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I was wondering, what kind of interesting geometric shapes (solids,
surfaces, etc.) have been or could be converted into buildings?
Mike
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SharkD <mik### [at] gmail com> wrote:
> I was wondering, what kind of interesting geometric shapes (solids,
> surfaces, etc.) have been or could be converted into buildings?
>
> Mike
Right rectangular prisms :)
Actually, a modified hyperbolic saddle has been used for a few arena roofs.
There are many others, I am sure.
-Reactor
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From: Kevin Wampler
Subject: Re: Geometric shapes that could be turned into buildings
Date: 19 Oct 2009 03:06:59
Message: <4adc1013$1@news.povray.org>
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SharkD wrote:
> I was wondering, what kind of interesting geometric shapes (solids,
> surfaces, etc.) have been or could be converted into buildings?
Boxes, clearly!
More seriously, how about a catenary curve? Quadrics and conic sections
are also pretty common, as are helices. Ditto for general developable
and ruled surfaces. More local geometric concepts based on discrete
differential geometry are also used occasionally, and although I haven't
seen many examples I think that minimal surfaces could be used pretty
effectively too. As far as actual buildings I think the Sagrada Familia
probably contains my favorite instances of mathematical forms in
architecture, but there are many others (although I can only recall a
few more off the top of my head).
Slightly more povray-oriented, the Infinite Spire is a nifty cool idea
related to this: http://www.oyonale.com/infinitespire.php?lang=en
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From: Invisible
Subject: Re: Geometric shapes that could be turned into buildings
Date: 19 Oct 2009 04:30:00
Message: <4adc2388$1@news.povray.org>
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SharkD wrote:
> I was wondering, what kind of interesting geometric shapes (solids,
> surfaces, etc.) have been or could be converted into buildings?
There's a building somewhere in Europe in the shape of a hypercube.
(Google repeatedly insists that no such object exists, but I damned well
know it does.) I have a vague feeling it's in France - but only becuase
I know French people are extremely weird...
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From: SharkD
Subject: Re: Geometric shapes that could be turned into buildings
Date: 19 Oct 2009 04:49:54
Message: <4adc2832@news.povray.org>
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On 10/19/2009 12:56 AM, Reactor wrote:
> Actually, a modified hyperbolic saddle has been used for a few arena roofs.
> There are many others, I am sure.
>
> -Reactor
I meant buildings made entirely out of weird geometric shapes and that
you can explore by walking in, not just selected portions of the buildings.
Mike
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From: SharkD
Subject: Re: Geometric shapes that could be turned into buildings
Date: 19 Oct 2009 04:52:08
Message: <4adc28b8$1@news.povray.org>
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On 10/19/2009 4:29 AM, Invisible wrote:
> SharkD wrote:
>> I was wondering, what kind of interesting geometric shapes (solids,
>> surfaces, etc.) have been or could be converted into buildings?
>
> There's a building somewhere in Europe in the shape of a hypercube.
> (Google repeatedly insists that no such object exists, but I damned well
> know it does.) I have a vague feeling it's in France - but only becuase
> I know French people are extremely weird...
I remember seeing something like this, but it wasn't a hypercube, rather
a model of an atom. And it was built for one of the World Fairs in the
50's-60's or somewhere around then.
It wasn't entirely functional either. More of an exhibit or art
installation.
Mike
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From: Invisible
Subject: Re: Geometric shapes that could be turned into buildings
Date: 19 Oct 2009 05:10:41
Message: <4adc2d11$1@news.povray.org>
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>> There's a building somewhere in Europe in the shape of a hypercube.
>> (Google repeatedly insists that no such object exists, but I damned well
>> know it does.) I have a vague feeling it's in France - but only becuase
>> I know French people are extremely weird...
>
> I remember seeing something like this, but it wasn't a hypercube, rather
> a model of an atom. And it was built for one of the World Fairs in the
> 50's-60's or somewhere around then.
>
> It wasn't entirely functional either. More of an exhibit or art
> installation.
