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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”.
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)
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?
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.
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. Zhatt22:51, 13 October 2005 (UTC)[reply]
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 Lime14:19, 5 March 2006 (UTC)[reply]
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. -Volfy04:11, 26 October 2005 (UTC)[reply]
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.
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. Zhatt20:17, 8 February 2006 (UTC)[reply]
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 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)[reply]
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. --Allefant20:36, 4 July 2007 (UTC)[reply]
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 Lime14:47, 5 July 2007 (UTC)[reply]
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. --Allefant15:21, 5 July 2007 (UTC)[reply]
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 Bobby16:35, 23 July 2007 (UTC)[reply]
"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)[reply]
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.
“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)[reply]
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)[reply]
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)[reply]
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)[reply]
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.
The sentence:
"A two-point drawing would have lines parallel to two different angles"
Does not make any sense.
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)[reply]
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)[reply]
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]], [[Ibn al-Haytham|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)[reply]
"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)[reply]
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 . 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. — Sebastian21:02, 8 March 2013 (UTC)[reply]
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. — Sebastian21:15, 8 March 2013 (UTC)[reply]
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"? — Sebastian21:32, 8 March 2013 (UTC)[reply]
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)[reply]
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)[reply]
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)[reply]
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)[reply]
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)[reply]
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)[reply]
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.
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.
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)[reply]
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)[reply]
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
![[2]](https://en.wikipedia.org/wiki/File:Andrea_Mantegna_-_The_Lamentation_over_the_Dead_Christ_-_WGA13981.jpg){kind=link}
