Talk:Perspective (graphical)

First discussion

"An exact replication of the image perceived by the eye is only possible when the picture plane is a spherical surface or portion of a spherical surface (with the center of the sphere located at the observer's eye). The distortion that occurs is similar to the distortions that occur when attempting to represent the globe (approximately spherical) on a flat surface (see perspective projection distortion)."

This is simply untrue (see my comment also under 'Perspective projection distortion'). There seems to me to be much confusion arising from the notion that perspective in some way emulates the behaviour of the retina. It doesn't: it allows a canvas (screen, etc) to emulate a window on the world, when viewed from a given point (and if you move your viewpoint with respect to the canvas, the correct perspective will be a different linear perspective, not a queer 'spherical' one.

---

Whereas the subject per force narrows the usage of the word Perspective from the subjective to eye/photo-visualization,

And whereas, in doing so, it per force addresses the technological aspects of eye/photo perspective,

And whereas the explanation of this technology derives from the phenomenon of graphical Projection,

It is hereby suggested that this page title be changed from Perspective (graphical) to Projective Perspective.

You may wish to write an article about Projective Perspective, but the question is exactly as it is stated: how to achieve the illusion of real world by graphical means: drawing, painting, photography. And please don't delete someone else's writing, especially if you offer no replacement to the introduced terms and discussed issues. Mikkalai 07:56, 8 Feb 2004 (UTC)

Apologies for the deletions….still a bit clumsy with protocols in Wiki….mea culpa.

I didn't think much about the scope of the article; I merely spawned it from the chaotic Perspective article. Of course, there are quite a few valid separate articles that can be created: --Pat 18:52, 21 Feb 2004 (UTC)

• perspective in technical drawing,
• in painting,
• in photography,
• in computer imaging,
• in psychology of vision.

Big job still to be done. Mikkalai 20:57, 9 Feb 2004 (UTC)

A better caption to Pietro Perugino's fresco than my fatuous one, anybody? Wetman 18:32, 13 Aug 2004 (UTC)

_________________________________________

The author of the Perspective article seems to associate the word with "Opinion", among other categories, and proceeds to address a number of subjects of which there is no end. Before he advances to that point the author makes the statement:

[In Visual arts and mathematics the word perspective is used in a technical sense to denote a way of representing three-dimensional objects in the plane (of painting, photoimage, drawing) aimed at proper rendering of depth relationships, see perspective as graphical representation.

From that statement one might advantageously narrow one’s attention to Perspective as a Graphical Representation or, as the title was apparently changed to, Perspective (graphical). Under that title, it is suggested that a preferred approach is to explain (the source of?) Perspective (graphical) phenomenon and leave technical how-tos and applications, say to painting, religious icons, etc., to others specializing in those areas. Pat Kelso

____________________________________________

"In most modern drawings/paintings the linear perspective is used: the further the objects are from the viewer, the smaller they are drawn and the closer they are positioned to the so-called vanishing point or points, so that the (drawing of the) most remote objects completely disappear in the vicinity of these points.

"Under the linear perspective the vanishing point or points are usually placed inside the painting with the illusion that it is "beyond" the drawing.

"Under the reversed perspective, or inverse perspective, or Byzantine perspective the further the objects, the larger they are drawn. (The latter name is because thes kind of perspective is observed in earlier Byzantine and Russian Orthodox icons.) Technically, the vanishing points are placed outside the painting with the illusion that they are "in front of" the painting."

‘Having difficulty with the above. E.g.,

The phrase “linear perspective” most commonly distinguishes between perspective in imaging and other perspectives as perspective in thought (opinion).

 - the "linear" in linear perspective
   refers to the fact that more distant
   objects diminish in size in a
   linear fashion (if you graph the
   drawn size of a 1-foot object vs.
   the distance from the viewer, the
   points will align into a line)
 - although I have never personally
   seen a non-linear perspective,
   it is possible to do so (for
   example, the points in the graph
   mentioned above could form a
   parabola)

“…the smaller they are drawn and the closer they are positioned to the so-called vanishing point or points, so that the (drawing of the) most remote objects completely disappear in the vicinity of these points.”

The closer the that object appears to the horizon line (not, vanishing points) in space the smaller the drawing of the object will appear. The nearness of the object to the horizon line within the frame of the picture has no bearing on it size. Many objects frequently crossover the horizon line within the frame of the picture without effect to their sizes.

"Under the linear perspective the vanishing point or points are usually placed inside the painting with the illusion that it is ‘beyond’ the drawing.”

Don’t follow. Please explain use of “inside” and “beyond”.

"Under the reversed perspective, or inverse perspective, or Byzantine perspective the further the objects, the larger they are drawn. (The latter name is because thes kind of perspective is observed in earlier Byzantine and Russian Orthodox icons.)

I have misgivings that reverse, inverse and Byzantine perspective needs be addressed under ‘linear perspective’. Sizes in these seem more a matter of emphasis than trying for an illusion of depth. Reverse Perspective is often the term used to describe the condition wherein the station-point is located between the picture plane and the object of projection.

“Technically, the vanishing points are placed outside the painting with the illusion that they are "in front of" the painting.”

Don’t follow again. Please explain use of “outside” and “in front of”.

Please forgive my opaqueness. Pat Kelso

______________________

deleted: "Axonometric perspective is in between the two others: the relative sizes of depicted objects do not depend on the distance to the actual ones."

Note Axonometric is a form of Orthographic Projection. Pat 18:52, 21 Feb 2004 (UTC)

---

The follosing piece is cut out of Perspective

Perspective can be drawn in an instinctive way (as in the visual fine arts such as painting, sketching, etching, etc.) as well as in a quantified, technical way (technical graphics using drafting instruments).

It is widely held that perspective as a means of graphic representation was discovered by Brunelleschi during the Renaissance period. However, it is likely that other civilsations knew the technique, for example, there is a particular painting in the Ajanta caves in India that employs a similar method.

IMO it must be incorporated into this artice.Mikkalai 20:41, 21 Feb 2004 (UTC)

______________________

...Don’ t quite follow …….. are you saying to restore the cutout above?

From Perspective projection distortion re Brunelleschi:

The physiological basis of foreshortening went undefined until the year 1000 when the Arabian mathematician and philosopher, Alhazen, in his Perspectiva, first explained that light projects conically into the eye. A method for presenting foreshortened geometry systematically on a plane surface was unknown for another 300 years. The artist Giotto may have been the first to recognize that the image beheld by the eye is distorted---that to the eye, parallel lines appear to intersect (in the manner of receding railroad tracks) whereas in "undistorted" nature, they do not.

