique projection Oblique projection is a simple type of technical drawing of graphical projection used for producing two-dimensional images of three-dimensional objects. The objects are not in perspective, so they do not correspond to any view of an object that can be obtained in practice, but the technique does yield somewhat convincing and useful images. Oblique projection is commonly used in technical drawing. The cavalier projection was used by French military artists in the 18th century to depict fortifications. Oblique projection was used almost universally by Chinese artists from the first or second centuries to the 18th century, especially when

neg: Rear-projection television Rear-projection television Rear-projection television (RPTV) is a type of large-screen television display technology. Until approximately 2006, most of the relatively affordable consumer large screen TVs up to used rear-projection technology. A variation is a video projector, using similar technology, which projects onto a screen. Three types of projection systems are used in projection TVs. CRT rear-projection TVs were the earliest, and while they were the first to exceed 40", they were also bulky and the picture was unclear at close range. Newer technologies include: DLP (reflective micromirror chip), LCD projectors, Laser TV and LCoS. They are capable of 1080p resolution,

neg: GSO projection with different physical particles and properties in spacetime. For example, the Type II and Type 0 string theories result from different GSO projections on the same worldsheet theory. Furthermore, the two distinct Type II theories, IIA and IIB, differ in their GSO projections. In building models of realistic string vacua (as opposed to toy models), one typically chooses a GSO projection which eliminates the tachyonic ground state of the string and preserves spacetime supersymmetry. GSO projection The GSO projection (named after Ferdinando Gliozzi, Joël Scherk, and David I. Olive) is an ingredient used in constructing a consistent model in superstring

neg: Arthur H. Robinson R. Coffin and Bessie Morris Coffin, on December 23, 1938, in Franklin County, Ohio. They had two children, a son and a daughter. After the death of his first wife, Robinson remarried in 1993. His second wife was Martha Elizabeth Rodabaugh Phillips (1914–2010), a widow, with whom he had attended school in Oxford, Ohio. Robinson was a prolific writer and influential philosopher on cartography: One of Robinson's most notable accomplishments is the Robinson projection. In 1961, Rand McNally asked Robinson to choose a projection for use as a world map that, among other criteria, was uninterrupted, had limited distortion, and

neg: Octant projection John Dee's maps of 1580". Others also accept explicitly both (map and projection) as authentic, although leaving in the air Leonardo's direct hand, giving the authorship of the work to one of his disciples as Nordenskjold states in his book "Facsimile-Atlas" (1889) confirmed by Dutton (1995) and many others: "on account of the remarkable projection..not by Leonardo himself, but by some ignorant clerk", or Keunig (1955) being more precise: "by one of his followers at his direction". Octant projection The octant projection or octants projection, is a type of projection proposed the first time, in 1508, by Leonardo da Vinci

neg: Octant projection Octant projection The octant projection or octants projection, is a type of projection proposed the first time, in 1508, by Leonardo da Vinci in his Codex Atlanticus. Leonardo's authorship would be demonstrated by Christopher Tyler, who stated "For those projections dated later than 1508, his drawings should be effectively considered the original precursors ...". In fact, there is a sketch of it on a page in the Codex Atlanticus manuscripts, made from the very hand of Leonardo, being Leonardo's sketch, the first known description of the "octant projection". The same page of the Codex contains sketches of eight other projections

neg: Azimuthal equidistant projection in the map and rotating the antenna to the angle indicated by the map. The map should be centered as nearly as possible to the actual antenna location. 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

neg: Independent component analysis those signal mixtures where this inner product provides an orthogonal projection of the signal mixtures. The remaining challenge is finding such a weight vector. One type of method for doing so is projection pursuit. Projection pursuit seeks one projection at a time such that the extracted signal is as non-Gaussian as possible. This contrasts with ICA, which typically extracts "M" signals simultaneously from "M" signal mixtures, which requires estimating a "M" × "M" unmixing matrix. One practical advantage of projection pursuit over ICA is that fewer than "M" signals can be extracted if required, where each source signal is extracted

neg: Von Neumann algebra other ways to divide factors into classes that are sometimes used: A factor is said to be of type I if there is a minimal projection "E ≠ 0", i.e. a projection "E" such that there is no other projection "F" with 0 < "F" < "E". Any factor of type I is isomorphic to the von Neumann algebra of "all" bounded operators on some Hilbert space; since there is one Hilbert space for every cardinal number, isomorphism classes of factors of type I correspond exactly to the cardinal numbers. Since many authors consider von Neumann algebras only on separable

