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Linear or point-projection perspective (from la, perspicere 'to see through') is one of two types of
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 fo ...
perspective in the
graphic arts A category of fine art, graphic art covers a broad range of visual artistic expression, typically two-dimensional, i.e. produced on a flat surface.
; the other is
parallel projection In three-dimensional geometry, a parallel projection (or axonometric 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 '' li ...
. 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 Three-dimensional space (also: 3D space, 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called ''parameters'') are required to determine the position of an element (i.e., point). This is the informal ...
scene in a
two-dimensional In mathematics, a plane is a Euclidean (flat), two-dimensional surface that extends indefinitely. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space. Planes can arise as s ...
medium, like
paper Paper is a thin sheet material produced by mechanically or chemically processing cellulose fibres derived from wood, rags, grasses or other vegetable sources in water, draining the water through fine mesh leaving the fibre evenly distributed ...
. 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 The Italian Renaissance ( it, Rinascimento ) was a period in Italian history covering the 15th and 16th centuries. The period is known for the initial development of the broader Renaissance culture that spread across Europe and marked the trans ...
painters and architects including
Masaccio Masaccio (, , ; December 21, 1401 – summer 1428), born Tommaso di Ser Giovanni di Simone, was a Florentine artist who is regarded as the first great Italian painter of the Quattrocento period of the Italian Renaissance. According to Vasari, ...
,
Paolo Uccello Paolo Uccello ( , ; 1397 – 10 December 1475), born Paolo di Dono, was an Italians, Italian (Florentine) Florentine painting, painter and mathematician who was notable for his pioneering work on visual Perspective (graphical), perspective in art. ...
,
Piero della Francesca Piero della Francesca (, also , ; – 12 October 1492), originally named Piero di Benedetto, was an Italian painter of the Early Renaissance. To contemporaries he was also known as a mathematician and geometer. Nowadays Piero della Francesca i ...
and
Luca Pacioli Fra Luca Bartolomeo de Pacioli (sometimes ''Paccioli'' or ''Paciolo''; 1447 – 19 June 1517) was an Italian mathematician, Franciscan friar, collaborator with Leonardo da Vinci, and an early contributor to the field now known as accounting ...
studied linear perspective, wrote treatises on it, and incorporated it into their artworks.


Overview

Perspective works by representing the light that passes from a scene through an imaginary rectangle (the picture plane), to the viewer's eye, as if a viewer were looking through a window and painting what is seen directly onto the windowpane. If viewed from the same spot as the windowpane was painted, the painted image would be identical to what was seen through the unpainted window. Each painted object in the scene is thus a flat, scaled down version of the object on the other side of the window.


One-point perspective

File:Perspective-1point.svg File:Perspectivephoto.jpg File:Inside Greenwich Foot Tunnel.jpg File:One point perspective.jpg File:Finnish national road 4 Vierumäki.jpg File:HK Hung Hum Station Corridor.jpg File:Railroad-Tracks-Perspective.jpg File:Tuileries Rivoli Perspective.jpg


Two-point perspective

File:College Street (9268126660).jpg File:Church Cottage at Boreham, Essex, England 2.jpg File:Harrington's hardware shop Broadstairs Kent England - inspiration for the 'Four Candles' Two Ronnies sketch 02.jpg File:Big Dam Film Festival Logo.jpg File:2-pt-sketchup.jpg


Three-point perspective

File:South tower of the Notre Dame.jpg File:ויקיפדיה אוהבת אתרי מורשת 2014 - תל אביב - בית ברלין פסובסקי או בית התאומים (15).JPG File:The Whitaker, Rawtenstall, formerly Rossendale Museum, Lancashire, England 2008.jpg


Curvilinear perspective

Additionally, a central vanishing point can be used (just as with one-point perspective) to indicate frontal (foreshortened) depth. File:cmglee Judge Business School rear.jpg File:194 - Buenos Aires - Casa Rosada - Janvier 2010.jpg


