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        riddles >> medium >> Orthogonal Views
        
(Message started by: william wu on May 17th, 2008, 2:44am)
Title: Orthogonal Views
Post by william wu on May 17th, 2008, 2:44am
See the picture below.

This cute puzzle has the nice properties of
(1) being accessible to anyone (e.g., 4 year olds), and
(2) initially appearing to be impossible. So it will drive you crazy until you figure it out :)
Title: Re: Orthogonal Views
Post by towr on May 17th, 2008, 4:25am
The only thing I can make of it gives numerous possible solutions, so it doesn't really keep my interest enough to drive me crazy.
Title: Re: Orthogonal Views
Post by rmsgrey on May 17th, 2008, 7:07am
[hide]a smooth curve resembling y=-x^2 on [-3,3] with a chord across the bottom[/hide]
Title: Re: Orthogonal Views
Post by SMQ on May 17th, 2008, 9:07am
Similar to what rmsgrey said (zipped to hide answer)

--SMQ
Title: Re: Orthogonal Views
Post by FiBsTeR on May 17th, 2008, 10:01am
I must be missing something; this is what I first thought of, and it still seems to fit the problem:
Title: Re: Orthogonal Views
Post by Barukh on May 17th, 2008, 10:23am

on 05/17/08 at 09:07:53, SMQ wrote:
Similar to what rmsgrey said (zipped to hide answer)

Cannot imagine how this solves the problem...

Could you draw a stereometric view?  ;)
Title: Re: Orthogonal Views
Post by Grimbal on May 17th, 2008, 3:15pm
Is this what you had in mind?
Title: Re: Orthogonal Views
Post by SMQ on May 17th, 2008, 8:29pm

on 05/17/08 at 10:23:49, Barukh wrote:
Could you draw a stereometric view?  ;)

Sure, stereometric and isometric both. ;)
Title: Re: Orthogonal Views
Post by Eigenray on May 17th, 2008, 10:38pm
Now how about an anaglyph image?  :)
Title: Re: Orthogonal Views
Post by Grimbal on May 18th, 2008, 2:38am
Why so complicated?
Title: Re: Orthogonal Views
Post by rmsgrey on May 18th, 2008, 4:19am

on 05/17/08 at 10:01:07, FiBsTeR wrote:
I must be missing something; this is what I first thought of, and it still seems to fit the problem:

It has extra edges on, which would conventionally be drawn in a projection - as silhouettes, the side view has a lot of possibilities even without poking additional holes through. The curved solutions solve the problem of the missing edges, but Grimbal's solution is even better.
Title: Re: Orthogonal Views
Post by SMQ on May 18th, 2008, 5:47am

on 05/17/08 at 22:38:17, Eigenray wrote:
Now how about an anaglyph image?  :)

If that's what floats your boat. :D (left eye is cyan)

--SMQ
Title: Re: Orthogonal Views
Post by Barukh on May 18th, 2008, 5:50am
Awesome, SMQ!  :D :D :D

What software are you using?
Title: Re: Orthogonal Views
Post by SMQ on May 18th, 2008, 6:09am

on 05/18/08 at 05:50:51, Barukh wrote:
What software are you using?

Povray (http://www.povray.org) for the rendering, and since I'm not on my normal computer with Photoshop at the moment, a quickie BASIC program to combine the anaglyph images and MS Paint for cropping and PNG conversion.

I've attached the Povray source for anyone interested.

--SMQ
Title: Re: Orthogonal Views
Post by Eigenray on May 18th, 2008, 9:55am
Awesome.

Now do Magic Eye!
Title: Re: Orthogonal Views
Post by SMQ on May 18th, 2008, 12:22pm
You just don't give up, do you? ;D

--SMQ
Title: Re: Orthogonal Views
Post by Eigenray on May 18th, 2008, 1:13pm
Impressive!