neg: Targeted projection pursuit an interactive scatter plot. Targeted projection pursuit has found applications in DNA microarray data analysis, protein sequence analysis, graph layout and digital signal processing. It is available as a package for the WEKA machine learning toolkit. Targeted projection pursuit Targeted projection pursuit is a type of statistical technique used for exploratory data analysis, information visualization, and feature selection. It allows the user to interactively explore very complex data (typically having tens to hundreds of attributes) to find features or patterns of potential interest. Conventional, or 'blind', projection pursuit, finds the most "interesting" possible projections in multidimensional data, using a search

neg: Newman projection Newman projection A Newman projection, useful in alkane stereochemistry, visualizes the conformation of a chemical bond from front to back, with the front atom represented by a dot and the back carbon as a circle. The front carbon atom is called "proximal", while the back atom is called "distal". This type of representation clearly illustrates the specific dihedral angle between the proximal and distal atoms. This diagram style is an alternative to a sawhorse projection, which views a carbon-carbon bond from an oblique angle, or a wedge-and-dash style, such as a Natta projection. These other styles can indicate the bonding

neg: Gall–Peters projection as the model of the earth for projection. Hence the sphere is mapped onto the vertical cylinder, and the cylinder is stretched to double its length. The stretch factor, 2 in this case, is what distinguishes the variations of cylindric equal-area projection. The various specializations of the cylindric equal-area projection differ only in the ratio of the vertical to horizontal axis. This ratio determines the "standard parallel" of the projection, which is the parallel at which there is no distortion and along which distances match the stated scale. There are always two standard parallels on the cylindric equal-area projection, each

neg: Gall–Peters projection a wider audience beginning in the early 1970s by means of the "Peters World Map". The name "Gall–Peters projection" seems to have been used first by Arthur H. Robinson in a pamphlet put out by the American Cartographic Association in 1986. 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 Schools began phasing in these maps in March 2017, becoming the first public school district and state in the United States to adopt Gall–Peters maps as their standard. The Gall–Peters projection achieved notoriety

neg: Perspective projection distortion points of intersection with a Projection Plane. No type of projection can perfectly map the imagery of three dimensional space onto a projection plane because of the image's (mapped on the retina-sphere) undevelopability. This is a distortion of the drawing in itself called perspective projection distortion, and refers to the difference between the drawing and the way the objects depicted on it would look if it was real, but there is another distortion caused by the difference between the location of the supposed observer situated for the drawing process and the location of the real observer of the drawing. These

neg: 3D projection 3D projection 3D projection is any method of mapping three-dimensional points to a two-dimensional plane. As most current methods for displaying graphical data are based on planar (pixel information from several bitplanes) two-dimensional media, the use of this type of projection is widespread, especially in computer graphics, engineering and drafting. When the human eye looks at a scene, objects in the distance appear smaller than objects close by. Orthographic projection ignores this effect to allow the creation of to-scale drawings for construction and engineering. Orthographic projections are a small set of transforms often used to show profile, detail or precise

neg: Targeted projection pursuit Targeted projection pursuit Targeted projection pursuit is a type of statistical technique used for exploratory data analysis, information visualization, and feature selection. It allows the user to interactively explore very complex data (typically having tens to hundreds of attributes) to find features or patterns of potential interest. Conventional, or 'blind', projection pursuit, finds the most "interesting" possible projections in multidimensional data, using a search algorithm that optimizes some fixed criterion of "interestingness" – such as deviation from a normal distribution. In contrast, targeted projection pursuit allows the user to explore the space of projections by manipulating data points directly in

neg: Astral projection astral bodies to distant rooms and see what was happening. However, such experiments haven't produced clear results. According to Bob Bruce of the Queensland Skeptics Association, astral projection is "just imagining", or "a dream state". Bruce writes that the existence of an astral plane is contrary to the limits of science. "We know how many possibilities there are for dimensions and we know what the dimensions do. None of it correlates with things like astral projection." Bruce attributes astral experiences such as "meetings" alleged by practitioners to confirmation bias and coincidences. Psychologist Donovan Rawcliffe has written that astral projection can

neg: True length True length In geometry, true length is any distance between points that is not foreshortened by the view type. In a three-dimensional Euclidean space, lines with true length are parallel to the projection plane. For example, in a top view of a pyramid, which is an orthographic projection, the base edges (which are parallel to the projection plane) have true length, whereas the remaining edges in this view are not true lengths. The same is true with an orthographic side view of a pyramid. If any face of a pyramid was parallel to the projection plane (for a particular view),

