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Vanishing Point
A vanishing point is a point (geometry), point on the projection plane, image plane of a graphical perspective, perspective rendering where the two-dimensional perspective projections of parallel (geometry), parallel lines in three-dimensional space appear to converge. When the set of parallel lines is perpendicular to a picture plane, the construction is known as one-point perspective, and their vanishing point corresponds to the station point, oculus, or "eye point", from which the image should be viewed for correct perspective geometry.Kirsti Andersen (2007) ''Geometry of an Art'', p. xxx, Springer, Traditional linear drawings use objects with one to three sets of parallels, defining one to three vanishing points. Italian Renaissance humanism, humanist polymath and architect Leon Battista Alberti first introduced the concept in his treatise on perspective in art, ''De pictura'', written in 1435. Straight Track geometry, railroad tracks are a familiar modern example. Vector ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intersection (set Theory)
In set theory, the intersection of two Set (mathematics), sets A and B, denoted by A \cap B, is the set containing all elements of A that also belong to B or equivalently, all elements of B that also belong to A. Notation and terminology Intersection is written using the symbol "\cap" between the terms; that is, in infix notation. For example: \\cap\=\ \\cap\=\varnothing \Z\cap\N=\N \\cap\N=\ The intersection of more than two sets (generalized intersection) can be written as: \bigcap_^n A_i which is similar to capital-sigma notation. For an explanation of the symbols used in this article, refer to the table of mathematical symbols. Definition The intersection of two sets A and B, denoted by A \cap B, is the set of all objects that are members of both the sets A and B. In symbols: A \cap B = \. That is, x is an element of the intersection A \cap B if and only if x is both an element of A and an element of B. For example: * The intersection of the sets and is . * The n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sistine Chapel
The Sistine Chapel ( ; ; ) is a chapel in the Apostolic Palace, the pope's official residence in Vatican City. Originally known as the ''Cappella Magna'' ('Great Chapel'), it takes its name from Pope Sixtus IV, who had it built between 1473 and 1481. Since that time, it has served as a place of both religious and functionary papal activity. Today, it is the site of the papal conclave, the process by which a new pope is selected. The chapel's fame lies mainly in the frescoes that decorate its interior, most particularly the Sistine Chapel ceiling and ''The Last Judgment (Michelangelo), The Last Judgment'', both by Michelangelo. During the reign of Sixtus IV, a team of Italian Renaissance painting, Renaissance painters including Sandro Botticelli, Pietro Perugino, Pinturicchio, Domenico Ghirlandaio and Cosimo Rosselli, created a series of frescoes depicting the ''Life of Moses'' and the ''Life of Christ'', offset by papal portraits above and ''trompe-l'œil'' drapery below. They w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fresco
Fresco ( or frescoes) is a technique of mural painting executed upon freshly laid ("wet") lime plaster. Water is used as the vehicle for the dry-powder pigment to merge with the plaster, and with the setting of the plaster, the painting becomes an integral part of the wall. The word ''fresco'' () is derived from the Italian adjective ''fresco'' meaning "fresh", and may thus be contrasted with fresco-secco or secco mural painting techniques, which are applied to dried plaster, to supplement painting in fresco. The fresco technique has been employed since antiquity and is closely associated with Italian Renaissance painting. The word ''fresco'' is commonly and inaccurately used in English to refer to any wall painting regardless of the plaster technology or binding medium. This, in part, contributes to a misconception that the most geographically and temporally common wall painting technology was the painting into wet lime plaster. Even in apparently '' buon fresco'' technology ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Delivery Of The Keys (Perugino)
The ''Delivery of the Keys'', or ''Christ Giving the Keys to Saint Peter'' is a fresco by the Italian Renaissance painter Pietro Perugino which was produced in 1481–1482 and is located in the Sistine Chapel, Rome. History The commission of the work originated in 1480, when Perugino was decorating a chapel in the Old St. Peter's Basilica in Rome. Pope Sixtus IV was pleased by his work, and decided to commission him also the decoration of the new Chapel he had built in the Vatican Palace. Due to the size of the work, Perugino was later joined by a group of painters from Florence, including Botticelli, Ghirlandaio and others. While the work was still being created, a visit from Alfonso II of Naples resulted in his addition to the far left of the group of foreground figures. To balance out the image, an apostle was added above St. Peter. Description The scene, part of the series of the ''Stories of Jesus'' on the chapel's northern wall, is a reference to Matthew 16 in which Je ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pietro Perugino
Pietro Perugino ( ; ; born Pietro Vannucci or Pietro Vanucci; – 1523), an Italian Renaissance painter of the Umbrian school, developed some of the qualities that found classic expression in the High Renaissance. Raphael became his most famous pupil. Early years Pietro Vannucci was born in Città della Pieve, Umbria, the son of Cristoforo Maria Vannucci. His nickname characterizes him as from Perugia, the chief city of Umbria. Scholars continue to dispute the socioeconomic status of the Vannucci family. While certain academics maintain that Vannucci worked his way out of poverty, others argue that his family was among the wealthiest in the town. His exact date of birth is not known, but based on his age at death that was mentioned by Vasari and Giovanni Santi, it is believed that he was born between 1446 and 1452. Pietro most likely began studying painting in local workshops in Perugia such as those of Bartolomeo Caporali or Fiorenzo di Lorenzo. The date of the first ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reverse Perspective
