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As I mentioned earlier, I wanted to model something like
Escher's "Moebius Strip II" (woodcut from 1963) for my
POVCOMP entry. But I didn't finish my macros early enough,
so I had to abandon my attempt.
Yesterday I sat down and finished the most important
macros and today I debugged them and rendered a scene that
shows a Möebius band that follows the path of a trefoil
knot.
To verify that it is a single Möebius band, try to follow
one of the edges of the band.
Although it is not the scene I planned, I find the shape
in it interesting.
--
Tor Olav
http://subcube.net
http://subcube.com
Post a reply to this message
Attachments:
Download 'trefoilmoebiusknot05.jpg' (43 KB)
Preview of image 'trefoilmoebiusknot05.jpg'
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Tor Olav Kristensen wrote:
>
> As I mentioned earlier, I wanted to model something like
> Escher's "Moebius Strip II" (woodcut from 1963) for my
> POVCOMP entry. But I didn't finish my macros early enough,
> so I had to abandon my attempt.
>
> Yesterday I sat down and finished the most important
> macros and today I debugged them and rendered a scene that
> shows a Möebius band that follows the path of a trefoil
> knot.
>
> To verify that it is a single Möebius band, try to follow
> one of the edges of the band.
>
> Although it is not the scene I planned, I find the shape
> in it interesting.
>
>
> ------------------------------------------------------------------------
>
As all ways, an excellent work.
Alberto
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Impressive!
The question from many fans: "Master, how did you do it?" ;-)
Thomas
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I'm allways admirative when I see your images. You're, for me, the
torus-master ;-)
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Amazing! It's a mesh, isn't it?
Florian
--
camera{look_at-y*10location<8,-3,-8>*10}#local a=0;#while(a<999)sphere{
#local _=.01*a-4.99;#local p=a*.01-5;#local c=.01*a-4.995;<sin(p*pi)*5p
*10pow(p,5)*.01>sin(c*c*c*.1)+1pigment{rgb 3}}#local a=a+1;#end
/******** http://www.torfbold.com ******** http://www.imp.org ********/
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Among other things, Tor Olav Kristensen saw fit to write:
> As I mentioned earlier, I wanted to model something like
> Escher's "Moebius Strip II" (woodcut from 1963) for my
> POVCOMP entry. But I didn't finish my macros early enough,
> so I had to abandon my attempt.
>
> Yesterday I sat down and finished the most important
> macros and today I debugged them and rendered a scene that
> shows a Möebius band that follows the path of a trefoil
> knot.
You do know similar things were also drawn by Escher (1965), don't you?
http://cybermuse.gallery.ca/cybermuse/youth/escher/enlargements/NGC_29143.jpg
--
light_source{9+9*x,1}camera{orthographic look_at(1-y)/4angle 30location
9/4-z*4}light_source{-9*z,1}union{box{.9-z.1+x clipped_by{plane{2+y-4*x
0}}}box{z-y-.1.1+z}box{-.1.1+x}box{.1z-.1}pigment{rgb<.8.2,1>}}//Jellby
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From: Tor Olav Kristensen
Subject: Re: Moebius Band as a Trefoil Knot
Date: 23 Oct 2004 10:01:29
Message: <417a6439@news.povray.org>
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Alberto Mendoza wrote:
...
> As all ways, an excellent work.
Thank you Alberto.
--
Tor Olav
http://subcube.net
http://subcube.com
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From: Tor Olav Kristensen
Subject: Re: Moebius Band as a Trefoil Knot
Date: 23 Oct 2004 10:01:53
Message: <417a6451@news.povray.org>
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Thomas de Groot wrote:
> Impressive!
> The question from many fans: "Master, how did you do it?" ;-)
Hehe... The main ingredients are my NURBS macros, my Frenet
Frame macros and the "New Surface Subdivision Suite" by John
VanSickle.
I can try to explain more later today.
--
Tor Olav
http://subcube.net
http://subcube.com
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LightBeam wrote:
> I'm allways admirative when I see your images. You're, for me, the
> torus-master ;-)
=)
I've been very fascinated by the shape and the topology of
tori all the time since I started to try to model smooth
and complex shapes in POV-Ray.
--
Tor Olav
http://subcube.net
http://subcube.com
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Florian Brucker wrote:
> Amazing! It's a mesh, isn't it?
Yes Florian, it's a mesh.
I think that this shape can also be made as an isosurface,
but I don't have enough computing power for that yet.
--
Tor Olav
http://subcube.net
http://subcube.com
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From: Tor Olav Kristensen
Subject: Re: Moebius Band as a Trefoil Knot
Date: 23 Oct 2004 10:02:42
Message: <417a6482@news.povray.org>
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Jellby wrote:
> Among other things, Tor Olav Kristensen saw fit to write:
>
>
>>As I mentioned earlier, I wanted to model something like
>>Escher's "Moebius Strip II" (woodcut from 1963) for my
>>POVCOMP entry. But I didn't finish my macros early enough,
>>so I had to abandon my attempt.
>>
>>Yesterday I sat down and finished the most important
>>macros and today I debugged them and rendered a scene that
>>shows a Möebius band that follows the path of a trefoil
>>knot.
>
>
> You do know similar things were also drawn by Escher (1965), don't you?
> http://cybermuse.gallery.ca/cybermuse/youth/escher/enlargements/NGC_29143.jpg
Yes I do , I should have mentioned that those images
together with Tom Longtin's first image on this page:
http://www.sover.net/%7Etlongtin/sub_page_3.htm
and M. Trott's little animation at this page:
http://mathworld.wolfram.com/TrefoilKnot.html
inspired me to make this image.
--
Tor Olav
http://subcube.net
http://subcube.com
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From: Tor Olav Kristensen
Subject: Re: Moebius Band as a Trefoil Knot
Date: 23 Oct 2004 10:24:19
Message: <417a6993@news.povray.org>
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Here is a version with a little more reflective
texture and better sadiosity settings.
--
Tor Olav
http://subcube.net
http://subcube.com
Post a reply to this message
Attachments:
Download 'trefoilmoebiusknot06.jpg' (78 KB)
Preview of image 'trefoilmoebiusknot06.jpg'
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Tor Olav Kristensen wrote:
> Here is a version with a little more reflective
> texture and better sadiosity settings.
>
>
> ------------------------------------------------------------------------
>
It's a technical masterpiece. Good work!
-Sam
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Tor Olav Kristensen wrote:
Very nice. But not up to your usual standard of "sharpness." The
rectangular holes are too obviously (seen by the distorted inside
"trim") stretched squares.
-Shay
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Shay wrote:
> Tor Olav Kristensen wrote:
>
> Very nice. But not up to your usual standard of "sharpness." The
> rectangular holes are too obviously (seen by the distorted inside
> "trim") stretched squares.
The mesh in this shape was only subdivided once, because my
PC does not have enough memory to handle a second subdivision.
That's why the corners of the holes suffer like you describe.
I wasn't sure if other would notice that.
But now I know, so maybe I should buy some more memory...
Thank you for commenting.
--
Tor Olav
http://subcube.net
http://subcube.com
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Neat! You might find this site interesting, not POV but
similar to some of you stuff.
http://www.rinusroelofs.nl/rhinoceros/rhinoceros-00.html
Jim Buddenhagen
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