neg: Gall–Peters projection between parallels of the Gall–Peters are a constant multiple of the distances between the parallels of the orthographic. That constant is . The name "Gall–Peters projection" seems to have been used first by Arthur H. Robinson in a pamphlet put out by the American Cartographic Association in 1986. Before 1973 it had been known, when referred to at all, as the "Gall orthographic" or "Gall's orthographic." Most Peters supporters refer to it only as the "Peters projection." During the years of controversy the cartographic literature tended to mention both attributions, settling on one or the other for the purposes of

neg: A Possible Projection of the Future / Childhood's End A Possible Projection of the Future / Childhood's End A Possible Projection of the Future / Childhood's End is American musician Al Kooper's fifth album, recorded for and released by Columbia Records in 1972. Begun with a vague storyline that failed to survive beyond the two title tracks, the album was recorded in London, England at George Martin's AIR Studios with one outtake from "New York City (You're A Woman)". Six original tracks were surrounded by covers of Bob Dylan ("The Man in Me", which Kooper had originally produced), Smokey Robinson ("Swept For You Baby") and even Jimmy Cliff ("Please

neg: Zaxxon Zaxxon "Zaxxon" was the first game to employ axonometric projection, which lent its name to the game ("AXXON" from "AXON"ometric projection). The type of axonometric projection is isometric projection: this effect simulated three dimensions from a third-person viewpoint. It was also the first arcade game to be advertised on television, with a commercial produced by Paramount Pictures for $150,000. The world record on "Zaxxon" is 4,680,740 points scored by Vernon Kalanikaus of Lā'ie, Hawai'i, on March 15, 1982, according to the Twin Galaxies Intergalactic Scoreboard. The object of the game is to hit as many targets as possible without being

neg: Cylindrical equal-area projection than radians, and use the equivalent formula: Stripping out unit conversion and uniform scaling, the formulae may be written: Hence the sphere is mapped onto a stretched vertical cylinder. The stretch factor "S" is what distinguishes the variations of cylindric equal-area projection. The various specializations of the cylindric equal-area projection differ only in the ratio of the vertical to horizontal axis. This ratio determines the "standard parallel" of the projection, which is the parallel at which there is no distortion and along which distances match the stated scale. There are always two standard parallels on the cylindric equal-area projection, each

neg: Mercator projection where distortion is minimal. Arno Peters stirred controversy when he proposed what is now usually called the Gall–Peters projection as "the" alternative to the Mercator. The projection he promoted is a specific parameterization of the cylindrical equal-area projection. In response, a 1989 resolution by seven North American geographical groups deprecated the use of cylindrical projections for general purpose world maps, which would include both the Mercator and the Gall–Peters. Many major online street mapping services (Bing Maps, OpenStreetMap, Google Maps, MapQuest, Yahoo! Maps, and others) use a variant of the Mercator projection for their map images called Web Mercator or

neg: Hammer retroazimuthal projection the projection is defined as: where and The latitude and longitude of the point to be plotted are "φ" and "λ" respectively, and the center point to which all azimuths are to be correct is given as "φ" and "λ". Hammer retroazimuthal projection The Hammer retroazimuthal projection is a modified azimuthal proposed by Ernst Hermann Heinrich Hammer in 1910. As a retroazimuthal projection, azimuths (directions) are correct from any point to the designated center point. Additionally, all distances from the center of the map are proportional to what they are on the globe. In whole-world presentation, the back and front

neg: Map projection the geoid are used to project maps from. A fundamental projection classification is based on the type of projection surface onto which the globe is conceptually projected. The projections are described in terms of placing a gigantic surface in contact with the earth, followed by an implied scaling operation. These surfaces are cylindrical (e.g. Mercator), conic (e.g. Albers), and plane (e.g. stereographic). Many mathematical projections, however, do not neatly fit into any of these three conceptual projection methods. Hence other peer categories have been described in the literature, such as pseudoconic, pseudocylindrical, pseudoazimuthal, retroazimuthal, and polyconic. Another way to classify

neg: Zaxxon which are unrelatable to the audience, such as events in one's personal life. In the ABC sitcom "Home Improvement", Randy plays "Zaxxon" at a bowling alley, attempting to set a record. Zaxxon "Zaxxon" was the first game to employ axonometric projection, which lent its name to the game ("AXXON" from "AXON"ometric projection). The type of axonometric projection is isometric projection: this effect simulated three dimensions from a third-person viewpoint. It was also the first arcade game to be advertised on television, with a commercial produced by Paramount Pictures for $150,000. The world record on "Zaxxon" is 4,680,740 points scored by