History


Early history

The earliest art paintings and drawings typically sized many objects and characters hierarchically according to their spiritual or thematic importance, not their distance from the viewer, and did not use foreshortening. The most important figures are often shown as the highest in a
composition Composition or Compositions may refer to: Arts and literature *Composition (dance), practice and teaching of choreography *Composition (language), in literature and rhetoric, producing a work in spoken tradition and written discourse, to include v ...
, also from
hieratic Hieratic (; grc, ἱερατικά, hieratiká, priestly) is the name given to a cursive writing system used for Ancient Egyptian and the principal script used to write that language from its development in the third millennium BC until the ris ...
motives, leading to the so-called "vertical perspective", common in the
art of Ancient Egypt Ancient Egyptian art refers to art produced in ancient Egypt between the 6th millennium BC and the 4th century AD, spanning from Prehistoric Egypt until the Christianization of Roman Egypt. It includes paintings, sculptu ...
, where a group of "nearer" figures are shown below the larger figure or figures; simple overlapping was also employed to relate distance. Additionally, oblique foreshortening of round elements like shields and wheels is evident in
Ancient Greek Ancient Greek includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Dark Ages (), the Archaic peri ...
red-figure pottery Red-figure vase painting is one of the most important styles of figural Greek vase painting. It developed in Athens around 520 BCE and remained in use until the late 3rd century BCE. It replaced the previously dominant style of black-figure vas ...
. Systematic attempts to evolve a system of perspective are usually considered to have begun around the fifth century BC in the art of ancient Greece, as part of a developing interest in illusionism allied to theatrical scenery. This was detailed within
Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of phil ...
's ''
Poetics Poetics is the theory of structure, form, and discourse within literature, and, in particular, within poetry. History The term ''poetics'' derives from the Ancient Greek ποιητικός ''poietikos'' "pertaining to poetry"; also "creative" an ...
'' as ''skenographia'': using flat panels on a stage to give the illusion of depth. The philosophers
Anaxagoras Anaxagoras (; grc-gre, Ἀναξαγόρας, ''Anaxagóras'', "lord of the assembly";  500 –  428 BC) was a Pre-Socratic Greek philosopher. Born in Clazomenae at a time when Asia Minor was under the control of the Persian Empire, ...
and
Democritus Democritus (; el, Δημόκριτος, ''Dēmókritos'', meaning "chosen of the people"; – ) was an Ancient Greek pre-Socratic philosopher from Abdera, primarily remembered today for his formulation of an atomic theory of the universe. No ...
worked out geometric theories of perspective for use with ''skenographia''.
Alcibiades Alcibiades ( ; grc-gre, Ἀλκιβιάδης; 450 – 404 BC) was a prominent Athenian statesman, orator, and general. He was the last of the Alcmaeonidae, which fell from prominence after the Peloponnesian War. He played a major role in t ...
had paintings in his house designed using ''skenographia'', so this art was not confined merely to the stage.
Euclid Euclid (; grc-gre, Wikt:Εὐκλείδης, Εὐκλείδης; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the ''Euclid's Elements, Elements'' trea ...
in his ''
Optics Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviole ...
'' () argues correctly that the perceived size of an object is not related to its distance from the eye by a simple proportion. In the first-century BC
fresco Fresco (plural ''frescos'' 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 plaste ...
es of the Villa of P. Fannius Synistor, multiple vanishing points are used in a systematic but not fully consistent manner. Chinese artists made use of
oblique projection Oblique projection is a simple type of technical drawing of graphical projection used for producing two-dimensional (2D) images of three-dimensional (3D) objects. The objects are not in perspective and so do not correspond to any view of an ...