I saw a building somewhere which was a working office block, but in the
shape of a hypercube. (Or rather, a 3D projection of one; a true
hypercube is obviously 4D.) As I say, I can't find any reference to it
now...
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From: clipka
Subject: Re: Geometric shapes that could be turned into buildings
Date: 19 Oct 2009 05:22:10
Message: <4adc2fc2$1@news.povray.org>
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SharkD schrieb:
> I meant buildings made entirely out of weird geometric shapes and that
> you can explore by walking in, not just selected portions of the buildings.
You mean, like the "Atomium" in Bruxelles?
http://en.wikipedia.org/wiki/Atomium
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From: clipka
Subject: Re: Geometric shapes that could be turned into buildings
Date: 19 Oct 2009 05:30:51
Message: <4adc31cb$1@news.povray.org>
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SharkD schrieb:
> I remember seeing something like this, but it wasn't a hypercube, rather
> a model of an atom. And it was built for one of the World Fairs in the
> 50's-60's or somewhere around then.
Not an atom, but atoms in a crystal lattice (allegedly iron; ironically,
the building was clad in Aluminum until 2004).
Expo '58, the "Atomium"; one of the architectural symbols of Belgium.
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SharkD wrote:
> I was wondering, what kind of interesting geometric shapes (solids,
> surfaces, etc.) have been or could be converted into buildings?
Actually, if you like crazy geometry, you could do worse than to wonder
around the inside of a Gothic cathedral...
http://www.elycathedral.org/media_centre/gallery/
http://www.salisburycathedral.org.uk/gallery.php
http://www.bristol-cathedral.co.uk/index.php?id=18
http://www.exeter-cathedral.org.uk/gallery/LibraryandArchive.ashx
http://www.gloucestercathedral.org.uk/index.php?page=gallery
http://www.sphericalimages.com/hereford_cathedral_virtual_tour/
http://www.cathedral.org.uk/historyheritage/architecture-the-cathedral.aspx
http://www.peterborough-cathedral.org.uk/phppage/gallery
http://www.rochestercathedral.org/virtual-tour/index.asp
http://www.stalbanscathedral.org.uk/photos/index.htm
Some of the geometric constructions these people came up with are pretty
amazing. (Not to mention the "minor detail" that as you stand in a
cathedral, there are many trillions of tonnes of stone, hundreds of feet
above your head, and it was all liften up there by people's bare hands...)
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From: clipka
Subject: Re: Geometric shapes that could be turned into buildings
Date: 19 Oct 2009 05:37:51
Message: <4adc336f$1@news.povray.org>
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Invisible schrieb:
> I saw a building somewhere which was a working office block, but in the
> shape of a hypercube. (Or rather, a 3D projection of one; a true
> hypercube is obviously 4D.) As I say, I can't find any reference to it
> now...
This one?
http://spacelab.wordpress.com/2009/02/16/food_container_remixed/
Googling for such stuff appears problematic: "hypercube architecture"
obviously leads to totally different stuff...
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From: Invisible
Subject: Re: Geometric shapes that could be turned into buildings
Date: 19 Oct 2009 05:44:56
Message: <4adc3518@news.povray.org>
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>> I saw a building somewhere which was a working office block, but in
>> the shape of a hypercube. (Or rather, a 3D projection of one; a true
>> hypercube is obviously 4D.) As I say, I can't find any reference to it
>> now...
>
> This one?
>
> http://spacelab.wordpress.com/2009/02/16/food_container_remixed/
Doesn't appear to be. This thing was many stories high.
> Googling for such stuff appears problematic: "hypercube architecture"
> obviously leads to totally different stuff...
And "hypercube building" tells you how to make a paper hypercube (or
construct one mathematically).
It's almost as Google-proof as "./" ;-)
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Invisible <voi### [at] devnull> wrote:
> Actually, if you like crazy geometry, you could do worse than to wonder
> around the inside of a Gothic cathedral...
