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From: Tor Olav Kristensen
Subject: Moebius Band as a Trefoil Knot
Date: 23 Oct 2004 00:10:24
Message: <4179a170@news.povray.org>
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


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From: Alberto Mendoza
Subject: Re: Moebius Band as a Trefoil Knot
Date: 23 Oct 2004 01:13:58
Message: <4179b056$1@news.povray.org>
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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From: Thomas de Groot
Subject: Re: Moebius Band as a Trefoil Knot
Date: 23 Oct 2004 07:38:47
Message: <417a0a87@news.povray.org>
Impressive!
The question from many fans: "Master, how did you do it?"  ;-)

Thomas


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From: LightBeam
Subject: Re: Moebius Band as a Trefoil Knot
Date: 23 Oct 2004 08:16:01
Message: <417a1341$1@news.povray.org>
I'm allways admirative when I see your images. You're, for me, the 
torus-master ;-)


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From: Florian Brucker
Subject: Re: Moebius Band as a Trefoil Knot
Date: 23 Oct 2004 09:27:03
Message: <417a23e7$1@news.povray.org>
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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From: Jellby
Subject: Re: Moebius Band as a Trefoil Knot
Date: 23 Oct 2004 09:28:59
Message: <417a245a@news.povray.org>
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 14:01:29
Message: <417a6439@news.povray.org>
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 14:01:53
Message: <417a6451@news.povray.org>
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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From: Tor Olav Kristensen
Subject: Re: Moebius Band as a Trefoil Knot
Date: 23 Oct 2004 14:02:03
Message: <417a645b$1@news.povray.org>
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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From: Tor Olav Kristensen
Subject: Re: Moebius Band as a Trefoil Knot
Date: 23 Oct 2004 14:02:21
Message: <417a646d$1@news.povray.org>
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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