from the first or second century until the 18th century. It is not certain how they came to use the technique; Dubery and Willats (1983) speculate that the Chinese acquired the technique from India, which acquired it from Ancient Rome, while others credit it as an indigenous invention of
Ancient China The earliest known written records of the history of China date from as early as 1250 BC, from the Shang dynasty (c. 1600–1046 BC), during the reign of king Wu Ding. Ancient historical texts such as the '' Book of Documents'' (early chapte ...
. Oblique projection is also seen in Japanese art, such as in the
Ukiyo-e Ukiyo-e is a genre of Japanese art which flourished from the 17th through 19th centuries. Its artists produced woodblock prints and paintings Painting is the practice of applying paint, pigment, color or other medium to a solid surfac ...
paintings of
Torii Kiyonaga Torii Kiyonaga ( ja, 鳥居 清長; 1752 – June 28, 1815) was a Japanese ukiyo-e artist of the Torii school. Originally Sekiguchi Shinsuke, the son of an Edo bookseller, from Motozaimokuchō Itchōme in Edo, he took on Torii Kiyonaga as a ...
(1752–1815). By the later periods of antiquity, artists, especially those in less popular traditions, were well aware that distant objects could be shown smaller than those close at hand for increased realism, but whether this convention was actually used in a work depended on many factors. Some of the paintings found in the ruins of Pompeii show a remarkable realism and perspective for their time. It has been claimed that comprehensive systems of perspective were evolved in antiquity, but most scholars do not accept this. Hardly any of the many works where such a system would have been used have survived. A passage in
Philostratus Philostratus or Lucius Flavius Philostratus (; grc-gre, Φιλόστρατος ; c. 170 – 247/250 AD), called "the Athenian", was a Greek sophist of the Roman imperial period. His father was a minor sophist of the same name. He was born probab ...
suggests that classical artists and theorists thought in terms of "circles" at equal distance from the viewer, like a classical semi-circular theatre seen from the stage. The roof beams in rooms in the Vatican Virgil, from about 400 AD, are shown converging, more or less, on a common vanishing point, but this is not systematically related to the rest of the composition. Medieval artists in Europe, like those in the Islamic world and China, were aware of the general principle of varying the relative size of elements according to distance, but even more than classical art were perfectly ready to override it for other reasons. Buildings were often shown obliquely according to a particular convention. The use and sophistication of attempts to convey distance increased steadily during the period, but without a basis in a systematic theory.
Byzantine art Byzantine art comprises the body of Christian Greek artistic products of the Eastern Roman Empire, as well as the nations and states that inherited culturally from the empire. Though the empire itself emerged from the decline of Rome and lasted ...
was also aware of these principles, but also used the
reverse perspective Reverse perspective, also called inverse perspective,. inverted perspective, divergent perspective, or Byzantine perspective, is a form of perspective drawing in which the objects depicted in a scene are placed between the projective point and t ...
convention for the setting of principal figures.
Ambrogio Lorenzetti Ambrogio Lorenzetti (; – 9 June 1348) or Ambruogio Laurati was an Italian painter of the Sienese school. He was active from approximately 1317 to 1348. He painted ''The Allegory of Good and Bad Government'' in the Sala dei Nove (Salon of Nine ...
painted a floor with convergent lines in his ''
Presentation at the Temple The Presentation of Jesus at the Temple (or ''in the temple'') is an early episode in the life of Jesus Christ, describing his presentation at the Temple in Jerusalem, that is celebrated by many churches 40 days after Christmas on Candlemas, ...
'' (1342), though the rest of the painting lacks perspective elements.


