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  Mobius Strip - mobius01_withsphere_small.jpg (0/1) (Message 1 to 3 of 3)  
From: Blane Bizzaro
Subject: Mobius Strip - mobius01_withsphere_small.jpg (0/1)
Date: 12 Oct 2002 16:06:14
Message: <3da844b5.542418@news.povray.org>
This is 1 frame from what I hope to be an animation of spheres rolling
around a mobius strip. I could use some help with the math. I already
know how to roll a sphere in a straight line regardless of the radius
of the sphere or it's x location, it's like this...

object {sphere {<0,0,0>0.25
        texture {pigment {checker color White color <.1, .6, .5> }
           finish { ambient 0 diffuse 1 phong 1 phong_size 80}}
                 rotate <0, 0, -clock*360*4>

//clock*4 because the radius of the sphere 0.25

      translate <-3, 0.25, 0>
      translate <2*pi*clock, 0, 0>}
       
            }

But so far, I don't know how to roll the sphere around the y axis with
an orbital axis that matches the major radius of the mobius strip.

I also don't know how to calculate the correct Y translation as the
sphere rolls along the face of the mobius strip. 

Any ideas or comments would be greatly appreciated.
Thanks All! 

 Thanks to Friedrich A.Lohmüller for his great ideas!
http://www.f-lohmueller.de/pov_tut/loop/povlup2e.htm


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From: Blane Bizzaro
Subject: Mobius Strip - mobius01_withsphere_small.jpg (1/1)
Date: 12 Oct 2002 16:06:34
Message: <3da8483f.1449919@mail.earthlink.net>



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From: Herman Serras
Subject: Re: Mobius Strip - mobius01_withsphere_small.jpg (0/1)
Date: 13 Oct 2002 07:15:42
Message: <3DA91E51.47F0ED18@pandora.be>
Blane Bizzaro wrote:
> 
> This is 1 frame from what I hope to be an animation of spheres rolling
> around a mobius strip. I could use some help with the math. I already
> know how to roll a sphere in a straight line regardless of the radius
> of the sphere or it's x location, it's like this...
> 
> object {sphere {<0,0,0>0.25
>         texture {pigment {checker color White color <.1, .6, .5> }
>            finish { ambient 0 diffuse 1 phong 1 phong_size 80}}
>                  rotate <0, 0, -clock*360*4>
> 
> //clock*4 because the radius of the sphere 0.25
> 
>       translate <-3, 0.25, 0>
>       translate <2*pi*clock, 0, 0>}
> 
>             }
> 
> But so far, I don't know how to roll the sphere around the y axis with
> an orbital axis that matches the major radius of the mobius strip.
> 
> I also don't know how to calculate the correct Y translation as the
> sphere rolls along the face of the mobius strip.
> 
> Any ideas or comments would be greatly appreciated.
> Thanks All!
> 
>  Thanks to Friedrich A.Lohmüller for his great ideas!
> http://www.f-lohmueller.de/pov_tut/loop/povlup2e.htm

Hello,
Some time ago I posted an animation of a sphere rolling along a
Möbiusstrip with only one "bend". It was a rather big file for what it
represented (as someone answered). I received a lot of help to reduce
the size of the file, but... I don't find the reduced file back on my
PC.
Nevertheless before going into the mathematics and constructing (and
reducing) the animation again:
- did you use functions to obtain the strip, or did you use a mesh?
- if you use functions you easily can obtain the position of the center
of the sphere in each position, by calculating (ex. by hand) the surface
normal in each point of the trajectory, if you use a mesh you have to do
this using a sort of smooth triangles 
- the sphere I used had a uniform color, so the rotation problem was
less difficult
Friendly greetings,
Herman
-- 
Herman Serras
Gent (Belgium)
http://cage.rug.ac.be/~hs/


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