Some cathedrals sure are spectacular piles of stone. I walked up one of the
towers on Cologne cathedral a couple of years ago - I can't believe people used
to do it without all the extra safety-oriented metalwork recent construction
engineers have put in. It was like mountaineering!
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>> Actually, if you like crazy geometry, you could do worse than to wonder
>> around the inside of a Gothic cathedral...
>
> Some cathedrals sure are spectacular piles of stone. I walked up one of the
> towers on Cologne cathedral a couple of years ago - I can't believe people used
> to do it without all the extra safety-oriented metalwork recent construction
> engineers have put in. It was like mountaineering!
Cathedrals used to occasionally collapse back then too. ;-)
Some of these places I stand there and stare at the intricate geometry
and wonder how the hell people *thought* of this stuff. Then again, if
you spend 300 years building one structure, involving a team of hundreds
of people, I guess you have time to think these things through. (Still,
if *I* did this, the building would end up as a mess of cool parts that
don't actually fit together properly...)
And then there's the stone carvings. Don't get me started on the stone
carvings...
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From: Michael Zier
Subject: Re: Geometric shapes that could be turned into buildings
Date: 19 Oct 2009 07:02:25
Message: <4ADC4822.80500@mirizi.de>
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Invisible wrote:
>>> I saw a building somewhere which was a working office block, but in
>>> the shape of a hypercube. (Or rather, a 3D projection of one; a true
>>> hypercube is obviously 4D.) As I say, I can't find any reference to
>>> it now...
>>
>> This one?
>>
>> http://spacelab.wordpress.com/2009/02/16/food_container_remixed/
>
> Doesn't appear to be. This thing was many stories high.
>
>> Googling for such stuff appears problematic: "hypercube architecture"
>> obviously leads to totally different stuff...
>
> And "hypercube building" tells you how to make a paper hypercube (or
> construct one mathematically).
>
> It's almost as Google-proof as "./" ;-)
You mean "Grande Arche" in Paris.
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From: Invisible
Subject: Re: Geometric shapes that could be turned into buildings
Date: 19 Oct 2009 07:07:52
Message: <4adc4888$1@news.povray.org>
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>> It's almost as Google-proof as "./" ;-)
>
> You mean "Grande Arche" in Paris.
http://en.wikipedia.org/wiki/Grande_Arche
Why yes, yes I do...
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On 10/19/2009 5:31 AM, Invisible wrote:
> SharkD wrote:
>> I was wondering, what kind of interesting geometric shapes (solids,
>> surfaces, etc.) have been or could be converted into buildings?
>
> Actually, if you like crazy geometry, you could do worse than to wonder
> around the inside of a Gothic cathedral...
I visited Mont Saint-Michel as a kid, and was amazed not so much by any
single architectural aspect, but more by the implausibility of the
entire scene, including surrounding town.
Mike
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Bill Pragnell wrote:
> Invisible <voi### [at] devnull> wrote:
>> Actually, if you like crazy geometry, you could do worse than to wonder
>> around the inside of a Gothic cathedral...
>
> Some cathedrals sure are spectacular piles of stone. I walked up one of the
> towers on Cologne cathedral a couple of years ago - I can't believe people used
> to do it without all the extra safety-oriented metalwork recent construction
> engineers have put in. It was like mountaineering!
>
>
http://en.wikipedia.org/wiki/Sagrada_Fam%C3%ADlia
That is all I'll say
--
Best Regards,
Stephen
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> I remember seeing something like this, but it wasn't a hypercube, rather a
> model of an atom. And it was built for one of the World Fairs in the
> 50's-60's or somewhere around then.
>
> It wasn't entirely functional either. More of an exhibit or art
> installation.
It was probably the "Atomium" in Brussels (which has been mentioned before).
http://en.wikipedia.org/wiki/Atomium
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TC <do-not-reply@i-do get-enough-spam-already-2498.com> wrote:
> > I remember seeing something like this, but it wasn't a hypercube, rather a
> > model of an atom. And it was built for one of the World Fairs in the
> > 50's-60's or somewhere around then.
> >
> > It wasn't entirely functional either. More of an exhibit or art
> > installation.