From other sources:

One of the first uses of perspective was in Giotto’s ‘Jesus Before the Caïf’, more that 100 years before Brunelleschi’s perspectival demonstrations galvanized the widespread use of convergent perspective of the Renaissance proper.

I suggest a confusion factor in the past discussions of perspective is distinguishing between ‘foreshortening’ and ‘perspective projection’. Note that both words are needed: all ‘foreshortening’ is not perspective projection but all ‘perspective projection’ is ‘foreshortening’. Artists use both, generalized 'foreshortening' often intuitively, specialized 'perspective projection', mechanically. The technically trained usually use the later except when sketching. As you noted 'foreshortening' but not 'perspective projection' is found on Indian caves. I suggest that Wiki consider narrowing its use of the term ‘perspective’, as it relates to visual matters, to ‘perspective projection’. Accordingly suggest Perspective (graphical) be moved to Perspective projection. Or better still, create a new catagory of, say, 'Visual arts foreshortening' under which all perspective subjects and presumably, also photography would appear.

Pat Kelso 01:07, Mar 20, 2004 (UTC)

I'm a newbie here at Wikipedia, and I don't wish to burst into the midst of the tea party, but I've seen no mention at all of atmospheric perspective. BillHealey 22:45, Oct 16, 2004 (UTC)

Merge

I've just merged all the information from Linear perspective in to Perspective (graphical). It's a real mess right now, but I'll be cleaning it up over the next few days. I'm also going to be re-writing a lot of the information so it's actaully understandable to a unexperienced person. Since no one has touched either article in a year, I hope no one will mind. Zhatt 22:51, 13 October 2005 (UTC)

I made linear perspective redirect here, rather then have the same information on two pages. Tried to clean up the whole One-point et cetera sections. There is certainly no reason to have the information on another page, when it works well as part of the general perspective page. Sir Isaac Lime 14:19, 5 March 2006 (UTC)

Van Eyck

The article references Van Eyck, but it doesn't say which one. Wikipedia already has two, and both painters, so which one is it? The name should also be a link. -Volfy 04:11, 26 October 2005 (UTC)

Nevermind, fixed it -Volfy 04:16, 26 October 2005 (UTC)

Cleanup Tag

I added a cleanup tag to this article as it's not following the manual of style in some areas and it's not really telling the reader what perspective is. It talks a lot about where it comes from, how to make it and why it works, but not what it is.

I've been drawing for some time now, and one of my favorite things to do is a strong perspective, but I don't understand half of what's being said in this article. The average person should be able to read this article and have a good understanding of the concept of perspective. I mean, there's barely even mention of the horizon in this article!

I also recreated the linear perspective article as all the content that was once that article has been edited out of this one.

A lot of work needs to be done on these articles. Maybe I'll be able to start on some of it later.

Zhatt 20:01, 8 February 2006 (UTC)

Sorry, a lot of the content that I thought was edited out was, in fact, and old vandal. I reverted, but there's still a lot to be done. Zhatt 20:17, 8 February 2006 (UTC)

I've removed the tag - it looks to me like these issues have been addressed. --OpenToppedBus - Talk to the driver 13:42, 18 April 2006 (UTC)

variscalar

Removed the following text:

freehand sketching aided by instruments.A photograph automatically shows a scene with correct perspective for the location of the camera. It follows that an artist wishing tp paint a picture of the scene with true perspective needs only to draw an accurate copy of the photograph. If his painting is to be of a different size from that of the photograph he must accurately scale it up or down. This may easily be done by using a Proportional Divider, sometimes called a Variscaler, set to give the scaling ratio which is required to fit the scene on to his painting support

As I see it, the problems are:

• A photograph is not technically correct perspective, it is simply what looks most correct to us. A photograph is technically spherically warped (as can bee seen when multiple photos are put together to make a larger picture.)
• It is not technically constructing perspective, it is simply copying a previous perspective construction. In the same vein, a xerox machine could be listed if you use it to make copies of a perspective drawing.

I moved it to its own item (cut down), but even that may be unnecessary. Sir Isaac Lime 21:39, 22 April 2006 (UTC)

- I would also like to add (though please note that the word "me" doesn't mean the original author of this part of the discussion) that the term "correct perspective" is oxymoronic as perspective, even as a means of graphical projection retains a certain matter of subjectiveness - i.e. every image or field of vision involves the viewer (or image as a representation of what the viewer sees) having some form of point of view being the basis of every image or field of view (I use the word field of view as a term to describe what a living person sees as an image just as susceptible to the "laws" of perspective as any artificial image).

By that I chose to say that there can be no universally "correct" perspective as there doesn't really exist any absolute measure or any ideal example of perspective (even though the general focal length and lens distortion of the human eye might serve as one, though this in turn would be a rather limited ideal/measure as human experience is subjective in much the same way), but rather a plethora of different perspectives and a certain amount of mathematical codifications of how to render these on a two-dimensional surface. —Preceding unsigned comment added by 193.157.244.71 (talk) 21:24, 24 October 2010 (UTC)

Merge (Perspective Projection)

(copied this over from Talk:Perspective_projection after merging --Allefant 19:29, 7 July 2007 (UTC)) Perspective projection and Perspective (graphical) seem to basically be about the same subject, I think they should be merged (i.e. take what contents is useful from the shorter one and work into the longer one), and decide which name to keep. I also did some literature search and fixed some factual errors with proper references in some of the smaller projection pages (i.e. linked from that views template) recently, so likely there's also still mistakes in the bigger articles (perspective and orthographic projection) - hopefully this can all be cleaned up eventually. --Allefant 20:36, 4 July 2007 (UTC)

Agreed. I think the [Perspective projection]] should probably just be merged & redirected into Perspective (graphical), just as linear perspective was. They all discuss the exact same thing. The "projection" template actually seems to be the main thing that Perspective projection has that Perspective (graphical) does not. The template, however, seems less important than the information that is already at the head of the article (the diagram of perspective & the table of contents). Perhaps it should be slipped into the "basic concept" section?Sir Isaac Lime 14:47, 5 July 2007 (UTC)

Yes, I think there's actually no information in the current Perspective projection text which is not already here, also the figure doesn't seem to fit the paragraph besides it. The list of concepts likely isn't that useful either as they are already used in the article (I think they all are), and that external spanish link should go away anyway. So the merge should be rather trivial. Whether or not Template:Views is really needed is another question - I'd just place it on Perspective (graphical) initially, and if it's not liked, maybe it should eventually be phased out from all articles who currently have it. --Allefant 15:21, 5 July 2007 (UTC)

Ok, I merged it now, and did not keep any contents. --Allefant 19:29, 7 July 2007 (UTC)

External links

I removed most of the external links. World of Escher is a commercial site that sells posters or something, two other links had only Spanish text. In general I see little point in putting examples of various types of perspective into the external links. If more illustrations would be helpful, they should be taken from free images and integrated into the article.—Graf Bobby 16:35, 23 July 2007 (UTC)

I add the page about Vincent van Gogh's Perspective Frame and links to the letters he wrote about perspective. Vincent van Gogh's Perspective Frame — Preceding unsigned comment added by Gallery-of-art (talk • contribs) 06:11, 31 March 2011 (UTC)

Foreshortening

This section is a little bit unclear. The image could use an example of a projection where foreshortening does not occur. SharkD (talk) 02:11, 21 December 2007 (UTC)

This section also contains the following:

"The line just drawn represents the ray of light travelling from the viewer's eye to the farthest edge of the square. This step is key to understanding perspective drawing."

