|
Projection
Projection or projections may refer to: Physics * Projection (physics), the action/process of light, heat, or sound reflecting from a surface to another in a different direction * The display of images by a projector Optics, graphics, and cartography * Map projection, reducing the surface of a three-dimensional planet to a flat map * Graphical projection, the production of a two-dimensional image of a three-dimensional object Chemistry * Fischer projection, a two-dimensional representation of a three-dimensional organic molecule * Haworth projection, a way of writing a structural formula to represent the cyclic structure of monosaccharides * Natta projection, a way to depict molecules with complete stereochemistry in two dimensions in a skeletal formula * Newman projection, a visual representation of a chemical bond from front to back Mathematics * Projection (mathematics), any of several different types of geometrical mappings ** Projection (linear algebra), a linear t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Map Projection
In cartography, a map projection is any of a broad set of Transformation (function) , transformations employed to represent the curved two-dimensional Surface (mathematics), surface of a globe on a Plane (mathematics), plane. In a map projection, coordinates, often expressed as latitude and longitude, of locations from the surface of the globe are transformed to coordinates on a plane. Projection is a necessary step in creating a two-dimensional map and is one of the essential elements of cartography. All projections of a sphere on a plane necessarily distort the surface in some way. Depending on the purpose of the map, some distortions are acceptable and others are not; therefore, different map projections exist in order to preserve some properties of the sphere-like body at the expense of other properties. The study of map projections is primarily about the characterization of their distortions. There is no limit to the number of possible map projections. More generally, proje ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
3D Projection
A 3D projection (or graphical projection) is a Design, design technique used to display a three-dimensional (3D) object on a two-dimensional (2D) surface. These projections rely on perspective (graphical), visual perspective and aspect analysis to Projection mapping, project a complex object for viewing capability on a simpler plane. 3D projections use the Primary Qualities, primary qualities of an object's basic shape to create a map of points, that are then connected to one another to create a visual element. The result is a graphic that contains conceptual properties to interpret the figure or image as not actually flat (2D), but rather, as a solid object (3D) being viewed on a 2D display. 3D objects are largely displayed on two-dimensional mediums (such as paper and computer monitors). As such, graphical projections are a commonly used design element; notably, in engineering drawing, technical drawing, drafting, and computer graphics. Projections can be calculated through ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graphical Projection
A 3D projection (or graphical projection) is a design technique used to display a three-dimensional (3D) object on a two-dimensional (2D) surface. These projections rely on visual perspective and aspect analysis to project a complex object for viewing capability on a simpler plane. 3D projections use the primary qualities of an object's basic shape to create a map of points, that are then connected to one another to create a visual element. The result is a graphic that contains conceptual properties to interpret the figure or image as not actually flat (2D), but rather, as a solid object (3D) being viewed on a 2D display. 3D objects are largely displayed on two-dimensional mediums (such as paper and computer monitors). As such, graphical projections are a commonly used design element; notably, in engineering drawing, drafting, and computer graphics. Projections can be calculated through employment of mathematical analysis and formulae, or by using various geometric and op ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Projection (linear Algebra)
In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself (an endomorphism) such that P\circ P=P. That is, whenever P is applied twice to any vector, it gives the same result as if it were applied once (i.e. P is idempotent). It leaves its image unchanged. This definition of "projection" formalizes and generalizes the idea of graphical projection. One can also consider the effect of a projection on a geometrical object by examining the effect of the projection on points in the object. Definitions A projection on a vector space V is a linear operator P\colon V \to V such that P^2 = P. When V has an inner product and is complete, i.e. when V is a Hilbert space, the concept of orthogonality can be used. A projection P on a Hilbert space V is called an orthogonal projection if it satisfies \langle P \mathbf x, \mathbf y \rangle = \langle \mathbf x, P \mathbf y \rangle for all \mathbf x, \mathbf y \in V. A projecti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Social Projection
In social psychology, social projection is the psychological process through which an individual expects behaviors or attitudes of others to be similar to their own. Social projection occurs between individuals as well as across ingroup and outgroup contexts in a variety of domains. Research has shown that aspects of social categorization affect the extent to which social projection occurs. Cognitive and motivational approaches have been used to understand the psychological underpinnings of social projection as a phenomenon. Cognitive approaches emphasize social projection as a heuristic, while motivational approaches contextualize social projection as a means to feel connected to others. In contemporary research on social projection, researchers work to further distinguish between the effects of social projection and self-stereotyping on the individual’s perception of others. History The term social projection was first coined by Floyd Allport in 1924. The idea refers to th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Projection (mathematics)