> It was probably the "Atomium" in Brussels (which has been mentioned before).
> http://en.wikipedia.org/wiki/Atomium
Looks like a regular cube to me...
--
- Warp
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SharkD wrote:
> I visited Mont Saint-Michel as a kid, and was amazed not so much by any
> single architectural aspect, but more by the implausibility of the
> entire scene, including surrounding town.
Is that that one that's on an island that's only an island at high tide?
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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Orchid XP v8 wrote:
> Is that that one that's on an island that's only an island at high tide?
That's the one! Very awesome.
--
Darren New, San Diego CA, USA (PST)
I ordered stamps from Zazzle that read "Place Stamp Here".
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Darren New wrote:
> Orchid XP v8 wrote:
>> Is that that one that's on an island that's only an island at high tide?
>
> That's the one! Very awesome.
Awake! Awak! St Micheal,
Your time is now at hand.
Thou thinkest not of the pilgrims
Which thron every foreign strand.
Why would I think of the pilgrams,
For healthy they are and free,
Dry foot they come awalking
Across the dry bed of the sea.
[Oh GOD I hate that song...]
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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Stephen escreveu:
> http://en.wikipedia.org/wiki/Sagrada_Fam%C3%ADlia
>
> That is all I'll say
whoa! A baroque work still going on today?!
--
a game sig: http://tinyurl.com/d3rxz9
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nemesis wrote:
> whoa! A baroque work still going on today?!
It's a cathedral, but I wouldn't call it baroque -- I consider it as
solidly rooted in an art nouveau style (in particular a substyle
particular to Gaudi). It's really an amazing building though, and I
hope to be able to see the completed version someday.
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Kevin Wampler <wam### [at] uwashingtonedu> wrote:
> nemesis wrote:
>
> > whoa! A baroque work still going on today?!
>
> It's a cathedral, but I wouldn't call it baroque -- I consider it as
> solidly rooted in an art nouveau style (in particular a substyle
> particular to Gaudi). It's really an amazing building though, and I
> hope to be able to see the completed version someday.
well, art nouveau is pretty baroque itself, with all the arabesques and
recursive decorative figures... :)
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nemesis wrote:
> well, art nouveau is pretty baroque itself, with all the arabesques and
> recursive decorative figures... :)
I had, of course, chosen to take a different meaning of Baroque, but
you're totally correct. You could probably even say that this is a
particularly baroque form of art nouveau -- everybody's happy! :-)
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On 10/19/2009 12:53 PM, Stephen wrote:
> Bill Pragnell wrote:
>
> http://en.wikipedia.org/wiki/Sagrada_Fam%C3%ADlia
>
> That is all I'll say
Over millions of years, pure candy forms into stalactites much like this.
Mike
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Warp schrieb:
>> http://en.wikipedia.org/wiki/Atomium
>
> Looks like a regular cube to me...
Aside from the extra ball in the center, it actually is.
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From: Saul Luizaga
Subject: Re: Geometric shapes that could be turned into buildings
Date: 20 Oct 2009 06:50:21
Message: <4add95ed@news.povray.org>
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SharkD wrote:
> I was wondering, what kind of interesting geometric shapes (solids,
> surfaces, etc.) have been or could be converted into buildings?
>
> Mike
I have seen so many fascinating POV-Ray rendered images that would be
impossible to remember or to suggest, but something I really would like
to see built is a Fractal Julia :-D
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From: Invisible
Subject: Re: Geometric shapes that could be turned into buildings
Date: 20 Oct 2009 06:51:24
Message: <4add962c@news.povray.org>
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Saul Luizaga wrote:
> I have seen so many fascinating POV-Ray rendered images that would be
> impossible to remember or to suggest, but something I really would like
> to see built is a Fractal Julia :-D
Meh. I'd like to see a 3D slice of the 4D cubic complex Mandelbrot set. ;-)
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SharkD wrote:
> On 10/19/2009 12:53 PM, Stephen wrote:
>> Bill Pragnell wrote:
>>
>> http://en.wikipedia.org/wiki/Sagrada_Fam%C3%ADlia
>>
>> That is all I'll say
>
> Over millions of years, pure candy forms into stalactites much like this.