Rays of light do not emanate from the eye. It is ironic that it is followed by an admonition that understanding this is key to comprehending perspective. Kcds (talk) 13:31, 4 July 2009 (UTC)

Roman Perspective

I believe the historical section jumps too quickly from classic Greece to the Middle Ages. There are several examples of Roman frescoes with excellent one point perspective: http://www.didaskalia.net/studyarea/visual_resources/rometemp3d.html Others can be found with a search for Skenographia or house of Augustus.

I have tested sight lines on a couple, and they demonstrate that the Romans had a fine understanding that the lines should meet at one point at eyelevel.

Carpets (talk) 14:26, 26 January 2008 (UTC)

It would be great to have more info on Roman perspective. Are there any articles you can find that discuss Roman perspective?Sir Isaac Lime (talk) 15:12, 26 January 2008 (UTC)

Not really, but here are links to one page each of three articles on the subject:

http://links.jstor.org/sici?sici=0075-4269(1999)119%3C161%3AVVOTSO%3E2.0.CO%3B2-O http://links.jstor.org/sici?sici=0002-9114(197210)76%3A4%3C454%3ARPPATA%3E2.0.CO%3B2-9 http://links.jstor.org/sici?sici=0002-9114(194504%2F06)49%3A2%3C134%3ATFOARS%3E2.0.CO%3B2-B

Alan M.G.Little seems to be the „expert“ on the subject. Here is a blurb about his book:

http://209.85.135.104/search?q=cache:DW2N1hfmz30J:www.jenniferreut.com/ppsite/perspace.htm+roman+perspective&hl=en&ct=clnk&cd=21

This is all the following site says about Vitruvius: http://www.dartmouth.edu/~matc/math5.geometry/unit11/unit11.html

“Vitruvius' Ten Books on Architecture which appeared about 25 B.C., was the only book on architecture to survive from antiquity. It profoundly influenced Renaissance architecture and thinking, including that of Alberti, who quoted Vitruvius in his Della pittura. Vitruvius wrote, Perspective is the method of sketching a front with the sides withdrawing into the background, the lines all meeting in the center of a circle. Unfortunately he didn't elaborate on that. Elsehere, Vitruvius' reference to Greek and Roman stage design, implied an understanding of the vanishing point.” That is from the 2nd chapter of his first book: http://www.lih.gre.ac.uk/histhe/vitruvius.htm From the Roman frescoes, Vitruvius only explained in one sentence what the artists already understood and practiced. No, I don’t want to edit the article, so anyone who agrees please do so. Carpets (talk) 13:36, 27 January 2008 (UTC)

The article is indeed flawed on this point. Perspective was not a post-medieval invention, but rather a technique developed in the Ancient world whose popularity waned to the extent that the concept essentially had to be rediscovered during the Renaissance. Kafka Liz (talk) 00:46, 10 June 2008 (UTC)

4th and 5th perspectives

Fourth and fifth perspectives should be added.[1].Mohamed Magdy (talk) 20:29, 19 February 2010 (UTC)

Picture missing?

The section "Example" seems to be referring to a picture that is not present on the page. It refers to the "gray lines", the "orange line". etc. —Preceding unsigned comment added by 12.77.148.61 (talk) 02:13, 9 March 2010 (UTC)

Confusing wording and run-on sentences

Specifically this part:

As the result when made into an infinite point version (i.e. when the amount of vanishing points exceeds the minimum amount required), a four point perspective image becomes a panorama that can go to a 360 degree view and beyond - when going beyond the 360 degree view the artist might depict an "impossible" room as the artist might depict something new when it's supposed to show part of what already exists within those 360 degrees.

This sentence seems to be missing a lot of punctuation, among other issues. "As the result" what? Try to simplify this sentence by removing sections that shouldn't change the overall meaning of the sentence (parenthetical remarks, for example, and anything after that misplaced hyphen).

As the result when made into an infinite point version, a four point perspective image becomes a panorama that can go to a 360 degree view and beyond.

Still confusing. Should there be a comma after "as the result"? If that's the case then "a four point perspective" doesn't make sense.

As a result of this sentence being confusing, I'm posing this "talk" section. As the result of this sentence being confusing is this talk section being posted I'd suggest changing it. In fact, I'd change the sentence to not begin with "as the result" since that obviously made my last sentence confusing too. Also I'm having a hard time figuring out how "as the result" can fit into a sentence that doesn't include the word "of" or "is" immediately following.

If I understood what this sentence was trying to say I'd go ahead and fix the run-on and fix the wording. Perhaps "A four point perspective, when made into an infinite point version, becomes a panorama with a view angle of 360 degrees and beyond." The sentence fragment after the hyphen is far more clear, though could still use a bit of rewording. --StarkRG (talk) 06:03, 17 April 2011 (UTC)

Mathematics

1. There is no evidence, as far as I know, that Giotto used an "algebraic means" to determine the spacing of the transversals. 2. The statement that "the apparent distance between a series of evenly spaced lines actually falls off with a sine dependence" is simply not true. "Sine" should read "inverse quadratic". 3. I also object the assertion that "To determine the ratio for each succeeding line, a recursive ratio must be used.[6]" The Bott's recursive formula is very cumbersome to use. For example it you want to determine the spacing of the 15th and 16th transversals you have to do 15 iterations. A simple algebraic formula is available (when the viewing distance and the height of the 'eye' are given. But these data or their equivalents are also needed to apply Bott's formula.) Therefore the word "must" in the original statement is misleading.

laotou@verizon.net — Preceding unsigned comment added by 96.227.227.193 (talk) 16:33, 11 November 2011 (UTC)

The discussion of the mathematics of perspective greatly minimizes the contribution of Alhazen and his theories on optics as outlined in Perspectiva. The single mention of Alhazen as learned by Biagio Pelacani da Parma, who simply influenced Alberti, downplays the contribution of the Islamicate world to the mathematical aspects of perspective. Since the header for the section is "Renaissance: mathematical basis," I am not sure if this fits in since it was written in 1028, technically before the Renaissance. However, I would like to highlight the contribution of Alhazen to the mathematics of perspecive a little bit more.--MartinezIJV (talk) 15:18, 5 April 2018 (UTC)

Although of course many say they just took it from the Indians.... Johnbod (talk) 23:22, 5 April 2018 (UTC)

I didn't know that. The source I was reading was focusing on the relationship between Islamic and European perspective. It does make sense, however, when I am reading what was already written in the article. What I was just wanting to make clear was where it all came from. If the chain doesn't stop in the Islamicate world, then that is also worthy noting.--MartinezIJV (talk) 21:57, 6 April 2018 (UTC)

Meaningless sentences

1) "A two-point drawing would have lines parallel to two different angles"

Lines can not be parallel to angles, only to other lines.