In mathematics, a projection is an idempotent mapping of a set (or other mathematical structure) into a subset (or sub-structure). In this case, idempotent means that projecting twice is the same as projecting once. The restriction to a subspace of a projection is also called a ''projection'', even if the idempotence property is lost. An everyday example of a projection is the casting of shadows onto a plane (sheet of paper): the projection of a point is its shadow on the sheet of paper, and the projection (shadow) of a point on the sheet of paper is that point itself (idempotency). The shadow of a three-dimensional sphere is a disk. Originally, the notion of projection was introduced in Euclidean geometry to denote the projection of the three-dimensional Euclidean space onto a plane in it, like the shadow example. The two main projections of this kind are: * The projection from a point onto a plane or central projection: If is a point, called the center of projection, then t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Projection (physics)
The vector projection (also known as the vector component or vector resolution) of a Vector (geometry), vector on (or onto) a nonzero vector is the orthogonal projection of onto a straight line parallel to . The projection of onto is often written as \operatorname_\mathbf \mathbf or . The vector component or vector resolute of perpendicular to , sometimes also called the vector rejection of ''from'' (denoted \operatorname_ \mathbf or ), is the orthogonal projection of onto the plane (geometry), plane (or, in general, hyperplane) that is orthogonal to . Since both \operatorname_ \mathbf and \operatorname_ \mathbf are vectors, and their sum is equal to , the rejection of from is given by: \operatorname_ \mathbf = \mathbf - \operatorname_ \mathbf. To simplify notation, this article defines \mathbf_1 := \operatorname_ \mathbf and \mathbf_2 := \operatorname_ \mathbf. Thus, the vector \mathbf_1 is parallel to \mathbf, the vector \mathbf_2 is orthogonal to \mathbf, and \ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vector Projection
The vector projection (also known as the vector component or vector resolution) of a vector on (or onto) a nonzero vector is the orthogonal projection of onto a straight line parallel to . The projection of onto is often written as \operatorname_\mathbf \mathbf or . The vector component or vector resolute of perpendicular to , sometimes also called the vector rejection of ''from'' (denoted \operatorname_ \mathbf or ), is the orthogonal projection of onto the plane (or, in general, hyperplane) that is orthogonal to . Since both \operatorname_ \mathbf and \operatorname_ \mathbf are vectors, and their sum is equal to , the rejection of from is given by: \operatorname_ \mathbf = \mathbf - \operatorname_ \mathbf. To simplify notation, this article defines \mathbf_1 := \operatorname_ \mathbf and \mathbf_2 := \operatorname_ \mathbf. Thus, the vector \mathbf_1 is parallel to \mathbf, the vector \mathbf_2 is orthogonal to \mathbf, and \mathbf = \mathbf_1 + \mathbf_2. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Power Projection
Power projection (or force projection or strength projection) in international relations is the capacity of a state to deploy and sustain forces outside its territory. The ability of a state to project its power into an area may serve as an effective diplomatic lever, influencing the decision-making processes and acting as a potential deterrent on other states' behavior. Pravda (Правда(17 Mar 2022) Zelenskyy explained the essence of the new military alliance U24 from Zelenskyy's night address verbatim: "I addressed the United States and all responsible states with a proposition to create a new U24 union: a new union that will ensure that each aggressor receives a coordinated world response quickly, effectively, and immediately - not in weeks, months, years, but for the first 24 hours after the attack." "We can no longer trust existing institutions. We cannot expect bureaucrats in international organisations to change fast enough, so we must look for new guar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fischer Projection
In chemistry, the Fischer projection, devised by Emil Fischer in 1891, is a two-dimensional representation of a three-dimensional organic molecule by projection. Fischer projections were originally proposed for the depiction of carbohydrates and used by chemists, particularly in organic chemistry and biochemistry. The use of Fischer projections in non-carbohydrates is discouraged, as such drawings are ambiguous and easily confused with other types of drawing. The main purpose of Fischer projections is to show the chirality of a molecule and to distinguish between a pair of enantiomers. Some notable uses include drawing sugars and depicting isomers. Conventions All bonds are depicted as horizontal or vertical lines. The carbon chain is depicted vertically, with carbon atoms sometimes not shown and represented by the center of crossing lines (see figure below). The orientation of the carbon chain is so that the first carbon (C1) is at the top. In an aldose, C1 is the carbon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Psychological Projection
Psychological projection is a defence mechanism of alterity concerning "inside" ''content'' mistaken to be coming from the "outside" Other. It forms the basis of empathy by the projection of personal experiences to understand someone else's subjective world. In its malignant forms, it is a defense mechanism in which the ego defends itself against disowned and highly negative parts of the self by denying their existence in themselves and attributing them to others, breeding misunderstanding and causing interpersonal damage. Projection incorporates blame shifting and can manifest as shame dumping. Projection has been described as an early phase of introjection. Historical precursors A prominent precursor in the formulation of the projection principle was Giambattista Vico. In 1841, Ludwig Feuerbach was the first enlightenment thinker to employ this concept as the basis for a systematic critique of religion. The Babylonian Talmud (500 AD) notes the human tendency toward ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Newman Projection
A Newman projection is a drawing that helps visualize the 3-dimensional structure of a molecule. This projection most commonly sights down a carbon-carbon bond, making it a very useful way to visualize the stereochemistry of alkanes. A Newman projection visualizes the Conformational isomerism, conformation of a chemical bond from front to back, with the front atom represented by the intersection of three lines (a dot) and the back atom as a circle. The front 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 projection is named after American chemist Melvin Spencer Newman, who introduced it in 1952 as a partial replacement for Fischer projections, which are unable to represent conformations and thus conformers properly.Newman, MS. ''Record. Chem. Progr. (Kresge-Hooker Sci. Lib.) 1952,'' 13'', 111'' This diagram style is an alternative to a sa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