Renaissance

It is generally accepted that
Filippo Brunelleschi Filippo Brunelleschi ( , , also known as Pippo; 1377 – 15 April 1446), considered to be a founding father of Renaissance architecture, was an Italian architect, designer, and sculptor, and is now recognized to be the first modern engineer, p ...
conducted a series of experiments between 1415 and 1420, which included making drawings of various Florentine buildings in correct perspective. According to
Vasari Giorgio Vasari (, also , ; 30 July 1511 – 27 June 1574) was an Italian Renaissance Master, who worked as a painter, architect, engineer, writer, and historian, who is best known for his work ''The Lives of the Most Excellent Painters, Sculpt ...
and
Antonio Manetti Antonio di Tuccio Manetti (6 July 1423 – May 26, 1497) was an Italian mathematician and architect from Florence. He is particularly noted for his investigations into the site, shape and size of Dante's ''Inferno''. Although Manetti never hims ...
, in about 1420, Brunelleschi demonstrated his discovery by having people look through a hole in the back of a painting he had made. Through it, they would see a building such as the
Florence Baptistery The Florence Baptistery, also known as the Baptistery of Saint John ( it, Battistero di San Giovanni), is a religious building in Florence, Italy, and has the status of a minor basilica. The octagonal baptistery stands in both the Piazza del D ...
. When Brunelleschi lifted a mirror in front of the viewer, it reflected his painting of the buildings which had been seen previously, so that the vanishing point was centered from the perspective of the participant. Brunelleschi applied the new system of perspective to his paintings around 1425. This scenario is indicative, but faces several problems. First of all, nothing can be said for certain about the perspective of the baptistery of San Giovanni, because Brunelleschi's panel is lost. Second, no other perspective painting by Brunelleschi is known. Third, in the account written by Antonio di Tuccio Manetti at the end of the 15th century on Brunelleschi's panel, there is not a single occurrence of the word experiment. Fourth, the conditions listed by Antonio di Tuccio Manetti are contradictory with each other. For example, the description of the eyepiece sets a visual field of 15° much narrower than the visual field resulting from the urban landscape described. This scenario is still debated, however, because Brunelleschi's tavoletta is lost, which does not allow a direct assessment of the correctness of his perspective construction, and because the conditions listed by Antonio di Tuccio Manetti in his ''Vita di Ser Brunellesco'' are inconsistent. Soon after Brunelleschi's demonstrations, nearly every artist in Florence and in Italy used geometrical perspective in their paintings and sculpture, notably
Donatello Donato di Niccolò di Betto Bardi ( – 13 December 1466), better known as Donatello ( ), was a Republic of Florence, Florentine sculptor of the Renaissance period. Born in Republic of Florence, Florence, he studied classical sculpture and use ...
,
Masaccio Masaccio (, , ; December 21, 1401 – summer 1428), born Tommaso di Ser Giovanni di Simone, was a Florentine artist who is regarded as the first great Italian painter of the Quattrocento period of the Italian Renaissance. According to Vasari, ...
,
Lorenzo Ghiberti Lorenzo Ghiberti (, , ; 1378 – 1 December 1455), born Lorenzo di Bartolo, was an Italian Renaissance sculptor from Florence, a key figure in the Early Renaissance, best known as the creator of two sets of bronze doors of the Florence Baptistery ...
,
Masolino da Panicale , death_date = ''c.'' 1447 , death_place = Florence , nationality = Italian , field = Painting, fresco , training = , movement = Italian Renaissance , works = frescoes in the Brancacci Chapel , patrons ...
,
Paolo Uccello Paolo Uccello ( , ; 1397 – 10 December 1475), born Paolo di Dono, was an Italians, Italian (Florentine) Florentine painting, painter and mathematician who was notable for his pioneering work on visual Perspective (graphical), perspective in art. ...
, and
Filippo Lippi Filippo Lippi ( – 8 October 1469), also known as Lippo Lippi, was an Italian painter of the Quattrocento (15th century) and a Carmelite Priest. Biography Lippi was born in Florence in 1406 to Tommaso, a butcher, and his wife. He was orp ...
. Not only was perspective a way of showing depth, it was also a new method of creating a composition. Visual art could now depict a single, unified scene, rather than a combination of several. Early examples include Masolino's ''St. Peter Healing a Cripple and the Raising of Tabitha'' (), Donatello's ''
The Feast of Herod The Feast of Herod refers to the episode in the Gospels following the Beheading of St. John the Baptist, when Salome presents his head to her parents. The account in the Book of Mark describes Herod holding a banquet on his birthday for his high ...
'' (), as well as Ghiberti's ''
Jacob and Esau The biblical Book of Genesis speaks of the relationship between fraternal twins Jacob and Esau, sons of Isaac and Rebecca. The story focuses on Esau's loss of his birthright to Jacob and the conflict that ensued between their descendant nations ...
'' and other panels from the east doors of the Florence Baptistery. Masaccio (d. 1428) achieved an illusionistic effect by placing the vanishing point at the viewer's eye level in his ''
Holy Trinity The Christian doctrine of the Trinity (, from 'threefold') is the central dogma concerning the nature of God in most Christian churches, which defines one God existing in three coequal, coeternal, consubstantial divine persons: God the F ...
