[x3d-public] Problem constructing Mobius strip by extrusion of rectangular cross-section

Mon Aug 28 15:12:28 PDT 2023

Hi Vince

A colleague to whom I posed the same question has provided the answer
(snippet enclosed)

As he describes it: In your file "mobius_rect.x3d", the Möbius strip
does not close because the rectangle is rotated around a point which
is not its center of symmetry. If you move the rectangle so that it is
centered at the origin, then after 180° rotation it will coincide with
itself and the Möbius strip will close correctly. Please find attached
the modified version "mobius_rect3.x3d".

A wonderfully simple answer, the possibility of which I was not aware.

I can now play with the scale to explore other forms. However I am not
yet sure whether it is possible to do this through any ROUTE operation

Tony

On 28/08/2023, Anthony Judge <anthony.judge at gmail.com> wrote:
> Enclosed are the Extrusion snippets for both models
>
> Tony
>
> On 28/08/2023, Anthony Judge <anthony.judge at gmail.com> wrote:
>> Just to be clear, I have successfully built models with the Mobius
>> strip, as indicated in the following
>>
>> https://www.laetusinpraesens.org/docs10s/images/tenperc_files/mobius_borro_three.x3d
>>
>> I enclose screen shots of the 2-twist and 1-twist version (thre latter
>> in wireframe)
>>
>> Tony
>>
>> On 28/08/2023, Anthony Judge <anthony.judge at gmail.com> wrote:
>>> Hi Vince
>>>
>>> Thanks for the interest.
>>>
>>> I could easily  share screen shots but the matter is so simple that
>>> sharing the Extrusion of a 2-twist 360 orientation along the spine,
>>> with the Extrusion of a 1-twist 180 orientation might be simplest? It
>>> is the latter which fails and the former which is correct, but not
>>> what I want.
>>>
>>> My thought is the difficulty is the manner in which the Extrusion
>>> relates the orientation to the spine. For the 180 degree case, what is
>>> effectively required is that the spine (or a "fake spine") follow the
>>> center of the rotating rectangular cross-section. Of course it does
>>> not. It follows one edge. So 360 connects up but 180 ends up offset.
>>>
>>> Of course I may have messed up with the parameters of the Extrusion
>>>
>>> Do you need the screen shots?
>>>
>>> Tony
>>>
>>> On 28/08/2023, vmarchetti at kshell.com <vmarchetti at kshell.com> wrote:
>>>> Tony
>>>>
>>>> This sounds like an interesting project for the X3D community to help
>>>> with.
>>>>
>>>> As a proof of concept, this X-ITE rendering shows it is possible to
>>>> render
>>>> Mobius-like geometry in X3D:
>>>> https://spri-open-resources.s3.us-east-2.amazonaws.com/trimobius/index.html
>>>>
>>>>
>>>> The X3D file that this page is rendering may be retrieved at
>>>> https://spri-open-resources.s3.us-east-2.amazonaws.com/trimobius/mobius.x3d
>>>>
>>>> If you can share screenshots or webpages with your not-satisfactory
>>>> results,
>>>> that may give us some hint as to what's going on, and also sharing code
>>>> may
>>>> also help us.
>>>>
>>>> Vince Marchettti
>>>> Web3D Consortium
>>>>
>>>>
>>>>
>>>>> On Aug 28, 2023, at 1:38 AM, Anthony Judge <anthony.judge at gmail.com>
>>>>> wrote:
>>>>>
>>>>> I have a working model of a Mobius strip, but it uses Indexed Faceset
>>>>> which I cannot manipulate as I had hoped to do. Basically I want to
>>>>> extend the edges of the strip, possibly dynamically.
>>>>>
>>>>> So as an alternative I extruded a thin rectangular cross-section along
>>>>> a circular spine, but modifying the orientation of each element along
>>>>> the spine through 180 degrees.
>>>>>
>>>>> This gives a correct result, except that the ends do not meet
>>>>> correctly -- the end is offset because it is rotated around the spine.
>>>>> This is apparent if I change the orientation through 360 degrees, when
>>>>> the ends do connect correctly -- but I have two twists in the strip,
>>>>> which is not what I need for a Mobius strip
>>>>>
>>>>> I can provide snippets of this simple issue and I can understand how
>>>>> the issue is created by using the spine/orientation combination with
>>>>> the extrusion.
>>>>>
>>>>> Any comments/help?
>>>>>
>>>>> Tony
>>>>>
>>>>> --
>>>>> Anthony Judge
>>>>> <anthony.judge at gmail.com>
>>>>> www.laetusinpraesens.org
>>>>>
>>>>> _______________________________________________
>>>>> x3d-public mailing list
>>>>> x3d-public at web3d.org
>>>>> http://web3d.org/mailman/listinfo/x3d-public_web3d.org
>>>>
>>>>
>>>
>>>
>>> --
>>> Anthony Judge
>>> <anthony.judge at gmail.com>
>>> www.laetusinpraesens.org
>>> https://en.wikipedia.org/wiki/Anthony_Judge
>>>
>>
>>
>> --
>> Anthony Judge
>> <anthony.judge at gmail.com>
>> www.laetusinpraesens.org
>> https://en.wikipedia.org/wiki/Anthony_Judge
>>
>
>
> --
> Anthony Judge
> <anthony.judge at gmail.com>
> www.laetusinpraesens.org
> https://en.wikipedia.org/wiki/Anthony_Judge
>

