Perspective (graphical): Difference between revisions

[[File:Staircase perspective.jpg|thumb|upright=1.3|Staircase in twosix-point perspective]]

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| video1=[httphttps://smarthistorywww.khanacademy.org/Brunelleschi.htmlhumanities/renaissance-reformation/early-renaissance1/beginners-renaissance-florence/v/linear-perspective-brunelleschi-s-experiement Linear Perspective: Brunelleschi's Experiment], [[SmarthistoryKhan Academy]]<ref name="smarth A">{{cite web | title=Linear Perspective: Brunelleschi's Experiment | publisher=[[Smarthistory]] at [[Khan Academy]] | url=httphttps://smarthistorywww.khanacademy.org/Brunelleschi.html | accesshumanities/renaissance-date=12 May 2013 | urlreformation/early-status=live | archiverenaissance1/beginners-url=https:renaissance-florence/v/web.archive.org/web/20130524153017/http://smarthistory.khanacademy.org/Brunelleschi.htmllinear-perspective-brunelleschi-s-experiement | archiveaccess-date=242 MayJune 20132024 }}</ref>

| video3=[http://www.artbabble.org/video/ngadc/empire-eye-magic-illusion-trinity-masaccio-part-2 Empire of the Eye: The Magic of Illusion: The Trinity-Masaccio, Part 2], [[National Gallery of Art]]<ref name="smarth C">{{cite web| title=Empire of the Eye: The Magic of Illusion: The Trinity-Masaccio, Part 2| publisher=[[National Gallery of Art]] at [[ArtBabble]]| url=http://www.artbabble.org/video/ngadc/empire-eye-magic-illusion-trinity-masaccio-part-2| access-date=12 May 2013| url-status=dead| archive-url=https://web.archive.org/web/20130501114331/http://www.artbabble.org/video/ngadc/empire-eye-magic-illusion-trinity-masaccio-part-2| archive-date=1 May 2013}}</ref> }}

Linear or point-projection '''perspective''' (from {{lang-etymology|la|{{wiktlat|perspicere}} '|to see through'}}) is one of two types of [[3D projection|graphical projection]] perspective in the [[graphic arts]]; the other is [[parallel projection]].{{fact|date=May 2022}} Linear perspective is an approximate representation, generally on a flat surface, of an image as it is seen by [[station point|the eye]]. Perspective drawing is useful for representing a [[three-dimensional space|three-dimensional]] scene in a [[plane (mathematics)|two-dimensional]] medium, like [[paper]]. It is based on the optical fact that for a person an object looks N times (linearly) smaller if it has been moved N times further from the eye than the original distance was.

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 ''{{em|foreshortening''}}, meaning that an object's dimensions along[[Parallel (geometry)|parallel]] to the [[line of sight]] appear shorter than its dimensions across[[perpendicular]] to 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.

=== OneExamples of one-point perspective ===

<gallery caption="Examples of one-point perspective" widths="180px" heights="120px">

=== TwoExamples of two-point perspective ===

<gallery caption="Examples of two-point perspective" widths="180px" heights="120px">

<gallery caption="== Examples of three-point perspective" ===
<gallery widths="180px" heights="120px">

=== CurvilinearExamples of curvilinear perspective ===

<gallery caption="Examples of curvilinear perspective" widths="180px" heights="120px">

It is generally accepted that [[Filippo Brunelleschi]] conducted [[Filippo Brunelleschi#Linear perspective|a series of experiments]] between 1415 and 1420, which included making drawings of various [[Florence|Florentine]] buildings in correct perspective.<ref>{{Cite book |last=Gärtner|first=Peter |title=Brunelleschi|year=1998 |location=Cologne |publisher=Konemann|language=frKönemann|isbn=978-3-8290-0701-6|page=23}}</ref> According to [[Vasari]] and [[Antonio Manetti]], 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]]. 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.{{sfn|Edgerton|2009|pp=44–46}} Brunelleschi applied the new system of perspective to his paintings around 1425.{{sfn|Edgerton|2009|p=40}}

This scenario is indicative, but faces several problems, that are still debated.

First of all, nothing can be said for certain about the correctness of his perspective construction of the baptisteryBaptistery of San Giovanni, because Brunelleschi's panel is lost.

Second, no other perspective painting or drawing by Brunelleschi is known. (In fact, Brunelleschi was not known to have painted at all.)

