1-point perspective Room with 2- and 3-point Objects possible?

[Robert_N]

Thanks a lot for your time, I assume this is the correct subforum for my question, if not, please excuse my mistake.

Is it possible to have a 1-, a 2- and a 3-vanishing-point perspective object in one room? I’d like to know this out of curiosity and for understanding and teaching drawing.

More specifically, I would like to know, whether it is possible to produce a drawing of a room with classic 1-point central perspective (i.e. Da Vinci’s painting of The Last Supper) and fill it with objects that are drawn in 2- and 3- point perspective, while still making sense, as in depicting a human’s impression in an idealized way without the objects contradicting each other.

1)
I imagine the following might be possible:
You put a box into the room, on the ground. The box is perfectly parallel on each side to the room and therefore follows the same single vanishing point while having two non-vanishing axes. Now you rotate the box around itself (ie 40°), like a bottle head, while still having it sit on the ground and remain one non-vanishing axis. Now the box follows two vanishing points, that probably lay outside of the room/image, in case of the last supper motive.

Check: Is this correct or is there no “right way” of drawing a 2-point box into a 1-point room?

2)
If the above assumption is correct, would rotating the box around another axis, by momentarily putting it on one corner like a Dreidel, create a 3-point perspective look, with 3 vanishing points surrounding the box?

3)
Is there any other way one might put all 3 linear perspectives into one image without using tricks such as attaching/stitching a 3-point scene to the top and bottom of the room, as it’s done in Disney movies? That would be a contradiction between 1 and 3 vanishing points, as the walls either follow 1 or 3.
Example (actually slightly rounded additionally):
http://one1more2time3.files.wordpress.com/2010/12/dance-of-hours-aaa.jpg[/PLAIN]

Thank you again for your time, looking forward to hear your opinions!

Robert

 

[DaveC426913]

Is it possible to have a 1-, a 2- and a 3-vanishing-point perspective object in one room? I’d like to know this out of curiosity and for understanding and teaching drawing.

More specifically, I would like to know, whether it is possible to produce a drawing of a room with classic 1-point central perspective (i.e. Da Vinci’s painting of The Last Supper) and fill it with objects that are drawn in 2- and 3- point perspective, while still making sense, as in depicting a human’s impression in an idealized way without the objects contradicting each other.

It is indeed possible to have a 3 vanishing point image one of the points visible in the image.

In an astonishing bit of synchronicity, I've been drawing exactly that in my sketchbook the last couple of nights.

But there are constraints. You can't have the visible VP in the middle of the image, it has to be to the side. Diagram 1 is OK because the distortion is not visible in any object. Diagram 2 is poor because an object draws attention to the area where the distortion is quite noticeable.

Now you rotate the box around itself (ie 40°), like a bottle head, while still having it sit on the ground and remain one non-vanishing axis. Now the box follows two vanishing points, that probably lay outside of the room/image, in case of the last supper motive.

Check: Is this correct or is there no “right way” of drawing a 2-point box into a 1-point room?

Nothing wrong with any of that.

3)
Is there any other way one might put all 3 linear perspectives into one image without using tricks such as attaching/stitching a 3-point scene to the top and bottom of the room, as it’s done in Disney movies? That would be a contradiction between 1 and 3 vanishing points, as the walls either follow 1 or 3.
Example (actually slightly rounded additionally):
http://one1more2time3.files.wordpress.com/2010/12/dance-of-hours-aaa.jpg[/PLAIN]

Ah well that's the trick, isn't it? You can't do it without distorting straight lines. By the way, it is not a "trick", it really does this. Take a picture with a camera and try to find a straight line in it. They are all curved (with few exceptions).

To get an image with minimally curved lines, you need to use a longer focal length (such as 50mm or more). Longer focal length = narrower field of view. Narrow field of view means it is impossible to get more than one vanishing point in the frame.BTW, note the those Disney scene panoramas can have any number of vanishing points up to and including 6.

 

[Robert_N]

Thanks for your quick reply.

In an astonishing bit of synchronicity, I've been drawing exactly that in my sketchbook the last couple of nights.

Lucky me!

To get an image with minimally curved lines, you need to use a longer focal length (such as 50mm or more). Longer focal length = narrower field of view. Narrow field of view means it is impossible to get more than one vanishing point in the frame.

My goal is not to get the vanishing points into the frame. My goal is to have objects inside the room that follow 1, 2 and 3 vanishing points. It’s fine if those lay way outside the image.
But I want the scene to incorporate only linear perspective, no curved distortions as with 4 or more vanishing points (fish eye).

