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From: Warp
Subject: Answer (Was: Impossible triangle)
Date: 7 Jul 2001 10:22:59
Message: <3b471b43@news.povray.org>
The most obvious trick in the image is, of course, the triangle itself
(one of the cubes is clipped by a plane so that the cube right behind it
shows up; also some of the cubes have a no_shadow applied to them in order
to avoid annoying and even revealing shadows).

  The other trick is, however, more difficult to see, and it's the apparent
perspective of the image.
  The camera is orthographic, so the perspective is fake.
  The pattern on the floor is not a gradient pattern, as it may seem, but
actually a radial pattern. The other cubes in the image are rotated so that
the look like they were "distorted" by the perspective althought they aren't.
The cube on the right is actually the intersection of two superellipsoids.


-- 
#macro N(D,I)#if(I<6)cylinder{M()#local D[I]=div(D[I],104);M().5,2pigment{
rgb M()}}N(D,(D[I]>99?I:I+1))#end#end#macro M()<mod(D[I],13)-6,mod(div(D[I
],13),8)-3,10>#end blob{N(array[6]{11117333955,
7382340,3358,3900569407,970,4254934330},0)}//                     - Warp -


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From: Tek
Subject: Re: Answer (Was: Impossible triangle)
Date: 7 Jul 2001 12:56:53
Message: <3b473f55@news.povray.org>
Clever!

I was trying to work out how you'd corrected the perspective on the triangle, so
all cubes appeared the same, but it never occured to me that you'd done the
exact opposite!

BTW, what's the texture on the cubes? It's pretty interesting.

--
Tek
http://www.evilsuperbrain.com


Warp <war### [at] tagpovrayorg> wrote in message news:3b471b43@news.povray.org...
>
>   The most obvious trick in the image is, of course, the triangle itself
> (one of the cubes is clipped by a plane so that the cube right behind it
> shows up; also some of the cubes have a no_shadow applied to them in order
> to avoid annoying and even revealing shadows).
>
>   The other trick is, however, more difficult to see, and it's the apparent
> perspective of the image.
>   The camera is orthographic, so the perspective is fake.
>   The pattern on the floor is not a gradient pattern, as it may seem, but
> actually a radial pattern. The other cubes in the image are rotated so that
> the look like they were "distorted" by the perspective althought they aren't.
> The cube on the right is actually the intersection of two superellipsoids.
>
>
> --
> #macro N(D,I)#if(I<6)cylinder{M()#local D[I]=div(D[I],104);M().5,2pigment{
> rgb M()}}N(D,(D[I]>99?I:I+1))#end#end#macro M()<mod(D[I],13)-6,mod(div(D[I
> ],13),8)-3,10>#end blob{N(array[6]{11117333955,
> 7382340,3358,3900569407,970,4254934330},0)}//                     - Warp -


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From: Warp
Subject: Re: Answer
Date: 7 Jul 2001 17:53:19
Message: <3b4784ce@news.povray.org>
Tek <tek### [at] evilsuperbraincom> wrote:
: BTW, what's the texture on the cubes? It's pretty interesting.

  It's just a granite pigment with the same granite normal with a "sine wave"
slope map..

-- 
#macro N(D,I)#if(I<6)cylinder{M()#local D[I]=div(D[I],104);M().5,2pigment{
rgb M()}}N(D,(D[I]>99?I:I+1))#end#end#macro M()<mod(D[I],13)-6,mod(div(D[I
],13),8)-3,10>#end blob{N(array[6]{11117333955,
7382340,3358,3900569407,970,4254934330},0)}//                     - Warp -


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From: David Fontaine
Subject: Re: Impossible triangle
Date: 7 Jul 2001 18:31:08
Message: <3B478BDD.C5C48896@faricy.net>
Warp wrote:
> 
>   The impossible triangle with cubes was first invented by the
> Swedish artist Oscar Reutersvard back in 1934.
> 
>   This image has two tricks. The first one is obvious (the triangle). But
> there's another trick which may not be obvious. Can you guess what it is?

The triangle is orthographic and the rest is not?

-- 
David Fontaine  <dav### [at] faricynet>  ICQ 55354965
My raytracing gallery:  http://davidf.faricy.net/


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From: David Fontaine
Subject: Re: Answer (Was: Impossible triangle)
Date: 7 Jul 2001 18:33:27
Message: <3B478C67.2212732D@faricy.net>
Warp wrote:
> 
>   The other trick is, however, more difficult to see, and it's the apparent
> perspective of the image.
>   The camera is orthographic, so the perspective is fake.