'' (), and in '' The Tribute Money'', it is placed behind the face of Jesus. In the late 15th century,
Melozzo da Forlì Melozzo da Forlì (c. 1438 – 8 November 1494) was an Italian Renaissance painter and architect. His fresco paintings are notable for the use of foreshortening. He was the most important member of the Forlì painting school. Biography ...
first applied the technique of foreshortening (in Rome, Loreto,
Forlì Forlì ( , ; rgn, Furlè ; la, Forum Livii) is a ''comune'' (municipality) and city in Emilia-Romagna, Northern Italy, and is the capital of the province of Forlì-Cesena. It is the central city of Romagna. The city is situated along the Via E ...
and others). This overall story is based on qualitative judgments, and would need to be faced against the material evaluations that have been conducted on Renaissance perspective paintings. Apart from the paintings of Piero della Francesca, which are a model of the genre, the majority of 15th century works show serious errors in their geometric construction. This is true of Masaccio's ''Trinity'' fresco and of many works, including those by renowned artists like Leonardo da Vinci. As shown by the quick proliferation of accurate perspective paintings in Florence, Brunelleschi likely understood (with help from his friend the mathematician
Toscanelli Paolo dal Pozzo Toscanelli (1397 – 10 May 1482) was an Italian mathematician, astronomer,, pp. 333–335 and cosmographer. Life Paolo dal Pozzo Toscanelli was born in Florence, the son of the physician Domenico Toscanelli. There is no ...
), but did not publish, the mathematics behind perspective. Decades later, his friend Leon Battista Alberti wrote ' (), a treatise on proper methods of showing distance in painting. Alberti's primary breakthrough was not to show the mathematics in terms of conical projections, as it actually appears to the eye. Instead, he formulated the theory based on planar projections, or how the rays of light, passing from the viewer's eye to the landscape, would strike the picture plane (the painting). He was then able to calculate the apparent height of a distant object using two similar triangles. The mathematics behind similar triangles is relatively simple, having been long ago formulated by Euclid. Alberti was also trained in the science of optics through the school of Padua and under the influence of
Biagio Pelacani da Parma Blasius of Parma (Biagio Pelacani da Parma) (c. 13501416) was an Italian philosopher, mathematician and astrologer. He popularised English and French philosophical work in Italy, where he associated both with scholastics and with early Renaissance ...
who studied
Alhazen Ḥasan Ibn al-Haytham, Latinized as Alhazen (; full name ; ), was a medieval mathematician, astronomer, and physicist of the Islamic Golden Age from present-day Iraq.For the description of his main fields, see e.g. ("He is one of the prin ...
's ''
Book of Optics The ''Book of Optics'' ( ar, كتاب المناظر, Kitāb al-Manāẓir; la, De Aspectibus or ''Perspectiva''; it, Deli Aspecti) is a seven-volume treatise on optics and other fields of study composed by the medieval Arab scholar Ibn al- ...
''. This book, translated around 1200 into Latin, had laid the mathematical foundation for perspective in Europe. Piero della Francesca elaborated on ''De pictura'' in his '' De Prospectiva pingendi'' in the 1470s, making many references to Euclid. Alberti had limited himself to figures on the ground plane and giving an overall basis for perspective. Della Francesca fleshed it out, explicitly covering solids in any area of the picture plane. Della Francesca also started the now common practice of using illustrated figures to explain the mathematical concepts, making his treatise easier to understand than Alberti's. Della Francesca was also the first to accurately draw the
Platonic solids In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all edges c ...
as they would appear in perspective.
Luca Pacioli Fra Luca Bartolomeo de Pacioli (sometimes ''Paccioli'' or ''Paciolo''; 1447 – 19 June 1517) was an Italian mathematician, Franciscan friar, collaborator with Leonardo da Vinci, and an early contributor to the field now known as accounting ...
's 1509 ''
Divina proportione ''Divina proportione'' (15th century Italian for ''Divine proportion''), later also called ''De divina proportione'' (converting the Italian title into a Latin one) is a book on mathematics written by Luca Pacioli and illustrated by Leonardo da V ...
'' (''Divine Proportion''), illustrated by
Leonardo da Vinci Leonardo di ser Piero da Vinci (15 April 14522 May 1519) was an Italian polymath of the High Renaissance who was active as a painter, Drawing, draughtsman, engineer, scientist, theorist, sculptor, and architect. While his fame initially res ...
, summarizes the use of perspective in painting, including much of Della Francesca's treatise. Leonardo applied one-point perspective as well as
shallow focus Shallow focus is a photographic and cinematographic technique incorporating a small depth of field. In shallow focus, one plane of the scene is in focus while the rest is out of focus. Shallow focus is typically used to emphasize one part of the i ...
to some of his works. Two-point perspective was demonstrated as early as 1525 by
Albrecht Dürer Albrecht Dürer (; ; hu, Ajtósi Adalbert; 21 May 1471 – 6 April 1528),Müller, Peter O. (1993) ''Substantiv-Derivation in Den Schriften Albrecht Dürers'', Walter de Gruyter. . sometimes spelled in English as Durer (without an umlaut) or Due ...
, who studied perspective by reading Piero and Pacioli's works, in his ''Unterweisung der messung'' ("Instruction of the measurement").


