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Perspective and intent in a Dali painting

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Jonathon13: Dali purposefully ignored the knowledge gained during the early Renaissance regarding the acurate portrayal of three dimensions on a two dimensional picture plane and distorted the lines of the cross in this painting.

The reason this painting is subtitled Corpus Hypercubus is because the cross is created from an unfolded hypercube. A hypercube is the four dimensional analogue of a typical three dimensional cube. You can view a picture of one here. In the same way that a three dimensional cube can be unfolded into a two dimensional image composed of six squares, a four dimensional hypercube can be "unfolded" into a three dimensional image of eight cubes. As you will notice, Dali's cross is made up of eight cubes.

By the way, as an aside: you should study 19th century art. Artists in many of the known movements began to challenge the notion that the artist's job was to portray the three dimensional world on a two dimensional surface as closely as possible. Hence, you have movements like Realism, in which artists experimented with the picture plane by abandoning such notions as vanishing points. The portrayal of space became increasingly (and intentionally) unrealistic. The effect from the beholder's perspective was that the picture appeared "flat." This effect was reinforced with other techniques. For example, many artists moved the light source directly in front of the painting so that they would not have to depict shadows. This heightened the effect of two dimensionality. If you read the writings of some of these artists, you will see that they were heavily influenced by Japanese woodblock prints. A good pictoral example of all of these ideas synthesized is Courbet's The Stone Breakers.

Edited by adrock3215
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As I said earlier, Dali's error was to use 2-point perspective in a painting which needs 3 points. The vertical lines are parallel to each other. They do not converge at a vanishing point, which is a very common method used by artists who don't fully understand perspective, even though it can lead to distortion -- they're usually not aware of the distortion.

Assuming that Dali wanted to be true to perspective, I do not understand why you seem to think that he was in error, that he should have used 3-point perspective instead of 2-point perspective. There is, after all, a valid use of 2-point perspective, and not every 2-point perspective (image) needs a 3rd vanishing point.

I know of no perspective principle, other than a judgement call, for when one has gone to the limits of 2-point perspective and needs to add a 3rd vanishing point.

The same applies to 1-point perspective. For example, this old painting by Piero della Francesca "Ideal City" (c. 1470) used 1-point perspective, and although the center portion looks normal, the right and left extremes look distorted. But what can you do? You can't add vanishing points to the left and to the right. No, the angle of view is too much to not appear distorted even with proper perspective, one-point in this case.

The problem has to do with the fact that we see with an angle of vision of about 60 degrees, I believe it is, and as long as the scene fits within that angle of view, with 1-point or 2-point perspective, we don't see distortions. There's a limit to what you can put on a 2D surface without distortions even if you are faithful to the science of perspective.

Given the angle of view in Dali's painting, "Corpus Hypercubus," even if he had decided to use a 3rd vanishing point, it would have been so distant above that the amount of convergence in the cross would have been very slight, even pointless. I myself do not find any noticeable distortion due to his keeping to only a 2-point perspective, even in the image you posted of that painting rotated 60 degrees, certainly nothing comparable to the noticeable distortion in the painting, "Ideal City."

I agree with you that Dali wasn't retarded. I would never claim that someone was retarded just because he was apparently limited to a basic understanding of 2-point perspective (and made common errors while using the 2-point system). Many great artists before and after him have had the same limits of knowledge, and they made the same kinds of errors.

Would you please indicate what the common errors in 2-point perspective that Dali made? Perhaps some image examples?

So, your theory is that Dali was a master of 3-point perspective but he avoided using it, and that he distorted the vertical axis on purpose?

I suppose it's possible that you're right. But then I have to wonder what reasons you think he might have had for his many other deviations from proper perspective, including in the horizontal axes of his "Corpus Hypercubus," as well as in his other paintings. I mean, I always assumed that his distortions were errors since they seem to have a certain consistency to them, and they're the same errors that most people make when they don't quite understand the art of perspective -- they suggest that he had a basic understanding of 2-point perspective but never learned how to properly apply some its features.