neg: Engineering drawing be classified by a letter classification in which each line is given a letter. In most cases, a single view is not sufficient to show all necessary features, and several views are used. Types of "views" include the following: A "multiview projection" is a type of orthographic projection that shows the object as it looks from the front, right, left, top, bottom, or back (e.g. the "primary views"), and is typically positioned relative to each other according to the rules of either first-angle or third-angle projection. The origin and vector direction of the projectors (also called projection lines) differs, as

neg: Time projection chamber anode plane can be organized into a 2D picture of a particle interaction. Such a picture is a projection of the 3D particle interaction onto a 2D plane whose normal vector is parallel to the wires in the specified anode plane. The 2D projections corresponding to each of the anode planes are combined to fully reconstruct the 3D interaction. The XENON series of dark-matter WIMP detectors use dual-phase (gas and liquid) TPCs. Time projection chamber In physics, a time projection chamber (TPC) is a type of particle detector that uses a combination of electric fields and magnetic fields together with

neg: Projection screen Projection screen A projection screen is an installation consisting of a surface and a support structure used for displaying a projected image for the view of an audience. Projection screens may be permanently installed, as in a movie theater; painted on the wall; or portable with tripod or floor rising models. as in a conference room or other non-dedicated viewing space. Another popular type of portable screens are inflatable screens for outdoor movie screening (open air cinema). Uniformly white or grey screens are used almost exclusively as to avoid any discoloration to the image, while the most desired brightness of

neg: Psychological projection projection and warns against it: "Do not taunt your neighbour with the bleach you yourself drank." Projection () was conceptualised by Sigmund Freud in his letters to Wilhelm Fliess, and further refined by Karl Abraham and Anna Freud. Freud considered that, in projection, thoughts, motivations, desires, and feelings that cannot be accepted as one's own are dealt with by being placed in the outside world and attributed to someone else. What the ego repudiates is split off and placed in another. Freud would later come to believe that projection did not take place arbitrarily, but rather seized on and exaggerated

neg: Television set classrooms and business primarily), DLP rear projection television sets, and digital signs. It is also used in about 85% of digital cinema projection, and in additive manufacturing as a power source in some printers to cure resins into solid 3D objects. A plasma display panel (PDP) is a type of flat panel display common to large TV displays or larger. They are called "plasma" displays because the technology utilizes small cells containing electrically charged ionized gases, or what are in essence chambers more commonly known as fluorescent lamps. Liquid-crystal-display televisions (LCD TV) are television sets that use Liquid-crystal displays to

neg: Jónsson–Tarski algebra order preserving automorphisms of the free Jónsson–Tarski algebra on one generator is the Thompson group "F". A Jónsson–Tarski algebra of type 2 is a set "A" with a product "w" from "A"×"A" to "A" and two "projection" maps "p" and "p" from "A" to "A", satisfying "p"("w"("a","a")) = "a", "p"("w"("a","a")) = "a", and "w"("p"("a"),"p"("a")) = "a". The definition for type > 2 is similar but with "n" projection operators. If "w" is any bijection from "A"×"A" to "A" then it can be extended to a unique Jónsson–Tarski algebra by letting "p"("a") be the projection of "w"("a") onto the "i"th factor.

neg: Hammer retroazimuthal projection Hammer retroazimuthal projection The Hammer retroazimuthal projection is a modified azimuthal proposed by Ernst Hermann Heinrich Hammer in 1910. As a retroazimuthal projection, azimuths (directions) are correct from any point to the designated center point. Additionally, all distances from the center of the map are proportional to what they are on the globe. In whole-world presentation, the back and front hemispheres overlap, making the projection a non-injective function. The back hemisphere can be rotated 180° to avoid overlap, but in this case, any azimuths measured from the back hemisphere must be corrected. Given a radius "R" for the projecting globe,

neg: Time projection chamber Time projection chamber In physics, a time projection chamber (TPC) is a type of particle detector that uses a combination of electric fields and magnetic fields together with a sensitive volume of gas or liquid to perform a three-dimensional reconstruction of a particle trajectory or interaction. The original TPC was invented by David R. Nygren, an American physicist, at Lawrence Berkeley Laboratory in the late 1970s. Its first major application was in the PEP-4 detector, which studied 29 GeV electron–positron collisions at the PEP storage ring at SLAC. A time projection chamber consists of a gas-filled detection volume in an

neg: Map projection typically employ a transverse Mercator or close variant for large-scale maps in order to preserve conformality and low variation in scale over small areas. For smaller-scale maps, such as those spanning continents or the entire world, many projections are in common use according to their fitness for the purpose, such as Winkel tripel, Robinson and Mollweide. Reference maps of the world often appear on compromise projections. Due to distortions inherent in any map of the world, the choice of projection becomes largely one of aesthetics. Thematic maps normally require an equal area projection so that phenomena per unit area are