Limitations

Perspective images are calculated assuming a particular vanishing point. In order for the resulting image to appear identical to the original scene, a viewer of the perspective must view the image from the exact vantage point used in the calculations relative to the image. This cancels out what would appear to be distortions in the image when viewed from a different point. These apparent distortions are more pronounced away from the center of the image as the angle between a projected ray (from the scene to the eye) becomes more acute relative to the picture plane. In practice, unless the viewer chooses an extreme angle, like looking at it from the bottom corner of the window, the perspective normally looks more or less correct. This is referred to as "Zeeman's Paradox". It has been suggested that a drawing in perspective still seems to be in perspective at other spots because we still perceive it as a drawing, because it lacks depth of field cues."...the paradox is purely conceptual: it assumes we view a perspective representation as a retinal simulation, when in fact we view it as a two dimensional painting. In other words, perspective constructions create visual symbols, not visual illusions. The key is that paintings lack the depth of field cues created by binocular vision; we are always aware a painting is flat rather than deep. And that is how our mind interprets it, adjusting our understanding of the painting to compensate for our position."
Retrieved on 25 December 2006


See also

*
Anamorphosis Anamorphosis is a distorted projection requiring the viewer to occupy a specific vantage point, use special devices, or both to view a recognizable image. It is used in painting, photography, sculpture and installation, toys, and film special e ...
*
Camera angle The camera angle marks the specific location at which the movie camera or video camera is placed to take a shot. A scene may be shot from several camera angles simultaneously. This will give a different experience and sometimes emotion. The diffe ...
*
Cutaway drawing A cutaway drawing, also called a cutaway diagram is a 3D graphics, technical drawing, drawing, diagram and or technical illustration, illustration, in which surface elements of a three-dimensional model are selectively removed, to make internal f ...
*
Perspective control Perspective control is a procedure for composing or editing photographs to better conform with the commonly accepted distortions in constructed perspective. The control would: * make all lines that are vertical in reality vertical in the image. ...
*
Perspective-taking Perspective-taking is the act of perceiving a situation or understanding a concept from an alternative point of view, such as that of another individual. A vast amount of scientific literature suggests that perspective-taking is crucial to human de ...
*
Trompe-l'œil ''Trompe-l'œil'' ( , ; ) is an artistic term for the highly realistic optical illusion of three-dimensional space and objects on a two-dimensional surface. ''Trompe l'oeil'', which is most often associated with painting, tricks the viewer into ...
*
Uki-e refers to a genre of ukiyo-e pictures that employs western conventions of linear perspective. Although they never constituted more than a minor genre, pictures in perspective were drawn and printed by Japanese artists from their introduction in ...
* Zograscope


Notes


References


Sources

*


Further reading

* * * * * * * * *


External links


A tutorial covering many examples of linear perspective

Teaching Perspective in Art and Mathematics through Leonardo da Vinci's Work
at
Mathematical Association of America The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university, college, and high school teachers; graduate and undergraduate students; pure a ...

Metaphysical Perspective in Ancient Roman-Wall Painting

How to Draw a Two Point Perspective Grid
a
Creating Comics
{{DEFAULTSORT:Perspective (Graphical) Perspective projection Technical drawing Functions and mappings Composition in visual art Italian inventions