As well, what are the deviations from proper perspective "in the horizontal axes" you are referring to in his painting, "Corpus Hypercubus"?

Even with the advantages of the tutorial that I posted...snip....

The tutorial you mention, what are you referring to? Are you talking about your initial question as to what was wrong with Dali's perspective in his painting, "Corpus Hypercubus"?

Thank you.

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Given the angle of view in Dali's painting, "Corpus Hypercubus," even if he had decided to use a 3rd vanishing point, it would have been so distant above that the amount of convergence in the cross would have been very slight, even pointless.

On the contrary, it's quite noticeable, the cross looks like it gets "fatter" the further up you go. It's most noticeable on the left edge of the cross-members. That cube looks like it is almost a handspan wider at the top than at the bottom.

I myself do not find any noticeable distortion due to his keeping to only a 2-point perspective, even in the image you posted of that painting rotated 60 degrees, certainly nothing comparable to the noticeable distortion in the painting, "Ideal City."

What image rotated 60 degrees? The other painting posted is not "Corpus Hypercubus."

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On the contrary, it's quite noticeable, the cross looks like it gets "fatter" the further up you go. It's most noticeable on the left edge of the cross-members. That cube looks like it is almost a handspan wider at the top than at the bottom.

One the contrary, it is not "quite noticeable" to me. (Unless you are going to insist that what is noticeable to you is in fact noticeable to me.) What distortion there may appear to be is due to the same issue as the one seen in Piero della Francesca "Ideal City" -- at some point, one pushes the limits of perspective drawing, and one starts to notice distortions.

To date, from a quick look, there have been seven images posted or linked to in this thread:

The first one was in the initial post (for this thread) by Thales, quoting a portion of a post by Jonathan13 in another thread:

*** Mod's note. Split from another topic. - sN ***

It's distorted. Can anyone here identify what's wrong with the perspective and proportions?

What image rotated 60 degrees? The other painting posted is not "Corpus Hypercubus."

The second one, posted or linked to by Jonathan, includes the same image (a portion of Dali's painting, "Corpus Hypercubus") rotated 60 degrees because he thought that doing so made the distortion more obvious:

The distortion can be easier for some people to see when the painting is rotated 60 degrees, like this, which can give it the impression that you're looking down on it from above.

The third image, posted or linked to in this thread by Jake_Ellison, was the following showing the entire painting, not just the portion which Jonathan13 had posted:

"Needs" a different perspective is a bit strong, as is the word "incorrect". You're suggesting that Dali made a mistake. If it had proper perspective, Jesus would be a lot smaller than Mary as well:

See it here.

The fourth image, posted or linked to in this thread by Thales, is an image of another of Dali's paintings showing that he understood that there can be instances in which a vertical vanishing point is warranted:

Here is another painting by Dali which shows perspective up/down:

See it here.

The fifth image, posted or linked to in this thread by JMeganSnow, was one by Michael Whelan. Although I understand that Dali believed in his own reincarnation, unless he did come back as Michael Whelan, I assume it's safe to say that it is not a painting by Dali.

One of my favorite modern artists, Michael Whelan, intentionally uses false perspective in some of his works to, in his own words, "create a sense of looming immensity". He tried it with the "correct" perspective and didn't like it as much--it lost a lot of the visual impact. So he fixed it..

The sixth image, posted or linked to in this thread by adrock3215, is an image of a hypercube, not a painting by Dali.

Jonathon13: Dali purposefully ignored the knowledge gained during the early Renaissance regarding the acurate portrayal of three dimensions on a two dimensional picture plane and distorted the lines of the cross in this painting.

The reason this painting is subtitled Corpus Hypercubus is because the cross is created from an unfolded hypercube. A hypercube is the four dimensional analogue of a typical three dimensional cube. You can view a picture of one here.