I can see what the writer intended to convey: the notion of two distinct vanishing points with two sets of lines converging on the two points, respectively. (There would be a constant angle between any line from the first set and any line from the second set, which I suspect was the idea underlying the use of "two different angles", although to introduce angles at all in this part of the description probably introduces unnecessary and confusing geometrical ideas).

Perhaps something like the following would be better: "A two-point drawing would have distinct sets of parallel lines converging on two different vanishing points" — Preceding unsigned comment added by 86.179.113.48 (talk) 07:43, 23 August 2012 (UTC)

There should be at least a reference to Aerial Perspective - the sense of depth conveyed by atmospheric effects, including reduced contrast, sharpness and, typically, a shift towards blue (usually) cause by atmospheric scattering of light. The justification is that this, too, is used in graphical arts to convey distance and depth. The reference should be in a separate, brief section with a link to the main article. — Preceding unsigned comment added by 86.179.113.48 (talk) 07:56, 23 August 2012 (UTC)

2) "The bottom of this triangle is the distance from the viewer to the wall."

This sentence equates a physical or theoretical object with a measurement.

The preceding sentence, "In viewing a wall, for instance, the first triangle has a vertex at the user's eye, and vertices at the top and bottom of the wall," implies that the "bottom of this triangle" runs from the viewer's eye to the bottom of the wall. This line does not describe the shortest distance from the viewer to the wall unless the viewer's eye is at floor level. I haven't read about similar triangles so I don't yet know how to correct this. 185.108.171.162 (talk) 3 November 2016

article hijacking

None of this says anything about linear perspective nor does it relate to Perspective in the sense of the article. I may have left too much. Prior to the Renaissance, Alhazen (al-Hasan Ibn al-Haytham, d. ca. 1041 AD), in his Book of Optics (Kitab al-manazir; known in Latin as De aspectibus or Perspectiva, written in 1021), explained that light projects conically into the eye.<ref>{{citation|first=Charles M.|last=Falco|title=Ibn al-Haytham and the Origins of Modern Image Analysis|date=12–15 February 2007|publisher=International Conference on Information Sciences, Signal Processing and its Applications}}</ref> Alhazen's geometrical, physical, physio-psychological optics resolved in this the ancient dispute between the mathematicians (Ptolemaic and Euclidean) and the physicists (Aristotelian) over the nature of vision and light. He also showed that vision is not merely a phenomenon of pure sensation (namely what results from the introduction of light rays into the eyes), but that it involves the faculties of judgment, imagination and memory.<ref>{{citation|title=A Philosophical Perspective on Alhazen's ''Optics''|author=[[Nader El-Bizri]]|journal=[[Arabic Sciences and Philosophy: A Historical Journal]]|volume=15|year=2005|publisher=[[Cambridge University Press]]|pages=189–218}}</ref> Alhazen's geometrical model of the cone of vision was theoretically sufficient to translate visible objects within a given setting into a painting, and this was also supported by his experimental affirmation of the visibility of spatial depth; hence of offering a proper ground for the idea of perspective.<ref>{{citation|title=La perception de la profondeur: Alhazen, Berkeley et [[Merleau-Ponty]]|author=Nader El-Bizri|journal=Oriens-Occidens, CNRS|volume=5|year=2004|publisher=[[Centre National de la Recherche Scientifique]]|pages=171–184}}</ref> Moreover, Alhazen presented a geometrical conception of place as spatial extension (a postulated void), and he refuted the Aristotelian account of topos as a surface of containment. Alhazen's mathematical definition of place was more akin to Plato's notion of Khôra or Chora as 'space', yet conceived on pure geometric grounds to facilitate the use of projections.<ref>{{citation|title=In Defense of the Sovereignty of Philosophy: al-Baghdadi's Critique of Ibn al-Haytham's Geometrisation of Place|author=Nader El-Bizri|journal=[[Arabic Sciences and Philosophy: A Historical Journal]]|volume=17|year=2007|publisher=[[Cambridge University Press]]|pages=57–80}}</ref> In all of this, Alhazen was concerned with optics, with vision, light and the nature of colour, as well as with experimentation and the use of optical instruments, and not with painting as such. Conical translations are mathematically difficult, so a drawing constructed using them would be incredibly time consuming. However, what Alhazen named a cone of vision (makhrut al-shu'a') corresponded also with the idea of a pyramid of vision, hence, offering a model that can be more easily projected in orthogonal drawings of side views and top views that are needed in the geometric construction of perspective. J8079s (talk) 03:46, 13 September 2012 (UTC)

"In contrast, natural scenes . . . have no vanishing points."

"In contrast, natural scenes often do not have any sets of parallel lines. Such a perspective would thus have no vanishing points."

"Any number of vanishing points are possible in a drawing, one for each set of parallel lines that are at an angle relative to the plane of the drawing." So a polygon with an even number of sides, 2n, would have n vanishing points. A circle being close to a polygon with an infinite number of sides would have an infinity of vanishing points. So rather than no vanishing points a natural scene would have an infinity. QuentinUK (talk) 18:29, 24 February 2013 (UTC)

Of course, there can be any number of focal points in a natural scene. But there are two flaws in your conclusion: (1) The word "would" does not follow from your argument; all you can say is "could". Even that is an useless overcomplication; while mathematically correct, it is just as absurd in the context of this article as if you insisted on replacing the number 2 with $\sum _{i=0}^{\infty }{\frac {1}{2^{i}}}$. Or do you have any useful application for an infinity of vanishing points?