>
> Mike
How about?
http://defencedebates.files.wordpress.com/2008/12/gaudi-house1.jpg
or
http://img.ffffound.com/static-data/assets/6/272046a2e89d53ab5039d45c8f83651e97055caa_m.jpg
or
http://www.xarj.net/wp-content/uploads/2007/04/gaudi2-barcelona.jpg
or even
http://www.sepal.org/gulick/graphics/gaudi-sagrada-familia_bg.jpg
--
Best Regards,
Stephen
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From: Stephen
Subject: Re: Geometric shapes that could be turned into buildings
Date: 20 Oct 2009 16:13:03
Message: <4ade19cf$1@news.povray.org>
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Invisible wrote:
> Saul Luizaga wrote:
>
>> I have seen so many fascinating POV-Ray rendered images that would be
>> impossible to remember or to suggest, but something I really would
>> like to see built is a Fractal Julia :-D
>
> Meh. I'd like to see a 3D slice of the 4D cubic complex Mandelbrot set. ;-)
A couple of years ago you posted the SDL code for a cubic Mandelbrot
which I turned into a df3 file. I hinted and hinted for you to do the
same for the classic Mandelbrot but we both move on.
--
Best Regards,
Stephen
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Stephen wrote:
> ...
Glad to see there's another Gaudi fan around here :)
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Kevin Wampler wrote:
> Stephen wrote:
>> ...
>
> Glad to see there's another Gaudi fan around here :)
In the late 80’s I went to Spain intending to go to Barcelona, Madrid,
Toledo etc. I never got further than Barcelona. I fell in love with
Gaudi and the city.
The only reason I came home was because the RSC put on The Rover by
Aphra Behn. (I had queued for days to get a day seat the year before)
--
Best Regards,
Stephen
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From: Saul Luizaga
Subject: Re: Geometric shapes that could be turned into buildings
Date: 20 Oct 2009 17:46:19
Message: <4ade2fab@news.povray.org>
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Invisible wrote:
> Saul Luizaga wrote:
>
>> I have seen so many fascinating POV-Ray rendered images that would be
>> impossible to remember or to suggest, but something I really would
>> like to see built is a Fractal Julia :-D
>
> Meh. I'd like to see a 3D slice of the 4D cubic complex Mandelbrot set. ;-)
I couldn't find any images of a 4D cubic complex Mandelbrot set but I
found a 'smallest absolute value of the orbit of the interior points of
the Mandelbrot set', 4D must be too crazy, man you need to suggest
something in 3D that won't take a team of Einsteins to make the blue
prints :-)
Post a reply to this message
Attachments:
Download 'utf-8' (29 KB)
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From: Saul Luizaga
Subject: Re: Geometric shapes that could be turned into buildings
Date: 20 Oct 2009 17:53:03
Message: <4ade313f$1@news.povray.org>
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In case you are interested and don't have it:
http://www.dhushara.com/DarkHeart/DarkHeart.htm
http://flashlight.slad.cz/files/bp_vis.pdf
http://www.evl.uic.edu/hypercomplex/html/book/book.pdf
http://www.evl.uic.edu/hypercomplex/html/book/book.pdf
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From: Invisible
Subject: Re: Geometric shapes that could be turned into buildings
Date: 21 Oct 2009 05:05:28
Message: <4adeced8$1@news.povray.org>
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I never did like hypercomplex numbers and quaternions very much. Neither
of them are true number fields, and the Julia sets they produce are just
slightly modified surfaces of revolution.
The complex cubic Mandelbrot set uses only complex arithmetic - a true
number field - and produces a 4D image that has genuine detail in every
direction. The resulting images look much more "natural" to my eyes,
whichever plane you slice it in.
As you say though, this object is not widely known.
(And there's no way you'd ever make a building out of it. It's far too
impractical...)
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