The seventh, and final, image, posted or linked to in this thread by me, is the image of the painting "Ideal City," not a painting by Dali.

The same applies to 1-point perspective. For example, this old painting by Piero della Francesca "Ideal City" (c. 1470) used 1-point perspective, and although the center portion looks normal, the right and left extremes look distorted.

There have only been two paintings by Dali for which images have been posted or linked to in this thread, one of Christ on a cross seen from above with a vertical vanishing point near the bottom of the picture, and three different images of Dali's "Corpus Hypercubus" -- two images were partials, one was whole. These images were the painting in discussion.

I have done a Google image search for "Corpus Hypercubus" and that painting, the one identified in this thread as being "Corpus Hypercubus" is the one I find in my search.

If that painting is not "Corpus Hypercubus" by Dali, would you provide a link to an image of the painting by Dali that is, "Corpus Hypercubus"?

Edited by Trebor
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One the contrary, it is not "quite noticeable" to me. (Unless you are going to insist that what is noticeable to you is in fact noticeable to me.) What distortion there may appear to be is due to the same issue as the one seen in Piero della Francesca "Ideal City" -- at some point, one pushes the limits of perspective drawing, and one starts to notice distortions.

This is NOT a pushing of limits of perspective. We are nowhere near its limits here. It is a failure (or conscious decision not) to use it properly. The distortion in Ideal City (which could be pushing it) is much less marked.

As for the other matter, when I scanned the thread, I looked for pictures actually visible and missed the links.

The rotated image makes it somewhat more obvious what the distortion is, and the fix would be obvious. If you don't see it there, dude, you are blind.

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As I mentioned in post #11, there are more deviations from true perspective in Dali's "Hypercubus" painting (as well as in his other works) than the one in the vertical axis that I've pointed out. There are also obvious deviations in the horizontal axes, but they're different types of deviations than in the vertical axis. Can anyone here identify them, demonstrate the means by which they can be measured, and explain why you think they're not errors but intentional distortions?

J

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To add to this, would you please give the names (and perhaps some links to images) of some of the others of Dali's paintings in which you say that you've noticed other deviations from normal perspective? You've said this a few times; some actual paintings would be helpful.

-------------------

As for this painting, and your current question, it seemed to me that his right-hand vanishing point for the cubed-cross is lower than the left-hand one. But, were the cross meant to be slightly tilted, then that would account for that, or perhaps I am incorrect. My means were crude.

Other than that, I assume that you're referring, for one thing perhaps, to the tiles and that they do not look square, but rectangular. (Of course, that would assumes that Mr. Dali intended for them to be square, not rectangular.)

Or, are you referring to the geometric shape, the platform, that the woman is standing on. As it is, it appears to either be non-square and skewed, perhaps slopping upward towards the cross and leaned to the right. It's angle — defined by the right-side edge — stands out in great contrast to the rest of the image, but points towards the cross. The "front" edge of that platform she's standing on, the edge in front of the woman's feet, would not vanish to the horizontal left perspective point. The platform, is either not squared or it's tilted, not horizontal. It is not in sync with the rest of the paintings perspective, and therefore stands out by contrast. Perhaps it suggests that she is on something unstable.

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My guess is that Ayn Rand liked the 1954 Crucifixion, that DOESN'T have the hypercube cross. (I attached it)

This is something I could see being her favorite painting. It reminds me of Howard Roark!

For a large version go here:

http://www.dali-gallery.com/html/galleries/paintings.htm

Click Art gallery. Then under Galleries choose paintings.

Then click gallery 19 and scroll down. (Colossus of Rhodes is also good)

post-6595-1248038113_thumb.jpg

Edited by Cello
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To add to this, would you please give the names (and perhaps some links to images) of some of the others of Dali's paintings in which you say that you've noticed other deviations from normal perspective? You've said this a few times; some actual paintings would be helpful.