-- 
Anthony Judge
<anthony.judge at gmail.com>
www.laetusinpraesens.org
https://en.wikipedia.org/wiki/Anthony_Judge
-------------- next part --------------
 <Extrusion DEF='Geom' beginCap='false' creaseAngle='1' crossSection='-0.5 0.05 0.5 0.05 0.5 -0.05 -0.5 -0.05 -0.5 0.05' endCap='false' orientation='0 0 1 0 0 1 0 0.07854 0 1 0 0.15708 0 1 0 0.23562 0 1 0 0.31416 0 1 0 0.3927 0 1 0 0.47124 0 1 0 0.54978 0 1 0 0.62832 0 1 0 0.70686 0 1 0 0.7854 0 1 0 0.86394 0 1 0 0.94248 0 1 0 1.02102 0 1 0 1.09956 0 1 0 1.1781 0 1 0 1.25664 0 1 0 1.33518 0 1 0 1.41372 0 1 0 1.49226 0 1 0 1.5708 0 1 0 1.64934 0 1 0 1.72788 0 1 0 1.80642 0 1 0 1.88496 0 1 0 1.9635 0 1 0 2.04204 0 1 0 2.12058 0 1 0 2.19912 0 1 0 2.27766 0 1 0 2.3562 0 1 0 2.43474 0 1 0 2.51328 0 1 0 2.59182 0 1 0 2.67036 0 1 0 2.7489 0 1 0 2.82744 0 1 0 2.90598 0 1 0 2.98452 0 1 0 3.06306 0 1 0 3.1416' scale='0.33 0.33' solid='false' spine='0.0 0.0 1.0 0.1564 0.0 0.9877 0.309 0.0 0.9511 0.454 0.0 0.891 0.5878 0.0 0.809 0.7071 0.0 0.7071 0.809 0.0 0.5878 0.891 0.0 0.454 0.9511 0.0 0.309 0.9877 0.0 0.1564 1.0 0.0 0.0 0.9877 0.0 -0.1564 0.9511 0.0 -0.309 0.891 0.0 -0.454 0.809 0.0 -0.5878 0.7071 0.0 -0.7071 0.5878 0.0 -0.809 0.454 0.0 -0.891 0.309 0.0 -0.9511 0.1564 0.0 -0.9877 0.0 0.0 -1.0 -0.1564 0.0 -0.9877 -0.309 0.0 -0.9511 -0.454 0.0 -0.891 -0.5878 0.0 -0.809 -0.7071 0.0 -0.7071 -0.809 0.0 -0.5878 -0.891 0.0 -0.454 -0.9511 0.0 -0.309 -0.9877 0.0 -0.1564 -1.0 0.0 0.0 -0.9877 0.0 0.1564 -0.9511 0.0 0.309 -0.891 0.0 0.454 -0.809 0.0 0.5878 -0.7071 0.0 0.7071 -0.5878 0.0 0.809 -0.454 0.0 0.891 -0.309 0.0 0.9511 -0.1564 0.0 0.9877 0.0 0.0 1.0'>
          <!-- spine is open, crossSection is closed -->
        </Extrusion>