neg: Psychological projection the unknown, there we project an archetypal image". Psychological projection is one of the medical explanations of bewitchment used to explain the behavior of the afflicted children at Salem in 1692. The historian John Demos asserts that the symptoms of bewitchment experienced by the afflicted girls were due to the girls undergoing psychological projection of repressed aggression. Jung wrote, "All projections provoke counter-projection when the object is unconscious of the quality projected upon it by the subject." Thus, what is unconscious in the recipient will be projected back onto the projector, precipitating a form of mutual acting out. In a

neg: Psychological projection an element that already existed on a small scale in the other person. (The related defence of projective identification differs from projection in that there the other person is expected to become identified with the impulse or desire projected outside, so that the self maintains a connection with what is projected, in contrast to the total repudiation of projection proper.) Melanie Klein saw the projection of good parts of the self as leading potentially to over-idealisation of the object. Equally, it may be one's conscience that is projected, in an attempt to escape its control: a more benign version of

neg: Exponential dichotomy constants α and β allow us to define the "spectral window" of the equilibrium point, (−α, β). The matrix "P" is a projection onto the stable subspace and "I" − "P" is a projection onto the unstable subspace. What the exponential dichotomy says is that the norm of the projection onto the stable subspace of any orbit in the system decays exponentially as "t" → ∞ and the norm of the projection onto the unstable subspace of any orbit decays exponentially as "t" → −∞, and furthermore that the stable and unstable subspaces are conjugate (because formula_4). An equilibrium point

neg: Interactive planning of the Organization provides a description of what the organization does. It can be illustrated by flow charts; identification of rules and customs practiced by the organization; disclosure of internal and external conflicts which affect organization performance; and identifying trends that could affect organization performance if it continued on the same path. Once the State of the Organization is made, the next critical step in formulating the mess starts with setting up a reference projection. A reference projection is a projection of the future of the organization based on two false assumptions: The reference projection should be formed based on

neg: Projection (relational algebra) names, and only know what ages are present. In addition, projection can be used to modify an attribute's value: if relation R has attributes a, b, and c, and b is a number, then formula_5 will return a relation nearly the same as R, but with all values for 'b' shrunk by half. The closely related concept in set theory (see: projection (set theory)) differs from that of relational algebra in that, in set theory, one projects onto ordered components, not onto attributes. For instance, projecting formula_6 onto the second component yields 7. Projection is relational algebra's counterpart of existential

neg: Perspective projection distortion is apparently distorted (foreshortened): to the eye, parallel lines appear to intersect (like the distant edges of a path or road), whereas in "un−distorted" nature, they do not. One of the first uses of perspective was in Giotto’s "Jesus Before the Caïf", more than 100 years before Filippo Brunelleschi’s perspectival demonstrations galvanized the proper widespread use of convergent perspective of the Renaissance. "Artificial perspective projection" was the name given by Leonardo da Vinci to what today is called "classical perspective projection" and, as noted above, is the result of a geometric protocol. 'Artificial perspective projection' is used here rather than

neg: TaskJuggler assignment being generated. TaskJuggler presently contains (as of version 2.3.0) no provision for generating a minimal schedule change from an existing schedule projection based on a hypothetical input, such as "what if I assign Bob for four hours to the documentation task?". One can, however, feed desired elements from one projection output back into the TJP as additional constraints as fixed assumptions relative to further refinements of the schedule projection. Iterative constraint refinement is a powerful technique, but lacks the immediacy of incremental recalculation in a spreadsheet when used in a similar capacity as a financial projection tool. The TaskJuggler

neg: Orthographic projection Orthographic projection Orthographic projection (sometimes orthogonal projection), is a means of representing three-dimensional objects in two dimensions. It is a form of parallel projection, in which all the projection lines are orthogonal to the projection plane, resulting in every plane of the scene appearing in affine transformation on the viewing surface. The obverse of an orthographic projection is an oblique projection, which is a parallel projection in which the projection lines are "not" orthogonal to the projection plane. The term "orthographic" is sometimes reserved specifically for depictions of objects where the principal axes or planes of the object are also

neg: Equirectangular projection Equirectangular projection The equirectangular projection (also called the equidistant cylindrical projection, geographic projection, or la carte parallélogrammatique projection, and which includes the special case of the plate carrée projection or geographic projection) is a simple map projection attributed to Marinus of Tyre, who Ptolemy claims invented the projection about AD 100. The projection maps meridians to vertical straight lines of constant spacing (for meridional intervals of constant spacing), and circles of latitude to horizontal straight lines of constant spacing (for constant intervals of parallels). The projection is neither equal area nor conformal. Because of the distortions introduced by this projection,

