Help me fight perspective!

January 22, 2010 1:10 PM

I want to make an optical illusion with wood. How can I fool the eye into thinking these pillars are all the same size?

I have a long plank of wood and I want to put pillars on it, so that if you raise the plank to eye-level, all pillars look the same size. I think this is possible, like widening the top of a tower to make it look straight, but I can't find any literature or formulas to make this work. I mean I know that I could just eyeball it, but I was really hoping to do this as precisely as possible. Any help would be great, thanks!

posted by Carillon to sports, hobbies, & recreation (11 answers total)

I don't have a specific reference for you, but I know there is a piece MOMA in N.Y. that does what you are talking about. Check out:

http://www.stimulatingpixels.com/images/moma/blocks-1.jpg
http://www.stimulatingpixels.com/images/moma/blocks-2.jpg
http://www.stimulatingpixels.com/images/moma/blocks-3.jpg

It's called Alogon #2 by Robert Smithson. Maybe you can look up more info on that and find some of the math behind it.

Also, probably worth looking up details on how M.C. Escher did his stuff.
posted by StimulatingPixels at 1:21 PM on January 22, 2010

(Now with links)

http://www.stimulatingpixels.com/images/moma/blocks-1.jpg

http://www.stimulatingpixels.com/images/moma/blocks-2.jpg

http://www.stimulatingpixels.com/images/moma/blocks-3.jpg
posted by StimulatingPixels at 1:23 PM on January 22, 2010

Yeah that's pretty much exactly the type of effect I am looking for. Cool looking exhibit too.
posted by Carillon at 1:26 PM on January 22, 2010

This sounds similar to an Ames Room, which might be a good place to start looking. (I've wanted to play in an Ames Room since I saw one on 321 Contact 25+ years ago!)
posted by usonian at 1:28 PM on January 22, 2010

I believe an object looks half its size when it is compared to the same object that is one half the distance away.

So a coke can at 4 feet is half the size of one at 2 feet.

This might work for you.
posted by travis08 at 1:28 PM on January 22, 2010

I've wanted to play in an Ames Room since I saw one on 321 Contact 25+ years ago!

There's one in the Maryland Science Center in Baltimore. At least there was, last time I was there.
posted by electroboy at 1:36 PM on January 22, 2010

Also, here are a few links to read on objects' apparent size.

apparent size
visual angle
angular diameter
posted by travis08 at 1:39 PM on January 22, 2010

AskMetafilter helped me (original thread) with a similar forced-perspective problem a while back. I went into it looking for a mathematical solution but was slowly reassured into approaching it from a more oblique (but no less accurate, in the final project) "back-to-front" direction that was quite clever.

The overlap between that project and your current project isn't 100%, but should be rather significant. I think the original thread may be of some use to you, and in the meantime I will be wracking my brain for the specific method that would best translate those findings to your current query.
posted by jjjjjjjijjjjjjj at 1:54 PM on January 22, 2010

This is really just a simple exercise in trigonometry. You want each of the pillars to subtend the same angle when viewed from a certain point. If you call this angle θ, then you want the height h of a pillar at distance d to satisfy

h = d tan(θ).

(I'm assuming here that the viewer's eyeball is very close to the plane of the plank, and that the pillars are perpendicular to the plank.) In other words, the height of a pillar should be directly proportional to the distance from the viewer's eyeball; you don't actually need to know what θ is, or how to take the tangent function.

Note also that if the pillars all have the same "real" width, then those that are closer to the viewer will appear wider. The solution is to make the closer pillars thinner; again, for optimal effect, the width of the pillars should be proportional to their distance from the viewer's eyeball. Finally, once you've built the object, you might have to do a bit more fine-tuning involving the shapes of the tops of the pillars (if the pillars are square, for example, the tops of the closer pillars will appear to be more sharply peaked than the more distant ones.) However, this should be enough to mock up a rough model, at least.
posted by Johnny Assay at 2:01 PM on January 22, 2010

I'm not sure I fully understand what you are doing but it sounds like you need to do a little work on vanishing points & perspective. I don't think you need any trig; it's just basic proportions.
posted by chairface at 2:13 PM on January 22, 2010

Thanks for the help all. I should have enough to go on with these links and advice, jj, if you can think of anything I would love to hear it.
posted by Carillon at 7:43 PM on January 22, 2010