How about an animated anaglyph/autostereogram of it rotating?   :P
Title: Re: Orthogonal Views
Post by william wu on May 19th, 2008, 1:33am
These answers, while perfectly legit, are a lot more complicated than I expected ... :o
Love the pictures!
Title: Re: Orthogonal Views
Post by towr on May 19th, 2008, 1:57am

on 05/19/08 at 01:33:48, william wu wrote:
These answers, while perfectly legit, are a lot more complicated than I expected ... :o
I don't think your solution works; if you cut a piece out of a cylinder at the height required by the front view (with the right width), you won't get a square as required in the top view..
Title: Re: Orthogonal Views
Post by JohanC on May 19th, 2008, 2:18am

on 05/19/08 at 01:57:42, towr wrote:
I don't think your solution works; if you cut a piece out of a cylinder at the height required by the front view (with the right width), you won't get a square as required in the top view..

Maybe an elliptical cylinder would work?
Title: Re: Orthogonal Views
Post by towr on May 19th, 2008, 2:42am

on 05/19/08 at 02:18:08, JohanC wrote:
Maybe an elliptical cylinder would work?
Then the top view wouldn't be a square.
Title: Re: Orthogonal Views
Post by william wu on May 19th, 2008, 12:30pm
Hmm, fair enough ... but, perhaps we can just slice the cylinder in half, lengthwise, to get the front view.
Title: Re: Orthogonal Views
Post by SMQ on May 19th, 2008, 12:39pm
Sorry, William, still won't work.  If, in the side view, you drew an isosceles triangle from the bottom corners to the top center it would pass exactly through the needed width of the top cut out (see diagram).  So any profile which is the same height, is convex on top, and passes through those same points must have some concave portions somewhere along its length.  No profile without at least one inflection point (on each side) can satisfy all the constraints of the given problem.

--SMQ
Title: Re: Orthogonal Views
Post by Sir Col on May 20th, 2008, 11:49am
When I went to school woodwork, metal work, and technical drawing lessons were compulsory for boys and I loved these types of puzzle. I used to give them to my students when I first started teaching, but it seems that over the years they've become a lost art. Here are two of my fiendishly hard favourites. Puzzle B is a variation of Williams, so it isn't really a challenge now you've seen his answer. However, puzzle A is still a nice one to have a stab at.
Title: Re: Orthogonal Views
Post by SMQ on May 20th, 2008, 12:29pm
I, too, am glad I had the chance to take technical drawing.  On the other hand, I helped to set up the CAD lab at my high school, so I guess I'm partly responsible for the demise of the art... :-/

Zipped solution to A attached. (And I notice you altered your diagram of B to better fit the "intended" solution. ;))

--SMQ
Title: Re: Orthogonal Views
Post by towr on May 20th, 2008, 12:48pm
See, for A, I just took [hide]a cube with three cores cut out[/hide] Why does it always need to be something fancy?
Title: Re: Orthogonal Views
Post by Sir Col on May 20th, 2008, 12:59pm

on 05/20/08 at 12:29:58, SMQ wrote:
(And I notice you altered your diagram of B to better fit the "intended" solution. ;))
--SMQ

You're right about changing it. I did it from memory originally and after noticing towr's comments I did an isometric projection and realised that it produced an impossible object.

And nice work with Puzzle A. You could, of course, have a concave version of the "dormer".
Title: Re: Orthogonal Views
Post by Sir Col on May 20th, 2008, 1:01pm
@towr: The plan (top) and (front) elevation views would have to include hidden lines indicated by dotted lines. As my diagram didn't include any dotted lines there are no "tunnels".
Title: Re: Orthogonal Views
Post by towr on May 20th, 2008, 1:13pm

on 05/20/08 at 13:01:37, Sir Col wrote:
@towr: The plan (top) and (front) elevation views would have to include hidden lines indicated by dotted lines. As my diagram didn't include any dotted lines there are no "tunnels".
Why doesn't anyone ever tell me the rules beforehand :P


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