neg: Group C nerve fiber This may result in abnormal sensory function or neuropathic pain. Remak bundles are thought to release certain trophic factors that promote the regeneration of the damaged axons. C fibers synapse to second-order projection neurons in the spinal cord at the upper laminae of the dorsal horn in the substantia gelatinosa. The second-order projection neurons are of the wide dynamic range (WDR) type, which receive input from both nociceptive terminals as well as myelinated A-type fibers. There are three types of second order projection neurons in the spinothalamic tract: wide dynamic range (WDR), high threshold (HT), and low threshold (LT). These

neg: True length all edges would demonstrate true length. Examples of views in which all edges have true length are nets. True length In geometry, true length is any distance between points that is not foreshortened by the view type. In a three-dimensional Euclidean space, lines with true length are parallel to the projection plane. For example, in a top view of a pyramid, which is an orthographic projection, the base edges (which are parallel to the projection plane) have true length, whereas the remaining edges in this view are not true lengths. The same is true with an orthographic side view of

neg: Plan (drawing) or projections is crucial to the legibility of plans. Each projection is achieved by assuming a vantage point from which to see the place or object, and a type of projection. These projection types are: There is no universal standard for sheet order, however the following describes a common approach: Where additional systems are complex and require many details for installation, specialized additional plan drawings may be used, such as: Plan (drawing) Plans are a set of drawings or two-dimensional diagrams used to describe a place or object, or to communicate building or fabrication instructions. Usually plans are drawn or

neg: Christopher Tyler Physics, in which the Schrödingerian superposition of states is expressed as an inherent property of the conception of probability held by the conscious investigator rather than a property of the physical system per se [FoM paper]. While this retains the role of consciousness in the quantum framework, by casting the superposition solely as a property of the neural conceptualization, it resolves many of the paradoxes of Quantum Physics within the domain of classical physics and avoids their antiscientific illogicality. The octant projection or octants projection is a type of projection proposed for the first time, in 1508, by Leonardo da

neg: Television set tuner, which makes them a type of TV display. It was originally developed in 1987 by Larry Hornbeck of Texas Instruments. While the DLP imaging device was invented by Texas Instruments, the first DLP based projector was introduced by Digital Projection Ltd in 1997. Digital Projection and Texas Instruments were both awarded Emmy Awards in 1998 for the DLP projector technology. DLP is used in a variety of display applications from traditional static displays to interactive displays and also non-traditional embedded applications including medical, security, and industrial uses. DLP technology is used in DLP front projectors (standalone projection units for

neg: Large-screen television technology be a suitably prepared wall, and the projector is placed in front of the screen. The setup of a rear-projection television is in some ways similar to that of a traditional television, the projector is contained inside the television box and projects the image from behind the screen. The following are different types of rear-projection televisions, which differ based on the type of projector and how the image (before projection) is created: In Laser Phosphor Display technology, first demonstrated in June 2010 at InfoComm, the image is provided by the use of lasers, which are located on the back of

neg: Behrmann projection in the Behrmann projection according to distance from the standard parallels. This projection is not equidistant. Behrmann projection The Behrmann projection is a cylindrical map projection described by Walter Behrmann in 1910. It is a member of the cylindrical equal-area projection family. Members of the family differ by their standard parallels, which are parallels along which the projection has no distortion. In the case of the Behrmann projection, the standard parallels are 30°N and 30°S. The projection shares many characteristics with other members of the family such as the Lambert cylindrical equal-area projection, whose standard parallel is the equator, and

neg: Von Neumann algebra the trace of a non-zero projection is non-zero and the trace of a projection is infinite if and only if the projection is infinite. Such a trace is unique up to rescaling. For factors that are separable or finite, two projections are equivalent if and only if they have the same trace. The type of a factor can be read off from the possible values of this trace as follows: If a von Neumann algebra acts on a Hilbert space containing a norm 1 vector "v", then the functional "a" → ("av","v") is a normal state. This construction can be

neg: Bonne projection Equator), and the Werner projection, when "φ" is 90° (i.e. the North or South Pole). 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. Bonne projection The Bonne projection is a pseudoconical equal-area map projection, sometimes called a dépôt de la guerre, modified Flamsteed, 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. Both Sylvano

neg: Guyou hemisphere-in-a-square projection Guyou hemisphere-in-a-square projection The Guyou hemisphere-in-a-square projection is a conformal map projection for the hemisphere. It is an oblique aspect of the Peirce quincuncial projection. The projection was developed by Émile Guyou of France in 1887. The projection can be computed as an oblique aspect of the Peirce quincuncial projection by rotating the axis 45 degrees. It can also be computed by rotating the coordinates −45 degrees before computing the stereographic projection; this projection is then remapped into a square whose coordinates are then rotated 45 degrees. The projection is conformal except for the four corners of each hemisphere’s square.