Here are some examples (it may take some time before the pictures appear in full resolution)

http://uofugeron.files.wordpress.com/2009/...nce-of-time.jpg

http://z.about.com/d/arthistory/1/0/c/i/da...oma_0708_02.jpg

http://z.about.com/d/arthistory/1/0/h/i/da...oma_0708_07.jpg

http://z.about.com/d/arthistory/1/0/i/i/da...oma_0708_08.jpg

http://z.about.com/d/arthistory/1/0/u/i/da...oma_0708_20.jpg

http://tinyurl.com/n48v7g

They all have some platform or a similar structure that logically would be horizontal, but that has the perspective of a strongly sloping surface (in most cases sloping upward seen from the viewer).

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Thank you, Tensorman. Very helpful.

Jonathan13, are those suitable for the distortions you say you've noticed in many others of Dali's paintings?

Hopefully she won't mind, but does anyone else notice some similar problem with Ifat's recently posted painting?

I do not mean some distortion in the figure, but in perspective.

Assuming that I am correct, perhaps Ifat will find this helpful.

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Where is the horizon? Where then is one's view point in relation to the figure? (Where does the horizon, the viewer's eye-level, intersect the figure?)

The horizon must be lower than the hills at the left side, somewhere between the hill/air border and the hill/water border at the left, it would intersect the figure somewhere at her left breast. That implies that the perspective of the figure is also wrong, unless you suppose that she's leaning to her left side, which is contradicted by the position of the rest of her body. From the figure alone you'd guess that the horizon is somewhere at the lower part of her neck.

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The horizon must be lower than the hills at the left side, somewhere between the hill/air border and the hill/water border at the left, it would intersect the figure somewhere at her left breast. That implies that the perspective of the figure is also wrong, unless you suppose that she's leaning to her left side, which is contradicted by the position of the rest of her body. From the figure alone you'd guess that the horizon is somewhere at the lower part of her neck.

I believe that we're in agreement.

Yes, the horizon (of the scene) is somewhere near the distant waterline -- where the water meets the distant shore. It can't be too high because our view of the figure seems to be one with our eye-level close to the height of her left breast, as you note. Actually a little below it, I'd say. The viewpoint seems to be that of someone standing beside her, a few feet away, standing lower in the water then the girl.

Water is level; it vanishes to the horizon. Whatever the observers height is above the water, his line of sight intersects the same height, in perspective, above the water, at any distance from the observer.

So, were someone else, about our height, standing in the water in the distance near he distant shore, their eyes at the same level as ours, the line from our eyes through their eyes would go to the horizon, would vanish to the horizon, intersecting with the horizon line. [Visualizing a person there can help give an estimate of where the horizon of the scene, as drawn, is.]

So, we're looking at the girl from her side, but we can see the top plane of her chest. But we're below her chest, so we should not be able to see the top plane, the front, of her chest given that she is leaning backwards, not unless, as you say, she is also leaned over towards us.

All of this is an assumption on my part, perhaps wrong. I assume that Ifat used some photo reference for her model, that she liked the pose and wanted to use it in a scene. (She did mention having a model to work from, but she didn't say whether her model was a photo or a live person.) To do such a thing, to put a figure into a scene, one has to be aware of the perspective not only of the scene but of the image of the figure that one has chosen to place in the scene. Just because the figure looks right in one context, doesn't mean it will in another context, largely due to perspective.

In my view, were Ifat to move the horizon way up, even above the girls distant, right elbow, then the whole picture would lose the sense that something is amiss. Why there, at the elbows?

I'm starting with the assumption that the girl is not leaning towards us or away from us, side to side, only leaning backwards. She looks comfortable, relaxed, not as though she's putting forth the effort to hold herself upright sideways.

As with my earlier point, any two points at the same height yet at different distance from us, the viewer, would be in line; they would vanish to the horizon, or the line drawn to connect them would do so. If our eye-level is that same height, then they will all line up with the horizon line.

In her figure, the two elbows come close to meeting this requirement. Close. So to me they suggest the best general height for a horizon, assuming that the figure is not going be changed to fit the existing scene, but the scent changed to fit the figure.