You might have a point if the article said something like "natural scenes have no parallel lines". But that's not what it's saying; it only stresses the important fact that for the practice of depicting natural scenes, vanishing points are often not always useful or meaningful. — Sebastian 21:02, 8 March 2013 (UTC)

On second thought; I think I understand what you meant. The word "Such" in the second sentence was ambiguous; I now reworded it. Does that address your concern? — Sebastian 21:21, 8 March 2013 (UTC)

Misunderstandings of foreshortening

I'm not happy with calling foreshortening a "technique". It isn't a technique in the sense of Art techniques and materials. The fact that it has to be practiced doesn't make it so, any more than "English" would be considered a technique. Or even less so: While English has been developed by people to serve as a tool for communication, foreshortening is a natural effect. — Sebastian 21:15, 8 March 2013 (UTC)

Melozzo's usage of upward foreshortening in his frescoes at Loreto.

There also seems to be some confusion as to what the term is applied to. Renaissance : Mathematical basis speaks of "the technique of upward foreshortening" in the context of the picture shown to the right. But I don't see anything that matches our definition of a "visual effect or optical illusion that causes an object or distance to appear shorter than it actually is". If anything, I see the opposite effect - a forelengthening: the cupola seems rather taller than it is. Since this usage of "foreshortening" is not referenced, I considered tagging or removing it. But then we wouldn't have a good context for the illustration, which is interesting in the context of perspective. Instead of "the technique of upward foreshortening", how about if we just say "an upward vanishing point"? — Sebastian 21:32, 8 March 2013 (UTC)

For someone drawing foreshortening is a "technique" in that it is a "specialized procedures and methods used in" drawing to show something that doesn't exist (like creating the illusion of a 3D body "feet on" in a 2D drawing [2]) by exaggerated squashing down, overlapping, or converging the drawing. Its learned in drawing, so its a technique. In photography its a phenomenon[3].

Your right, the Loreto Fresko.jpg is a poor illustration of foreshortening. The people are squashed, vertically foreshortened, but the architecture is so removed from a real object you could never tell what the artist did to it. The invented nature of the architecture also makes it a poor illustration of a vanishing point. Fountains of Bryn Mawr (talk) 23:09, 8 March 2013 (UTC)

Melozzo da Forli, Angel with Tambourine, fresco from the apse of Santi Apostoli (Rome)

Would this better illustrate the concept? Ewulp (talk) 09:09, 9 March 2013 (UTC)

Dubious

The section "Present : Computer graphics" is factually quite vague. The statements that a raytracer computes "one ray for every pixel" or "does not have to compute the trajectories of millions of rays of light that pass from a light source, hit an object, and miss the viewer" might be true for the simplest possible program but not for any high-end raytracer that is actually used in production (cf. "photon mapping" or "Monte Carlo raytracing").

It is also unclear what is meant by a "modified version of perspective". Maybe the use of linear algebra to compute projections of points? Also the statement "the scene is a set of points" is not really true. A "set of triangles" could be a bit more accurate but neither an universal way of representing surfaces in CAD or other software.

"thus bypassing any descriptive geometry theorems used in perspective drawing." what theorems? and how are they bypassed? does this mean not utilizing vantage points? As well as some other parts of this article, this seems to ignore the fact that these "N-point" perspectives are drawing aids, not an integral part of human vision, reality, nor the mathematics perspective projections. — Preceding unsigned comment added by 84.253.217.60 (talk) 10:59, 15 June 2013 (UTC)

In reply to Mikkalai 07:56, 8 Feb 2004, above, there does seem confusion. “Picture plane is a spherical surface!”

From the top, and to be very deliberate: Perspective projection is a branch of Perspective (graphical). Therefore, perspective projection is graphical. It is a graphical approximation of a view in human vision. The similarity between perspective projection and human vision is that they both have vanishing points and horizon lines; therefore, the factor that makes perspective projection seem realistic, like human vision, is the presence of vanishing points and horizon lines. Since perspective projection owes its vanishing points and horizon lines to the presence of vanishing points and horizon lines in human visions, it behooves one to investigate how vanishing points and horizon lines are imposed in human vision.

The eyeball is spherical. Therefore, a straight line in nature is manifested by a gnomic projection to the retina-sphere; a gnomic projection to the retina-sphere creates a great-circle of intersection with the retina-sphere. For this phenomenon to occur, the gnomic projection must intersect the center of the retina-sphere, i.e., the focal point of the eye. So the question now becomes: How can one claim that the focal-point of the eye is located at the center of the retina-sphere (and not, as often depicted, on the retina-sphere proper)? It is because the cylindrical photoreceptors that transmit the light-ray signals to the nervous system are perpendicular to the retina-sphere. To wit: Per Brodal. The Central Nervous System, (p. 193): “As mentioned, the retina contains interneurons in addition to the photoreceptors, bipolars, and ganglion cells (Figure 7.4). The horizontal {Per Brodal employs the convention that the retina is “horizontal” - RPK} cells send their processes in the plane {i.e., spherical surface - RPK} of the retina ─ that is, perpendicular to the orientation of the photoreceptors and the bipolars to the retina{-sphere}." Therefore, for the light rays to reach the nervous system, they must pass through the perpendicular photoreceptors, parallel to the axes. Geometry tells us, this can only occur if the light rays first pass through the center of the retina-sphere, i.e., the focal point of the human eye.

If parallel lines are gnomically projected to the retina-sphere each line will create a great circle of intersection. The points of intersection of the great circles are the vanishing points on the retina-sphere and which converge at two points on the horizon line.

The horizon line on the retina-sphere is the great circle of intersection with a plane parallel to the plane defined by the parallel lines.

Of course, the retina-sphere with the images of the parallel lines cannot be perfectly developed onto a flat surface. Therefore, a graphical portrayal of the images must be approximated by established protocols. Pat Kelso (talk) 01:50, 31 May 2014 (UTC)

Un-encyclopedic additions.

I have reverted out these additions because they do not seem to be encyclopedic. The article should not contain how-to information WP:NOTHOWTO, unreferenced counter arguments, and comments on the text belong on this talk page. Fountains of Bryn Mawr (talk) 22:36, 28 December 2014 (UTC)

Methods of construction/WP:NOTHOWTO cleanup

There are five methods listed in "Methods of construction" and a section "Example" right below it explaining (some of it?). I suggest there should be 5 sub-headings under "Methods of construction" explaining each method. All the text in "Example" should be cleaned up/truncated since it reads as a "how-to" and put under (one of those 5 sections?). I question all of this because its so badly written its hard to tell what goes where. The information in "Example" reads like a combination of "Freehand sketching", constructing some form of "perspective grid" and "Mimicry". The claim that there are 5 methods needs supporting reference. Fountains of Bryn Mawr (talk) 16:36, 30 December 2014 (UTC)

Definition of perspective

The page reads: "The two most characteristic features of perspective are that objects are smaller as their distance from the observer increases; that they are foreshortened..." I think it would be better: The two most characteristic features of perspective are A)that objects appear to be smaller as their distance from the observer increases and B) that they are foreshortened... Juan Kis Solt (talk) 15:55, 31 December 2014 (UTC)

Staircase in two-point perspective

The first image in the page "Staircase in two-point perspective." doesn´t have any further explanation nor is it realted to any part of the page´s information.