Third, in the account written by Antonio Manetti in his ''Vita di TuccioSer ManettiBrunellesco'' 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.<ref>{{cite book | author=Dominique Raynaud | title=L'Hypothèse d'Oxford. Essai sur les origines de la perspective | publisher=Presses universitaires de France | location=Paris | year=1998 | pages=132–141}}</ref><ref>{{cite book |last1=Raynaud |first1=Dominique |title=Optics and the Rise of Perspective |place=Oxford |publisher=Bardwell Press |date=2014 |pages=1–2]}}</ref>

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<ref>{{cite journal |last1=Field |first1=J. V. |last2=Lunardi |first2=R. |last3=Settle |first3=T. B. |title=The perspective scheme of Masaccio's Trinity fresco |journal=Nuncius |date=1989 |volume=4 |issue=2 |pages=31–118 |id={{INIST|11836604}} |doi=10.1163/182539189X00680 }}</ref><ref>{{cite book | author=Dominique Raynaud | title=L'Hypothèse d'Oxford | publisher=Presses universitaires de France | location=Paris | year=1998 | pages=72–120}}</ref> and of many works, including those by renowned artists like Leonardo da Vinci.<ref>{{cite book |doi=10.1007/978-3-319-42721-8_4 |chapter=Fact and Fiction Regarding Masaccio's Trinity Fresco |title=Studies on Binocular Vision |series=Archimedes |year=2016 |last1=Raynaud |first1=Dominique |volume=47 |pages=53–67 |isbn=978-3-319-42720-1 }}</ref><ref>{{cite book |first1=Dominique |last1=Raynaud | chapter=Las fuentes ópticas de Leonardo | title=Leonardo da Vinci. Perspectiva y visión |editor1-first=Luis |editor1-last=Ramón-Laca |publisher=UAH |location=Alcalá de Henares | year=2020 | pages=61–62 |isbn=978-84-18254-89-5 |oclc=1243556932 }}</ref>

As shown by the quick proliferation of accurate perspective paintings in Florence, Brunelleschi likely understood (with help from his friend the mathematician [[Toscanelli]]),<ref>{{cite book |last1=Vasari |first1=Giorgio |title=Stories of the Italian Artists |date=1885 |publisher=Scribner & Welford |page=53 |url=https://books.google.com/books?id=jmBJAQAAIAAJ&pg=PA53 |quote=Messer Paolo dal Pozzo Toscanelli, having returned from his studies, invited Filippo with other friends to supper in a garden, and the discourse falling on mathematical subjects, Filippo formed a friendship with him and learned geometry from him. }}</ref> but did not publish, the mathematics behind perspective. Decades later, his friend [[Leon Battista Alberti]] wrote ''{{nowrap|[[De pictura]]}}'' ({{circa|1435|lk=no}}), 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.{{Efn|In viewing a wall, for instance, the first triangle has a [[Vertex (geometry)|vertex]] at the user's eye, and vertices at the top and bottom of the wall. The bottom of this triangle is the distance from the viewer to the wall. The second, similar triangle, has a point at the viewer's eye, and has a length equal to the viewer's eye from the painting. The height of the second triangle can then be determined through a simple ratio, as proven 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]] who studied [[Alhazen]]'s ''[[Book of Optics]]''.<ref>{{cite book | last=El-Bizri | first=Nader | author-link=Nader El-Bizri | chapter=Classical Optics and the Perspectiva Traditions Leading to the Renaissance | pages=[https://archive.org/details/renaissancetheor00hend/page/n23 11]–30 | editor1-last=Hendrix | editor1-first=John Shannon | editor1-link=John Shannon Hendrix | editor2-last=Carman | editor2-first=Charles H. | title=Renaissance Theories of Vision (Visual Culture in Early Modernity) | url=https://archive.org/details/renaissancetheor00hend | url-access=limited | date=2010 | location=Farnham, Surrey | publisher=[[Ashgate Publishing]] | isbn=978-1-409400-24-0}}</ref> This book, translated around 1200 into Latin, had laid the mathematical foundation for perspective in Europe.<ref>{{cite book|title=Florence and Baghdad: Renaissance art and Arab science|last=Hans|first=Belting|date=2011|publisher=Belknap Press of Harvard University Press |isbn=978-0-674-05004-4|edition=1st English |location=Cambridge, Massachusetts |pages=90–92 |oclc=701493612}}</ref>

Two-point perspective was demonstrated as early as 1525 by [[Albrecht Dürer]], who studied perspective by reading Piero and Pacioli's works, in his ''Unterweisung der messungMessung'' ("Instruction of the measurementMeasurement").<ref>{{cite journal |doi=10.2307/3619717 |title=The Portrait of Fra Luca Pacioli |journal=[[The Mathematical Gazette]] |volume=77 |issue=479 |page=206 |year=1993 |last1=MacKinnon |first1=Nick|jstor=3619717 |s2cid=195006163 }}</ref>

* {{Cite book | lastlast1=Pérez-Gómez, |first1=Alberto | firstlast2=and Pelletier, |first2=Louise | title=Architectural Representation and the Perspective Hinge | publisher=MIT Press | location=Cambridge, Massachusetts | year=1997}}

* {{cite book |doi=10.1007/978-3-319-42721-8 |title=Studies on Binocular Vision |series=Archimedes |year=2016 |volume=47 |isbn=978-3-319-42720-1 |s2cid=151589160 |first1=Dominique |last1=Raynaud |bibcode=2016sbvo.book.....R }}