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Curvilinear Perspective
Curvilinear perspective, also five-point perspective, is a graphical projection used to draw 3D objects on 2D surfaces. It was formally codified in 1968 by the artists and art historians André Barre and Albert Flocon in the book ''La Perspective curviligne'',Albert Flocon and André Barre, ''La Perspective curviligne'', Flammarion, Éditeur, Paris, 1968 which was translated into English in 1987 as ''Curvilinear Perspective: From Visual Space to the Constructed Image'' and published by the University of California Press.Albert Flocon and André Barre, ''Curvilinear Perspective: From Visual Space to the Constructed Image'', (Robert Hansen, translator), University of California Press, Berkeley and Los Angeles, California, 1987 Curvilinear perspective is sometimes colloquially called fisheye perspective, by analogy to a fisheye lens. History Earlier, less mathematically precise versions can be seen in the work of the miniaturist Jean Fouquet. Leonardo da Vinci in a lost notebook sp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Barrel Distortion
In geometric optics, distortion is a deviation from rectilinear projection; a projection in which straight lines in a scene remain straight in an image. It is a form of aberration in optical systems, optical aberration. Radial distortion Although distortion can be irregular or follow many patterns, the most commonly encountered distortions are radially symmetric, or approximately so, arising from the symmetry of a photographic lens. These ''radial distortions'' can usually be classified as either ''barrel'' distortions or ''pincushion'' distortions. Mathematically, barrel and pincushion distortion are quadratic function, quadratic, meaning they increase as the ''square'' of distance from the center. In mustache distortion the quartic function, quartic (degree 4) term is significant: in the center, the degree 2 barrel distortion is dominant, while at the edge the degree 4 distortion in the pincushion direction dominates. Other distortions are in principle possible ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carel Fabritius
Carel Pietersz. Fabritius (; bapt. 27 February 1622 – 12 October 1654) was a Dutch painter. He was a pupil of Rembrandt and worked in his studio in Amsterdam. Fabritius, who was a member of the Delft School, developed his own artistic style and experimented with perspective and lighting. Among his works are ''A View of Delft'' (1652; National Gallery, London), '' The Goldfinch'' (1654), and '' The Sentry'' (1654). Biography Carel Pietersz. Fabritius was born in February 1622 in Middenbeemster, a village in the ten-year-old Beemster polder in the Dutch Republic, and was baptized on 27 February of that year.Carel Fabritius . Retrieved ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics And Art
Mathematics and art are related in a variety of ways. Mathematics has itself been described as an art motivated by beauty. Mathematics can be discerned in arts such as music, dance, painting, architecture, sculpture, and textiles. This article focuses, however, on mathematics in the visual arts. Mathematics and art have a long historical relationship. Artists have used mathematics since the 4th century BC when the Greek sculptor Polykleitos wrote his ''Canon'', prescribing proportions conjectured to have been based on the ratio 1: for the ideal male nude. Persistent popular claims have been made for the use of the golden ratio in ancient art and architecture, without reliable evidence. In the Italian Renaissance, Luca Pacioli wrote the influential treatise '' De divina proportione'' (1509), illustrated with woodcuts by Leonardo da Vinci, on the use of the golden ratio in art. Another Italian painter, Piero della Francesca, developed Euclid's ideas on perspective in treat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Perspective
Linear or point-projection perspective (from la, perspicere 'to see through') is one of two types of 3D projection, graphical projection perspective in the graphic arts; the other is parallel projection. Linear perspective is an approximate representation, generally on a flat surface, of an image as it is seen by the eye. Perspective drawing is useful for representing a three-dimensional scene in a two-dimensional medium, like paper. The most characteristic features of linear perspective are that objects appear smaller as their distance from the observer increases, and that they are subject to ''foreshortening'', meaning that an object's dimensions along the line of sight appear shorter than its dimensions across the line of sight. All objects will recede to points in the distance, usually along the horizon line, but also above and below the horizon line depending on the view used. Italian Renaissance painters and architects including Masaccio, Paolo Uccello, Piero della Fran ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perspective Projection Distortion
Perspective may refer to: Vision and mathematics * Perspectivity, the formation of an image in a picture plane of a scene viewed from a fixed point, and its modeling in geometry ** Perspective (graphical), representing the effects of visual perspective in graphic arts ** Aerial perspective, the effect the atmosphere has on the appearance of an object as it is viewed from a distance ** Perspective distortion (photography), the way that viewing a picture from the wrong position gives a perceived distortion ** Perspective (geometry), a relation between geometric figures ** Vue d'optique or perspective view, a genre of etching popular during the second half of the 18th century and into the 19th. Entertainment * ''Perspective'' (P-Model album), 1982 * ''Perspective'' (America album), 1984 * ''Perspective'' (Jason Becker album), 1996 * ''Perspective'' (Lawson album), 2016 * ''Perspective'', a 2010 album by Prague * Perspective (EP), an EP by Tesseract * ''Perspectives'' (album), t ... [...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 that 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 (i.e. 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] |