neg: Gall stereographic projection Gall stereographic projection The Gall stereographic projection, presented by James Gall in 1855, is a cylindrical projection. It is neither equal-area nor conformal but instead tries to balance the distortion inherent in any projection. The projection is conventionally defined as: where "λ" is the longitude from the central meridian in degrees, "φ" is the latitude, and "R" is the radius of the globe used as the model of the earth for projection. It is a perspective projection if the point of projection is allowed to vary with longitude: the point of projection being on the equator on the opposite side

neg: Parallel projection Parallel projection A parallel projection is a projection of an object in three-dimensional space onto a fixed plane, known as the "projection plane" or "image plane", where the "rays", known as "lines of sight" or "projection lines", are parallel to each other. It is a basic tool in descriptive geometry. The projection is called "orthographic" if the rays are perpendicular (orthogonal) to the image plane, and "oblique" or "skew" if they are not. A parallel projection is a particular case of "projection" in mathematics and "graphical projection" in technical drawing. Parallel projections can be seen as the limit of a

neg: Mollweide projection Mollweide projection The Mollweide projection is an equal-area, pseudocylindrical map projection generally used for global maps of the world or night sky. 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 (or Carl) Brandan Mollweide (1774–1825) of Leipzig in 1805. It was reinvented and popularized in 1857 by Jacques Babinet, who gave it the

neg: Mollweide projection "x" and "y". Mollweide projection The Mollweide projection is an equal-area, pseudocylindrical map projection generally used for global maps of the world or night sky. 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 (or Carl) Brandan Mollweide (1774–1825) of Leipzig in 1805. It was reinvented and popularized in 1857 by Jacques Babinet, who

neg: Compositing seats of the Roman Colosseum were actually built, while the upper galleries (complete with moving spectators) were computer graphics, composited onto the image above the physical set. For motion pictures originally recorded on film, high-quality video conversions called "digital intermediates" enable compositing and other operations of computerized post production. Digital compositing is a type of matting, and one of four basic compositing methods. The others are physical compositing, multiple exposure, and background projection, a method which utilizes both front projection and rear projection. In physical compositing the separate parts of the image are placed together in the photographic frame and

neg: Geographic coordinate system dependent on the particular location at which the map is projected. The set of parameters can vary based on type of project and the conventions chosen for the projection. For the transverse Mercator projection used in UTM, the parameters associated are the latitude and longitude of the natural origin, the false northing and false easting, and an overall scale factor. Given the parameters associated with particular location or grin, the projection formulas for the transverse Mercator are a complex mix of algebraic and trigonometric functions. The Universal Transverse Mercator (UTM) and Universal Polar Stereographic (UPS) coordinate systems both use a

neg: Torbal was quickly followed by a series of scales based upon the same principle. This scale was an optical projection type that was intended for both laboratory and industrial use. The first decade was a digital weight loader which was used to bring the beam close enough to a null position so that the next three digits could be read directly off of an optical projection screen. Many people claimed that the optical portion of the scale was accurate to four places, however, reading a linear dial projection to four places without a vermier is a real feat. In this scale

neg: Projection keyboard simply being used to type, some laser keyboard systems can function as a virtual mouse or even as a virtual piano, such as the crowd-funded iKeybo. Projection keyboard A projection keyboard is a form of computer input device whereby the image of a virtual keyboard is projected onto a surface: when a user touches the surface covered by an image of a key, the device records the corresponding keystroke. Some connect to Bluetooth devices, including many of the latest smartphone, tablet, and mini-PC devices with Android, iOS or Windows platform. An optical virtual keyboard was invented and patented by IBM

neg: Movie projector black. Usually there's an audio POP that play 48 frames (2 seconds at 24 frame per second) before first frame of action (FFOA) that helps to sync audio and video during printing processes or postproduction. Most motion picture lenses are of the spherical variety. Spherical lenses do not distort the image intentionally. Used alone for standard and cropped wide screen projection, and in conjunction with an anamorphic adapter for anamorphic wide screen projection, the spherical lens is the most common and versatile projection lens type. Anamorphic filming uses only special lenses, and requires no other modifications to the camera, projector