I was right!  :)

-- 
David Fontaine  <dav### [at] faricynet>  ICQ 55354965
My raytracing gallery:  http://davidf.faricy.net/


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From: Warp
Subject: Re: Impossible triangle
Date: 7 Jul 2001 22:28:43
Message: <3b47c55a@news.povray.org>
David Fontaine <dav### [at] faricynet> wrote:
: The triangle is orthographic and the rest is not?

  Everything in the image is orthographic.
  I can't imagine any way of creating an orthographic and a perspective image
at the same time with one render and no external files... :)

  The background looks like it has perspective, but that's the fake. Things
are only rotated so that they look like that, and the pattern in the floor
is the radial pattern.

-- 
#macro N(D,I)#if(I<6)cylinder{M()#local D[I]=div(D[I],104);M().5,2pigment{
rgb M()}}N(D,(D[I]>99?I:I+1))#end#end#macro M()<mod(D[I],13)-6,mod(div(D[I
],13),8)-3,10>#end blob{N(array[6]{11117333955,
7382340,3358,3900569407,970,4254934330},0)}//                     - Warp -


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From: Sander
Subject: Re: Impossible triangle
Date: 8 Jul 2001 11:03:54
Message: <MPG.15b2950129801e2b9897f8@NEWS.POVRAY.ORG>
In article <3B478BDD.C5C48896@faricy.net>, David Fontaine says...
> Warp wrote:
> > 
> >   The impossible triangle with cubes was first invented by the
> > Swedish artist Oscar Reutersvard back in 1934.
> > 
> >   This image has two tricks. The first one is obvious (the triangle). But
> > there's another trick which may not be obvious. Can you guess what it is?
> 
> The triangle is orthographic and the rest is not?
> 
> 
I was right first: beat you with about 10h 54m 32 s :))
-- 
Regards,  Sander


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From: Sander
Subject: Re: Answer (Was: Impossible triangle)
Date: 8 Jul 2001 11:06:35
Message: <MPG.15b295a4e234c2d49897f9@NEWS.POVRAY.ORG>
In article <3b471b43@news.povray.org>, Warp says...
> 
>   The most obvious trick in the image is, of course, the triangle itself
> (one of the cubes is clipped by a plane so that the cube right behind it
> shows up; also some of the cubes have a no_shadow applied to them in order
> to avoid annoying and even revealing shadows).
> 
>   The other trick is, however, more difficult to see, and it's the apparent
> perspective of the image.
>   The camera is orthographic, so the perspective is fake.
>   The pattern on the floor is not a gradient pattern, as it may seem, but
> actually a radial pattern. The other cubes in the image are rotated so that
> the look like they were "distorted" by the perspective althought they aren't.
> The cube on the right is actually the intersection of two superellipsoids.
> 
I was looking for a sign on one of the shadowless cubes where there 
would be a break: stupid not to have thought of clipping... 

Cleverly done, though :)
-- 
Regards,  Sander


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From: David Fontaine
Subject: Re: Impossible triangle
Date: 8 Jul 2001 22:53:16
Message: <3B491ACE.A5D1098A@faricy.net>
Warp wrote:
> 
> David Fontaine <dav### [at] faricynet> wrote:
> : The triangle is orthographic and the rest is not?
> 
>   Everything in the image is orthographic.
>   I can't imagine any way of creating an orthographic and a perspective image
> at the same time with one render and no external files... :)
> 
>   The background looks like it has perspective, but that's the fake. Things
> are only rotated so that they look like that, and the pattern in the floor
> is the radial pattern.

Well, obviously you can't have both perspectives in the same render... 
I thought perhaps you did perspective and faked the orthographic part so
they'd line up, but your way sounds easier.

-- 
David Fontaine  <dav### [at] faricynet>  ICQ 55354965
My raytracing gallery:  http://davidf.faricy.net/


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From: Harry
Subject: Re: Impossible triangle
Date: 9 Jul 2001 00:47:35
Message: <3B493766.BFB886C5@bigfoot.com>
Fantastic Image! 

I've read the explanations, looked again and again at the picture
and still don't understand all that was done.

I would love to see the .pov code that did this, but understand 
completely if you were a bit "possessives" of this. Would you at least
consider a rendering from a different camera angle so those as
dense as I could begin to understand how you are managing such 
a deceptive image?


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