Convex Mirror
A curved mirror is a mirror with a curved reflecting surface. The surface may be either ''convex'' (bulging outward) or ''concave'' (recessed inward). Most curved mirrors have surfaces that are shaped like part of a sphere, but other shapes are sometimes used in optical devices. The most common non-spherical type are parabolic reflectors, found in optical devices such as reflecting telescopes that need to image distant objects, since spherical mirror systems, like spherical Lens (optics), lenses, suffer from spherical aberration. Distorting mirrors are used for entertainment. They have convex and concave regions that produce deliberately distorted images. They also provide highly magnified or highly diminished (smaller) images when the object is placed at certain distances. Convex mirrors A convex mirror or diverging mirror is a curved mirror in which the reflective surface bulges towards the light source. Convex mirrors reflect light outwards, therefore they are not used to f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cartesian Coordinates
A Cartesian coordinate system (, ) in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length. Each reference coordinate line is called a ''coordinate axis'' or just ''axis'' (plural ''axes'') of the system, and the point where they meet is its ''origin'', at ordered pair . The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two axes, expressed as signed distances from the origin. One can use the same principle to specify the position of any point in three-dimensional space by three Cartesian coordinates, its signed distances to three mutually perpendicular planes (or, equivalently, by its perpendicular projection onto three mutually perpendicular lines). In general, ''n'' Cartesian coordinates (an element of real ''n''-space) specify the point in an ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fisheye Lens
A fisheye lens is an ultra wide-angle lens that produces strong visual distortion intended to create a wide panoramic or hemispherical image. Fisheye lenses achieve extremely wide angles of view, well beyond any rectilinear lens. Instead of producing images with straight lines of perspective ( rectilinear images), fisheye lenses use a special mapping ("distortion"; for example: equisolid angle, see below), which gives images a characteristic convex non-rectilinear appearance. The term ''fisheye'' was coined in 1906 by American physicist and inventor Robert W. Wood based on how a fish would see an ultrawide hemispherical view from beneath the water (a phenomenon known as Snell's window). Their first practical use was in the 1920s for use in meteorology to study cloud formation giving them the name "whole-sky lenses". The angle of view of a fisheye lens is usually between 100 and 180 degrees, although lenses covering up to 280 degrees exist (see below). Their focal lengths dep ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Perspective
Linear or point-projection perspective (from la, perspicere 'to see through') is one of two types of 3D projection, graphical projection perspective in the graphic arts; the other is parallel projection. Linear perspective is an approximate representation, generally on a flat surface, of an image as it is seen by the eye. Perspective drawing is useful for representing a three-dimensional scene in a two-dimensional medium, like paper. The most characteristic features of linear perspective are that objects appear smaller as their distance from the observer increases, and that they are subject to ''foreshortening'', meaning that an object's dimensions along the line of sight appear shorter than its dimensions across the line of sight. All objects will recede to points in the distance, usually along the horizon line, but also above and below the horizon line depending on the view used. Italian Renaissance painters and architects including Masaccio, Paolo Uccello, Piero della Fran ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rectilinear Grid
A regular grid is a tessellation of ''n''-dimensional Euclidean space by congruent parallelotopes (e.g. bricks). Its opposite is irregular grid. Grids of this type appear on graph paper and may be used in finite element analysis, finite volume methods, finite difference methods, and in general for discretization of parameter spaces. Since the derivatives of field variables can be conveniently expressed as finite differences, structured grids mainly appear in finite difference methods. Unstructured grids offer more flexibility than structured grids and hence are very useful in finite element and finite volume methods. Each cell in the grid can be addressed by index (i, j) in two dimensions or (i, j, k) in three dimensions, and each vertex has coordinates (i\cdot dx, j\cdot dy) in 2D or (i\cdot dx, j\cdot dy, k\cdot dz) in 3D for some real numbers ''dx'', ''dy'', and ''dz'' representing the grid spacing. Related grids A Cartesian grid is a special case where the elements are uni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