neg: Gall–Peters projection Gall–Peters projection The Gall–Peters projection is a rectangular map projection that maps all areas such that they have the correct sizes relative to each other. Like any equal-area projection, it achieves this goal by distorting most shapes. The projection is a particular example of the 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 is credited with describing the projection in 1855 at a science convention. He published a paper on it in 1885. Peters brought the projection to

neg: Behrmann projection Behrmann projection The Behrmann projection is a cylindrical map projection described by Walter Behrmann in 1910. It is a member of the cylindrical equal-area projection family. Members of the family differ by their standard parallels, which are parallels along which the projection has no distortion. In the case of the Behrmann projection, the standard parallels are 30°N and 30°S. The projection shares many characteristics with other members of the family such as the Lambert cylindrical equal-area projection, whose standard parallel is the equator, and the Gall–Peters projection, whose standard parallels are 45°N and 45°S. While equal-area, distortion of shape increases

neg: Orthographic projection in cartography orthographic map projection. In a wide sense, all projections with the point of perspective at infinity (and therefore parallel projecting lines) are considered as orthographic, regardless of the surface onto which they are projected. These kinds of projections distort angles and areas close to the poles. An example of an orthographic projection onto a cylinder is the Lambert cylindrical equal-area projection. Orthographic projection in cartography The use of orthographic projection in cartography dates back to antiquity. Like the stereographic projection and gnomonic projection, orthographic projection is a perspective (or azimuthal) projection, in which the sphere is projected onto a tangent

neg: Guyou hemisphere-in-a-square projection Like other conformal polygonal projections, the Guyou is a Schwarz–Christoffel mapping. Its properties are very similar to those of the Peirce quincuncial: Guyou hemisphere-in-a-square projection The Guyou hemisphere-in-a-square projection is a conformal map projection for the hemisphere. It is an oblique aspect of the Peirce quincuncial projection. The projection was developed by Émile Guyou of France in 1887. The projection can be computed as an oblique aspect of the Peirce quincuncial projection by rotating the axis 45 degrees. It can also be computed by rotating the coordinates −45 degrees before computing the stereographic projection; this projection is then remapped into

neg: Winkel tripel projection 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 "Tripel" (German for "triple") refers to Winkel's goal of minimizing three kinds of distortion: area, direction, and distance. where "λ" is the longitude minus that of the central meridian of the projection, "φ" is the latitude, "φ" is the standard parallel for the equirectangular projection, sinc is

neg: Stereographic projection equal-area fisheye to a stereographic projection. The stereographic projection has been used to map spherical panoramas. This results in effects known as a "little planet" (when the center of projection is the nadir) and a "tube" (when the center of projection is the zenith). The popularity of using stereographic projections to map panoramas over other azimuthal projections is attributed to the shape preservation that results from the conformality of the projection. Stereographic projection In geometry, the stereographic projection is a particular mapping (function) that projects a sphere onto a plane. The projection is defined on the entire sphere, except at

neg: Craig retroazimuthal projection longitude "λ" of the fixed location of interest, the projection is defined by: But when "λ" − "λ" = 0, "y" above is undefined, so instead use the ratio's continuous completion: Craig retroazimuthal projection The Craig retroazimuthal map projection was created by James Ireland Craig in 1909. It is a modified cylindrical projection. As a retroazimuthal projection, it preserves directions from everywhere to one location of interest that is configured during construction of the projection. The projection is sometimes known as the Mecca projection because Craig, who had worked in Egypt as a cartographer, created it to help Muslims find

neg: Orthographic projection parallel with the projection plane, but these are better known as "multiview projections". Furthermore, when the principal planes or axes of an object in an orthographic projection are "not" parallel with the projection plane, but are rather tilted to reveal multiple sides of the object, the projection is called an "axonometric projection". Sub-types of "multiview projection" include "plans", "elevations" and "sections". Sub-types of "axonometric projection" include "isometric", "dimetric" and "trimetric projections". A lens providing an orthographic projection is known as an object-space telecentric lens. A simple orthographic projection onto the plane "z" = 0 can be defined by the following

neg: Orthographic projection in cartography Orthographic projection in cartography The use of orthographic projection in cartography dates back to antiquity. Like the stereographic projection and gnomonic projection, orthographic projection is a perspective (or azimuthal) projection, in which the sphere is projected onto a tangent plane or secant plane. The "point of perspective" for the orthographic projection is at infinite distance. It depicts a hemisphere of the globe as it appears from outer space, where the horizon is a great circle. The shapes and areas are distorted, particularly near the edges. The orthographic projection has been known since antiquity, with its cartographic uses being well documented.