Otherwise it could say: "Staircase in two-point perspective" for whose drawing six vanishing points have been used: two horizontal (for the treads and breathing spaces), two in height (for the ramps) and two auxiliary (measuring points). But although all this is true, it would be confusing to the neophyte, so I would leave out "in two point" because that particular part does not contribute to explain what can be seen. Besides that, I would move it to the part of the page it should be in.

How can I get authorization to make the corresponding editions on the page?Juan Kis Solt (talk) 15:55, 31 December 2014 (UTC)

Foreshortening

I created another image which shows the effects of foreshortening. SharkD  Talk  02:34, 10 December 2015 (UTC)

Origin of oblique projection

I wanted to discuss about this source : "Dubery and Willats (1983:33) write that 'Oblique projection seems to have arrived in China from Rome by way of India round about the first or second century AD."

This assertion seems rather weak and the authors themselves seems to agree with that so I would like to see their primary sources on that, we also have to consider that : - The earliest painting depicting some kind of perspective dates from the 5 to 3rd century BC in Changsha with the "Man riding a dragon" https://en.wikipedia.org/wiki/Silk_painting_depicting_a_man_riding_a_dragon Remark how the neck and his robe is painted showing depth. - Earliest Greeco-roman paintings which are from similar period (6th-5th-4th century) are completely in 2D and no attempt at perspective are made : https://en.wikipedia.org/wiki/Pitsa_panels or https://en.wikipedia.org/wiki/Tomb_of_the_Diver and https://en.wikipedia.org/wiki/Tomb_of_the_Leopards - Roman paintings is a direct descendant of Greek painting and there is also no paintings with perspective dating earlier than the 1st century BC (or at the very least 2nd century). - The lack of paintings in India from the 1st century with perspective which I have failed to found any.

With our current understanding, the origin of the first attempt at perspective is not specific to the greeco-roman world. — Preceding unsigned comment added by Shekil123 (talk • contribs) 12:12, 31 March 2016 (UTC)

The matter is of some interest, even if the sources do not state they have absolute confidence in the origins. It is not all right to rely on your own research, nor on what you can or can't find on Wikipedia, which by definition is not to be a reliable source. I suggest that we make a statement similar to the quotation in the cited source, as it represents the best guess of these authorities. Simply removing the claim seems somewhat bizarre. I'll reword it now, feel free to tweak it if need be. Chiswick Chap (talk) 13:21, 31 March 2016 (UTC)

Works for me, it's not my own research really because I'm just pointing out existing pieces of evidence. — Preceding unsigned comment added by Shekil123 (talk • contribs) 13:27, 31 March 2016 (UTC)

OK then, thanks, but we can't draw any conclusions from what images are on Wikimedia Commons, for example: they may be a random sample, a biased sample, or something else. They are not guaranteed to show earliest work or anything like that. The most we can say is, if we do have an image, then that work exists. We can't conclude anything from what isn't there. Chiswick Chap (talk) 13:31, 31 March 2016 (UTC)

Actually, I linked to the wiki image because it was the best quality I could find, it comes from the website of the museum of Hunan at Changsha where it currently located (being excavated there): http://www.hnmuseum.com/hnmuseum/eng/collection/collectionContent.jsp?infoid=0137fecd76e34028848337deb0d205ea

This is actually a pretty famous painting and is one of the relics prohibited from leaving china, here's art historian at UC Berkley James Cahill talking about it : https://www.youtube.com/watch?v=KJ4S-jCh4iE Also good additions, it helps in nuancing the issue.

Thanks. I'm all for famous paintings. Chiswick Chap (talk) 07:55, 1 April 2016 (UTC)

Zero-point perspective

The article says, "A zero-point perspective view is equivalent to an elevation." Can someone explain this? How does a perspective projection suddenly become a parallel perspective due to irregularities of the subject being drawn? I don't understand this. SharkD  Talk  20:56, 5 May 2017 (UTC)

Mantegna

It seems odd to cite the 'Lamentation' of Mantegna as an example of 'perfected' foreshortening technique when it definitely is not. The linked article on that painting itself recognises that the feet are far too small to be in accurate perspective. I would add that the head is far too large (unless Jesus was hydrocephalic) and the shoulders are probably too broad.109.149.91.155 (talk) 14:05, 20 August 2017 (UTC)

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Single vanishing point perspective

I don't understand a single vanishing point perspective, can some explain this Tshire777 (talk) 14:23, 14 May 2019 (UTC)

Paragraph about visual perception

I'd like to offer you to insert the following section as the first section after the introduction. I hope you all agree. Sciencia58 (talk) 15:57, 16 April 2021 (UTC)

Visual perception of perspective in real space

Visual perception of perspective in real space, in rooms, in settlements and in nature, is a result of several optical impressions and the interpretation by the visual system. The angle of vision plays an important role for the apparent size. Objects closer to the eye are perceived as larger while objects further away appear subjectively smaller.<ref>''[https://www.univie.ac.at/mikroskopie/1_grundlagen/optik/Grundlagen%20der%20Optik.pdf Grundlagen der Optik].'' page 24.</ref> Still the interpretation by the visual system can be more precise when seen in context with other structures in the visual field, especially convergent lines which are important in depth perception. Vision with two eyes, stereoscopic vision, is not essential for the perception of perspective, but it enhances the impression of the spatial. Regardless of whether the light rays entering the eye come from a three-dimensional space or from a two-dimensional image, they hit the inside of the eye on a surface, the retina. What a person sees in this process is based on a reconstruction by the visual system, in which one and the same retinal image can be interpreted both two-dimensionally and three-dimensionally. If a three-dimensional interpretation has been recognised, this receives preference and determines perception.<ref>Georg Eisner: ''[http://www.eisner-georg.ch/Andere/Perspektive/Perspektiven.pdf Perspektive und Visuelles System – Wege zur Wahrnehmung des Raumes]'' page 102–103 </ref>

• 
• 
  Context-dependent interpretation of the size.
• 
  The horizon line is at the height of the armrests.
• 
  View from a window on the 2nd floor of a house.
• 
  Mountain peak near the snow line and several mountain peaks above the snow line.
• 

In spatial vision, the horizontal line of sight can play a role. In the picture taken from the window of a house, the horizontal line of sight is at the level of the second floor (yellow line). Below this line, the further away objects are, the higher up in the visual field they appear. Above the horizontal line of sight, objects that are further away appear lower than those that are more nearby. To represent such spatial impressions graphically, one can use a vanishing point.<ref>Georg Eisner: ''[http://www.eisner-georg.ch/Andere/Perspektive/Perspektiven.pdf Perspektive und Visuelles System – Wege zur Wahrnehmung des Raumes]'' page 181</ref> When looking into far distances, perspective effects also partially result from the angle of vision. Measurements and calculations can be used to determine the proportion of the curvature of the earth in the subjectively perceived proportions.