Reverse perspective, also called inverse perspective,. inverted perspective, divergent perspective, or Byzantine perspective, is a form of perspective (graphical), perspective drawing where the objects depicted in a scene are placed between the projective point and the viewing plane. Objects further away from the viewing plane are drawn as larger, and closer objects are drawn as smaller, in contrast to the more conventional linear perspective where closer objects appear larger.. Lines that are parallel in three-dimensional space are drawn as diverging against the horizon, rather than converging as they do in linear perspective. Technically, the vanishing points are placed outside the painting with the illusion that they are "in front of" the painting. The name Byzantine perspective comes from the use of this perspective in Byzantine art, Byzantine and Russian Orthodox Church, Russian Orthodox icons; it is also found in the art of many pre-Renaissance cultures, and was sometimes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Curvilinear Perspective
Curvilinear perspective, also five-point perspective, is a graphical projection used to draw 3D objects on 2D surfaces, for which (straight) lines on the 3D object are projected to curves on the 2D surface that are typically not straight (hence the qualifier "curvilinear"). 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Horizon
The horizon is the apparent curve that separates the surface of a celestial body from its sky when viewed from the perspective of an observer on or near the surface of the relevant body. This curve divides all viewing directions based on whether it intersects the relevant body's surface or not. The ''true horizon'' is a theoretical line, which can only be observed to any degree of accuracy when it lies along a relatively smooth surface such as that of Earth's oceans. At many locations, this line is obscured by terrain, and on Earth it can also be obscured by life forms such as trees and/or human constructs such as buildings. The resulting intersection of such obstructions with the sky is called the ''visible horizon''. On Earth, when looking at a sea from a shore, the part of the sea closest to the horizon is called the offing. Pronounced, "Hor-I-zon". The true horizon surrounds the observer and it is typically assumed to be a circle, drawn on the surface of a perfectly sph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sightline
The line of sight, also known as visual axis or sightline (also sight line), is an imaginary line between a viewer/observation, observer/wikt:spectator, spectator's eye(s) and a subject of interest, or their relative direction (geometry), relative direction. The subject may be any definable object taken note of or to be taken note of by the observer, at any distance more than least distance of distinct vision. In optics, refraction of a ray due to use of lenses can cause Distortion (optics), distortion. Shadows, patterns and movement can also influence line of sight interpretation (as in optical illusions). The term "line" typically presumes that the light by which the observed object is seen travels as a straight ray (optics), ray, which is sometimes not the case as light can take a curved/angulated path when reflection (physics), reflected from a mirror, refracted by a lens or density changes in the optical medium, traversed media, or gravitational lens, deflected by a gravitatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Point At Infinity
In geometry, a point at infinity or ideal point is an idealized limiting point at the "end" of each line. In the case of an affine plane (including the Euclidean plane), there is one ideal point for each pencil of parallel lines of the plane. Adjoining these points produces a projective plane, in which no point can be distinguished, if we "forget" which points were added. This holds for a geometry over any field, and more generally over any division ring. In the real case, a point at infinity completes a line into a topologically closed curve. In higher dimensions, all the points at infinity form a projective subspace of one dimension less than that of the whole projective space to which they belong. A point at infinity can also be added to the complex line (which may be thought of as the complex plane), thereby turning it into a closed surface known as the complex projective line, CP1, also called the Riemann sphere (when complex numbers are mapped to each point). In the c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Projective Geometry
In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared to elementary Euclidean geometry, projective geometry has a different setting (''projective space'') and a selective set of basic geometric concepts. The basic intuitions are that projective space has more points than Euclidean space, for a given dimension, and that geometric transformations are permitted that transform the extra points (called "Point at infinity, points at infinity") to Euclidean points, and vice versa. Properties meaningful for projective geometry are respected by this new idea of transformation, which is more radical in its effects than can be expressed by a transformation matrix and translation (geometry), translations (the affine transformations). The first issue for geometers is what kind of geometry is adequate for a novel situation. Unlike in Euclidean geometry, the concept of an angle does not ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