For that reason, I'd say that the horizon for the picture, if the perspective of the girl isn't changed, should be a bit above the elbows. That would make the perspective of the figure fit into the perspective of the scene.

Else, the perspective of the figure needs to be changed to fit the scene.

Edited by Trebor
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As for this painting, and your current question, it seemed to me that his right-hand vanishing point for the cubed-cross is lower than the left-hand one. But, were the cross meant to be slightly tilted, then that would account for that, or perhaps I am incorrect. My means were crude.

The vanishing point could be very slightly lower, but that's not what I'm talking about. A minor discrepancy like that could be slight skewing due to how the image was photographed or scanned, and might not be in the original painting.

Other than that, I assume that you're referring, for one thing perhaps, to the tiles and that they do not look square, but rectangular. (Of course, that would assumes that Mr. Dali intended for them to be square, not rectangular.)

Or, are you referring to the geometric shape, the platform, that the woman is standing on. As it is, it appears to either be non-square and skewed, perhaps slopping upward towards the cross and leaned to the right. It's angle — defined by the right-side edge — stands out in great contrast to the rest of the image, but points towards the cross. The "front" edge of that platform she's standing on, the edge in front of the woman's feet, would not vanish to the horizontal left perspective point. The platform, is either not squared or it's tilted, not horizontal. It is not in sync with the rest of the paintings perspective, and therefore stands out by contrast. Perhaps it suggests that she is on something unstable.

No, I wasn't talking about any of those issues, which could be intentional deviations -- I think they're probably not all intentional, but some of them could be. The things that I'm talking about involve inconsistencies in the proportions of Dali's divisions of objects and spaces, and just to be clear, when I said that the problems are in the horizontal axes, I didn't mean just the horizontal planes, buy also vertical planes as they diminish to the vanishing points on the horizon line.

Thank you, Tensorman. Very helpful.

Jonathan13, are those suitable for the distortions you say you've noticed in many others of Dali's paintings?

Yes, some of the proportion problems appear in those examples, but they're not the paintings that I had in mind since they're mostly done in 1-point perspective (not that they don't also have their own set of problems that are peculiar to Dali's use of 1-point perspective).

If I have time later this week, I'll try to post some images illustrating the issues that I'm talking about.

J

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Just for the sake of clarity, you've quoted me as saying:

...snip...

The vanishing point could be very slightly lower, but that's not what I'm talking about. A minor discrepancy like that could be slight skewing due to how the image was photographed or scanned, and might not be in the original painting.

...snip...

In that portion of my message which you quoted, I did not say that. I'm sure that it was just a simple, inadvertant error, but I thought I should say something.

No, I wasn't talking about any of those issues, which could be intentional deviations -- I think they're probably not all intentional, but some of them could be. The things that I'm talking about involve inconsistencies in the proportions of Dali's divisions of objects and spaces, and just to be clear, when I said that the problems are in the horizontal axes, I didn't mean just the horizontal planes, buy also vertical planes as they diminish to the vanishing points on the horizon line.

The only thing else that stands out readily to me, with respect to this Dali painting, is the alignment of the four small cubes and the Christ figure with the large, cube-structured cross.

There's an ambiguity due to the fact that the small cubes are in front of the Christ, overlapping him, and the Christ is in front of the large cross, but some of the edges of those four small cubes critically align with some of the edges in the large, cubed, forward projecting portion of the cross, behind the Christ.

Were the four cubes aligned with the "X" axis of the large cross, they would not be where they are; they'd be further up and to the left in the picture frame. Same for the Christ.

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In that portion of my message which you quoted, I did not say that. I'm sure that it was just a simple, inadvertant error, but I thought I should say something.

Thanks. You're right that it was an error. Somehow I neglected to separate my comment from yours when responding to you about one vanishing point being lower than the other.

I've tried to correct the post, but it appears that its editability window has expired.

J

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