Sciencia58 (talk) 09:00, 16 April 2021 (UTC) Sciencia58 (talk) 09:18, 16 April 2021 (UTC) Sciencia58 (talk) 11:34, 16 April 2021 (UTC) Sciencia58 (talk) 12:34, 16 April 2021 (UTC)

Its kind of wordy and confusing. Actually I can't make out what you are trying to explain after reading it several times. The first paragraph seems to be a stand alone lead in to support the second paragraph, perhaps that should be expanded elsewhere. Its single sourced to someones essay and reads like an essay. At least three of the image examples are unreadable at thumb size. Images need to be clear and readable at thumb. Fountains of Bryn Mawr (talk) 13:44, 16 April 2021 (UTC)

Perspective vision and depth perception are not exactly the same, although they are strongly related. The article should not only explain what perspective images look like and how they are created, but also why human eyes recognise them as such. It is good for the comprehensibility of the article, even for the layman, to describe the most important neuro-physiological processes first. Then the details are dealt with in the following sections. I didn't use one source but two. There is a plenty of other sources saying the same things in Englisch that can be added if you think it is necessary for such statements, which are more or less trivial for a biologist and neurophysiologist. The photos could also be shown in a different layout so that they are larger and easier to see without having to click on them. I always click on all the pictures in Wikipedia. That's what this function is for. Sciencia58 (talk) 14:15, 16 April 2021 (UTC)

This is what the article in the German Wikipedia looks like [4]. Sciencia58 (talk) 14:18, 16 April 2021 (UTC)

This article is graphical Perspective, representation on a flat surface of an image as it is seen by the eye, so a treatise on Visual perception is off topic. The suggested text straddles Visual perception, depth perception and (estimated size?). Within paragraphs it seems to stray off into further topics that are not explained or well written, which again just makes it confusing. Fountains of Bryn Mawr (talk) 20:50, 16 April 2021 (UTC)

I am sorry for those who are confused by interdisciplinary approaches. It is true that this article is specifically about the graphic representation of perspective. Yes, it would also be possible to place the section on perception in the article depth perception or, alternatively, to make a small article of its own out of it, with an introductory sentence and link to the article Perspective (graphical). Sciencia58 (talk) 07:03, 17 April 2021 (UTC) Sciencia58 (talk) 07:18, 17 April 2021 (UTC)

I have added another picture that I think needs no explanation. Sciencia58 (talk) 07:22, 17 April 2021 (UTC)

Eliminate one of the two pictures of cubes

The two pictures of the cubes showing how a perspective drawing is generated are the same, just different shading. One of the two should be eliminated. I vote to eliminate the first one and keep the second one, --Gciriani (talk) 19:32, 13 April 2023 (UTC)

References

Uncited material in need of citations

I am moving the following uncited material here until it can be properly supported with inline citations of reliable, secondary sources, per WP:V, WP:NOR, WP:CS, WP:NOR, WP:IRS, WP:PSTS, et al. This diff shows where it was in the article. Nightscream (talk) 19:45, 3 September 2022 (UTC)