I’m especially curious if my logic of “creating one vanishing point per axis” is faulty.

1)
We start with 3 dimensions and axes of a cube. In the central/1-point perspective one axis starts to vanish to 1 vanishing point, 2 remain unchanged (perfectly parallel, never meet).

2)
Now we rotate around another axis and get 2 vanishing axes and two corresponding vanishing points. But the vertical lines still remain perfectly parallel.

3)
When I assumed that rotating the cube so said third axis would not be parallel either, would create yet another, third vanishing point, two illustrators told me I was wrong, because “that’s not how things work”. I’m not convinced.

Does rotating around an axis always create a new vanishing point? To me it seems that way. The distortion might be too little to be obvious though and the vanishing points would probably be quite far outside of the image.

 

[DaveC426913]

I’m especially curious if my logic of “creating one vanishing point per axis” is faulty.

Yeah. I'm starting to see a problem too.

1)
We start with 3 dimensions and axes of a cube. In the central/1-point perspective one axis starts to vanish to 1 vanishing point, 2 remain unchanged (perfectly parallel, never meet).

Cool. Though note, this is already artificial. In the real world you cannot have this. It is impossible to have a 3 dimensional object represented in two dimensions without some form of distortion. No two straight parallel lines can ever appear truly straight in an image.

Here's why. Each of the 2 straight lines (let's go with the top front and bottom front edges of the cube) can be simplistically represented by at least 3 points: left corner, one in the middle, right corner. There is no way that these 6 points can be simultaneously equidistant from the observer (or image plane). At least 2of the 6 points must be closer or farther away, therefore they will appear closer together in the image, therefore they have a vanishing point. See diagram 1.

2)
Now we rotate around another axis and get 2 vanishing axes and two corresponding vanishing points. But the vertical lines still remain perfectly parallel.

You don't need another axis. The first one will do. If you rotate around its vertical axis (let's say 1 degree counterclockwise), you will create a new VP as the front face goes from parallel into perspective. Your original VP, which was centre frame, moves a little to the left, while your new one for the face of the cube, goes from infinity at left-and-right to something-less-than-infinity-to-the-right.
See diagram 2.

3)
When I assumed that rotating the cube so said third axis would not be parallel either, would create yet another, third vanishing point, two illustrators told me I was wrong, because “that’s not how things work”. I’m not convinced.

Does rotating around an axis always create a new vanishing point?

Depends on how many you started with. If any rotation causes any plane to go from orthagonal-to-the-line-of-sight, then it will go
from a VP at infinity (i.e. no VP)
to a VP-at-less-than-infinity (i.e. a new VP).

 

[Robert_N]

Though note, this is already artificial. In the real world you cannot have this.

Right, that’s why I’m asking in regard to the idealized representation of a perfect 1-point-perspective room. Are there any “rules” for objects which are not following this one vanishing point or is combining these ways of visual representation in a coherent way impossible?

 

[DaveC426913]

Right, that’s why I’m asking in regard to the idealized representation of a perfect 1-point-perspective room. Are there any “rules” for objects which are not following this one vanishing point or is combining these ways of visual representation in a coherent way impossible?

I'm afraid I have no answer to that because I don't really understand it. You'd have to ask more specifically.

 

[Robert_N]

Please excuse the delay of my reply. I made this video to illustrate my question unfortunately I’m not allowed to post a link to it yet.

The URL is

www. vimeo .com [Slash] 43313385

Sorry for the crappy voice!

 

[DaveC426913]

Please excuse the delay of my reply. I made this video to illustrate my question unfortunately I’m not allowed to post a link to it yet.

The URL is

www. vimeo .com [Slash] 43313385

Sorry for the crappy voice!

You could certainly put all three type of perspective in the same illo. You must remember that perspective objects in illos are approximations, since you will not get those straight line anywhere in a real image. (You can have a very limited number of straight lines in a real image. All the rest will be distorted into curves.)

So, in a drawing where there is a 3-point perspective box, you can certainly draw a 1-point perspective box, but it would not be accurate.

 

[Robert_N]

You could certainly put all three type of perspective in the same illo. You must remember that perspective objects in illos are approximations, since you will not get those straight line anywhere in a real image. (You can have a very limited number of straight lines in a real image. All the rest will be distorted into curves.)

So, in a drawing where there is a 3-point perspective box, you can certainly draw a 1-point perspective box, but it would not be accurate.

Well but then you could also say the room isn’t accurate because it consists of straight lines. The human eye, its distortions and all the error of perception aren’t accurate in any way, we got that out of the way. The question is, does a 3-point-p. object work with a 1-point-p. room or are they incompatible due to their rules? Does it work with a 2-point-p. object but not with a 3-point-p. object for example?

Here’s a different way to look at it. If we take a the first simple box in the video, drawn in 1-point-p. and rotate it 90° in any direction, without moving it away, it will look identical, because it’s a cube. This means we can rotate it to make the front side the new upside. By doing this we turn the parallel borders to the left and right of the front side into the distorted borders of the top side that follow the single vanishing point.
If however we stop half of the way, at 45°, shouldn’t we be in between the two states, meaning in between no distortion (parallel) and the vanishing point of the top side? We would see the vanishing point wander from infinity (above the image) slowly down the room until it meets with the old vanishing point and the box looks identical again.

Add the original rotation for the 2-point-p. and you have rotated it about two axes. To me it seems impossible to draw the box rotated about two axes without using 3 vanishing points unless an orthogonal view would be applied which clearly is incompatible with the room.

 

[DaveC426913]

Well but then you could also say the room isn’t accurate because it consists of straight lines. The human eye, its distortions and all the error of perception aren’t accurate in any way, we got that out of the way.

Let's be clear here. We're not talking about inaccuracies in perception or distortions. The limited straight lines are a fact of the geometry. Any time a 3 dimensional space is projected into a 2 dimensional space, you're going to run into this limitation of straight lines to a greater or lesser degree - no matte how idealized you make the scenario.

The question is, does a 3-point-p. object work with a 1-point-p. room or are they incompatible due to their rules? Does it work with a 2-point-p. object but not with a 3-point-p. object for example?

Here’s a different way to look at it. If we take a the first simple box in the video, drawn in 1-point-p. and rotate it 90° in any direction, without moving it away, it will look identical, because it’s a cube. This means we can rotate it to make the front side the new upside. By doing this we turn the parallel borders to the left and right of the front side into the distorted borders of the top side that follow the single vanishing point.
If however we stop half of the way, at 45°, shouldn’t we be in between the two states, meaning in between no distortion (parallel) and the vanishing point of the top side? We would see the vanishing point wander from infinity (above the image) slowly down the room until it meets with the old vanishing point and the box looks identical again.

Add the original rotation for the 2-point-p. and you have rotated it about two axes. To me it seems impossible to draw the box rotated about two axes without using 3 vanishing points unless an orthogonal view would be applied which clearly is incompatible with the room.

Well, yes. If you rotated it about two axes, you'd end up with three vanishing points. That's pretty straightforward.Perhaps it would be worth pointing out that even a one point perspective cube is a falsehood. It will not have straight edges. i.e. it will not have vanishing points at infinity. Vanishing points are a drawing hack.

Start with a one foot square, projects on a 2D image from a distance of 10 feet. Look at the front top and bottom edges and at the midpoints of them. Those points are one foot apart, and 10 feet from the observer.

Now look at the end points of the front top and bottom edge. They are more than 10 feet away; they are (10[sup2[/sup]+5²)^1/2 feet away. Therefore, they will be slightly closer together in the 2D image than the points that are only 10 feet away. Even the 1-point perspective cube is represented incorrectly.

 

[Robert_N]

Well, yes. If you rotated it about two axes, you'd end up with three vanishing points. That's pretty straightforward.

I’m sure it is to you but not to the illustrators and physicists/mathematicians I have asked so far, the later being very interested in the question while the former claimed it simply wouldn’t have 3 vanishing points and to think about it would be a waste of time, so thank you very much for your answer, now I can sleep at night.

Now look at the end points of the front top and bottom edge. They are more than 10 feet away; they are (10[sup2[/sup]+52)1/2 feet away. Therefore, they will be slightly closer together in the 2D image than the points that are only 10 feet away. Even the 1-point perspective cube is represented incorrectly.

I’ll have to read that a couple more times until I get it but thank you for the detailed explanation!

 

[DaveC426913]

I’m sure it is to you but not to the illustrators and physicists/mathematicians I have asked so far, the later being very interested in the question while the former claimed it simply wouldn’t have 3 vanishing points and to think about it would be a waste of time, so thank you very much for your answer, now I can sleep at night.

Sorry, I didn't mean it that way. I was simply granting what I saw as a provisional conclusion.

If you have a cube with three sets of parallel lines and you rotate it it through one axis, one set of parallel lines will have a vanishing point short of infinity. Rotate again, and another will.

I’ll have to read that a couple more times until I get it but thank you for the detailed explanation!

A diagram for clarity.