Extended content

Overview Because each portion of the painted object lies on the straight line from the viewer's eye to the equivalent portion of the real object it represents, the viewer sees no difference (sans depth perception) between the painted scene on the windowpane and the view of the real scene. All perspective drawings assume the viewer is a certain distance away from the drawing. Objects are scaled relative to that viewer. An object is often not scaled evenly: a circle can be flattened to an eccentric ellipse and a square can appear as a trapezoid or any other convex quadrilateral. This distortion is referred to as foreshortening. Perspective drawings have a horizon line, which is often implied. This line, directly opposite the viewer's eye, represents objects infinitely far away. They have shrunk, in the distance, to the infinitesimal thickness of a line. It is analogous to (and named after) the Earth's horizon. Any perspective representation of a scene that includes parallel lines has one or more vanishing points in a perspective drawing. A one-point perspective drawing means that the drawing has a single vanishing point, usually (though not necessarily) directly opposite the viewer's eye and usually (though not necessarily) on the horizon line. All lines parallel with the viewer's line of sight recede to the horizon towards this vanishing point. This is the standard "receding railroad tracks" phenomenon. A two-point drawing would have lines parallel to two different angles. Any number of vanishing points are possible in a drawing, one for each set of parallel lines that are at an angle relative to the plane of the drawing. Perspectives consisting of many parallel lines are observed most often when drawing architecture (architecture frequently uses lines parallel to the x, y, and z axes). Because it is rare to have a scene consisting solely of lines parallel to the three Cartesian axes (x, y, and z), it is rare to see perspectives in practice with only one, two, or three vanishing points; even a simple house frequently has a peaked roof which results in a minimum of six sets of parallel lines, in turn corresponding to up to six vanishing points. Of the many types of perspective drawings, the most common categorizations of artificial perspective are one-, two- and three-point. The names of these categories refer to the number of vanishing points in the perspective drawing. In this photograph, atmospheric perspective is demonstrated by variously distant mountains Aerial perspective Main article: Aerial perspective Aerial (or atmospheric) perspective depends on distant objects being more obscured by atmospheric factors, so farther objects are less visible to the viewer. As the distance between an object and a viewer increases, the contrast between the object and its background decreases, and the contrast of any markings or details within the object also decreases. The colours of the object also become less saturated and shift towards the background colour. Aerial perspective can be combined with, but does not depend on, one or more vanishing points. One-point perspective A drawing has one-point perspective when it contains only one vanishing point on the horizon line. This type of perspective is typically used for images of roads, railway tracks, hallways, or buildings viewed so that the front is directly facing the viewer. Any objects that are made up of lines either directly parallel with the viewer's line of sight or directly perpendicular (the railroad ties/sleepers) can be represented with one-point perspective. These parallel lines converge at the vanishing point. One-point perspective exists when the picture plane is parallel to two axes of a rectilinear (or Cartesian) scene—a scene which is composed entirely of linear elements that intersect only at right angles. If one axis is parallel with the picture plane, then all elements are either parallel to the picture plane (either horizontally or vertically) or perpendicular to it. All elements that are parallel to the picture plane are drawn as parallel lines. All elements that are perpendicular to the picture plane converge at a single point (a vanishing point) on the horizon. Two-point perspective A drawing has two-point perspective when it contains two vanishing points on the horizon line. In an illustration, these vanishing points can be placed arbitrarily along the horizon. Two-point perspective can be used to draw the same objects as one-point perspective, rotated: looking at the corner of a house, or at two forked roads shrinking into the distance, for example. One point represents one set of parallel lines, the other point represents the other. Seen from the corner, one wall of a house would recede towards one vanishing point while the other wall recedes towards the opposite vanishing point. Two-point perspective exists when the picture plane is parallel to a Cartesian scene in one axis (usually the z-axis) but not to the other two axes. If the scene being viewed consists solely of a cylinder sitting on a horizontal plane, no difference exists in the image of the cylinder between a one-point and two-point perspective. Two-point perspective has one set of lines parallel to the picture plane and two sets oblique to it. Parallel lines oblique to the picture plane converge to a vanishing point, which means that this set-up will require two vanishing points. Three-point perspective Three-point perspective is often used for buildings seen from above (or below). In addition to the two vanishing points from before, one for each wall, there is now one for how the vertical lines of the walls recede. For an object seen from above, this third vanishing point is below the ground. For an object seen from below, as when the viewer looks up at a tall building, the third vanishing point is high in space. Three-point perspective exists when the perspective is a view of a Cartesian scene where the picture plane is not parallel to any of the scene's three axes. Each of the three vanishing points corresponds with one of the three axes of the scene. One, two and three-point perspectives appear to embody different forms of calculated perspective, and are generated by different methods. Mathematically, however, all three are identical; the difference is merely in the relative orientation of the rectilinear scene to the viewer. Curvilinear perspective By superimposing two perpendicular, curved sets of two-point perspective lines, a four-or-above-point curvilinear perspective can be achieved. This perspective can be used with a central horizon line of any orientation, and can depict both a worm's-eye and bird's-eye view at the same time. Foreshortening Two different projections of a stack of two cubes, illustrating oblique parallel projection foreshortening ("A") and perspective foreshortening ("B") Foreshortening is the visual effect or optical illusion that causes an object or distance to appear shorter than it actually is because it is angled toward the viewer. Additionally, an object is often not scaled evenly: a circle often appears as an ellipse and a square can appear as a trapezoid. Although foreshortening is an important element in art where visual perspective is being depicted, foreshortening occurs in other types of two-dimensional representations of three-dimensional scenes. Some other types where foreshortening can occur include oblique parallel projection drawings. Foreshortening also occurs when imaging rugged terrain using a synthetic-aperture radar system. In painting, foreshortening in the depiction of the human figure was improved during the Italian Renaissance, and the Lamentation over the Dead Christ by Andrea Mantegna (1480s) is one of the most famous of a number of works that show off the new technique, which thereafter became a standard part of the training of artists. (Andrea Mantegna is also an author of the Frescoes in the Camera degli Sposi; in which a part called "The oculus" uses foreshortening represented by the figures which look down upon the watchers.) History Rudimentary attempts to create the illusion of depth were made in ancient times, with artists achieving isometric projection by the Middle Ages. Various early Renaissance works depict perspective lines with an implied convergence, albeit without a unifying vanishing point. It is commonly accepted that the first to master perspective was Italian Renaissance architect Filippo Brunelleschi, who developed the adherence of perspective to a vanishing point in the early fifteenth century. It is said that his discovery was immediately influential on subsequent Renaissance art and was explored contemporaneously in manuscripts by Leon Battista Alberti, Piero della Francesca and others. Early history Various paintings and drawings from the Middle Ages show amateur attempts at projections of objects, where parallel lines are successfully represented in isometric projection, or by nonparallel ones without a vanishing point. In the Late Antique period use of perspective techniques declined. The art of the new cultures of the Migration Period had no tradition of attempting compositions of large numbers of figures and Early Medieval art was slow and inconsistent in relearning the convention from classical models, though the process can be seen underway in Carolingian art. Other artists of the greater proto-Renaissance, such as Melchior Broederlam, strongly anticipated modern perspective in their works but lacked the constraint of a vanishing point. Renaissance Perspective remained, for a while, the domain of Florence. Jan van Eyck, among others, failed to utilize a consistent vanishing point for the converging lines in paintings, as in the Arnolfini Portrait (1434). Gradually, and partly through the movement of academies of the arts, the Italian techniques became part of the training of artists across Europe, and later other parts of the world. Perspective features heavily in the research of the 17th-century architect, geometer, and optician Girard Desargues on perspective, optics and projective geometry, as well as the theorem named after him. Limitations For a typical perspective, however, the field of view is narrow enough (often only 60 degrees) that the distortions are similarly minimal enough that the image can be viewed from a point other than the actual calculated vantage point without appearing significantly distorted. When a larger angle of view is required, the standard method of projecting rays onto a flat picture plane becomes impractical. As a theoretical maximum, the field of view of a flat picture plane must be less than 180 degrees (as the field of view increases towards 180 degrees, the required breadth of the picture plane approaches infinity). To create a projected ray image with a large field of view, one can project the image onto a curved surface. To have a large field of view horizontally in the image, a surface that is a vertical cylinder (i.e., the axis of the cylinder is parallel to the z-axis) will suffice (similarly, if the desired large field of view is only in the vertical direction of the image, a horizontal cylinder will suffice). A cylindrical picture surface will allow for a projected ray image up to a full 360 degrees in either the horizontal or vertical dimension of the perspective image (depending on the orientation of the cylinder). In the same way, by using a spherical picture surface, the field of view can be a full 360 degrees in any direction. For a spherical surface, all projected rays from the scene to the eye intersect the surface at a right angle. Just as a standard perspective image must be viewed from the calculated vantage point for the image to appear identical to the true scene, a projected image onto a cylinder or sphere must likewise be viewed from the calculated vantage point for it to be precisely identical to the original scene. If an image projected onto a cylindrical surface is "unrolled" into a flat image, different types of distortions occur. For example, many of the scene's straight lines will be drawn as curves. An image projected onto a spherical surface can be flattened in various ways: An image equivalent to an unrolled cylinder A portion of the sphere can be flattened into an image equivalent to a standard perspective An image similar to a fisheye photograph

Illustrations

At first I thought, many of the images are just more of the same, and intended to remove one or two. But looking at the examples for "One-point perspective", nearly all of them, except for the graphic, the bad first one and pic of the rails, have actually two-point perspective, since their traversing lines are not parallel to the picture plane. So I'll remove these. Sorry. MenkinAlRire 19:52, 28 September 2023 (UTC)