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Modelling challenge: Möbius strip - model this as a seamless solid with no visible joins!


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  • Vectorworks, Inc Employee

Hello,

For a bit of fun here's a holiday challenge. Can you model a Möbius strip that's about 10m long, 200mm wide and extruded 1000mm or of similar proportions? It has to have a thickness.

 

Some of you might yawn at this no doubt, and it is dependant on the Deform tool of course. It's actually quite hard to bend so that there is no visible join. I will post my solution in due course.

 

 

Screenshot 2022-12-29 at 4.28.36 pm.png

 

 

 

 

 

 

 

 

Cheers,

Peter

Edited by Peter Neufeld.
Added orbit movie
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  • Vectorworks, Inc Employee

Damn! That was quick! Anyone else?

 

Hard to work out the steps but it looks like you split the twisted solid and bent each side 180º then used the Intersect Solids command - but I'm unsure? Different to my option but probably more accurate.

 

Google translate isn't that great with CAD commands it seems. I like "Create wool body".

 

IMG_2078.jpeg

 

 

You have a lot of NURBS commands in your workspace that I have no idea what they are:

 

Screenshot 2022-12-29 at 7.43.36 pm.png

 

 

 

Anyone else willing to give this a try not using Tobi's method?

 

Cheers,

Peter

 

 

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Love @Tobias Kern’s simple and elegant solution. Several of us horsed around with this 10 years ago with V2013 Lofts,  before Deform feature was added. Never quite made it work. (long thread in old format, images removed, so rather unhelpful):

https://forum.vectorworks.net/index.php?/topic/36141-mobius-strip/#comment-179482?

 

Strangely, one can extract the two edges of @Tobias Kern completed möbius and successfully compose then loft them - short connect for edge möbius, longer connect for the main face.or just extract the surfaces.  Also interesting, neither möbius surface shells to make a thickened möbius. Always two components. The normals cannot be reversed in any combo to produce coincident shell ends. 
 

@Peter Neufeld. Many thanks for this thread. Your screenshot did not reveal your technique. Or, I’m being dense. Can you elaborate?

 

The “Create wool body” command is not available in my workspace.  I’m guessing it has modes for Ewe, Ram, and Lamb? Maybe even Array Herd mode? 
 

 -B

 

Edited by Benson Shaw
Bo Peep went to sleep
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  • Vectorworks, Inc Employee

Hello Benson,

Yes I saw that 2013 thread as I wanted to make one of these things. It took me a while to figure out my answer and I've done a quick 47 sec video showing how I did it. I thought though I'd see what other ideas were out there and so I might wait for a while to see if anyone else gets it right before posting. Just for a bit of fun. Give it a go (wool command notwithstanding!).

 

Cheers,

Peter

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  • Vectorworks, Inc Employee

Another excellent result Tobi!

It's a bit tricky and time consuming that way and not really a solid though although I didn't explicitly state it had to be (but I meant it to be). However a great result. How do you navigate around the NURBS without losing focus with the Loft tool? Is that a middle mouse thing, I only have an Apple mouse without one?.

 

If no one else attempts then I'll post my way soon.

Cheers,

Peter 

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10 hours ago, Benson Shaw said:

Strangely, one can extract the two edges of @Tobias Kern completed möbius

 

 

Extracting an edge from a solid that the "deform" tool has been used on seems to produce a NURBs curve where the XY plane of its "normal" rotates along its length.

 

(When I say "XY plane of its normal" I'm probably using technically incorrect terms. But if you activate the working plane tool and trace the cursor along the NURBs curve, it rotates)

 

I wanted to see if I could exploit this using the "extrude along path tool". I did manage to produce some twisted strips. However, I can't see any way to directly manipulate this property of a NURBs curve, and wasn't able to make a circular NURBs curve whose "XY plane of its normal" rotates by 180 degrees from start to finish.

 

I don't think this kind of manipulation is possible. But, NURBs curves and the EAP tool are both very poorly documented in VW so exactly how they each work continues to remain a mystery to me and I end up resorting to trial and error.

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@Tobias Kern your loft is nice, but twists 360.  None of the surfaces is a Möbius. This is what drove us nuts on the earlier thread. The vwx NURBS “Close” function does not operate if the start to end twist is 180 (or odd integer multiple). A coincident duplicate profile at end position should resolve this, but I could never make it work.  The loft rubber band  “picker” does not allow choice of selection eg one cannot interrupt the loft to paste in a duplicate profile, or Send to Back an existing duplicate, or B key xray, or other way to extend the rubber band to desired end point.  
 

Still trying to concoct another alternative for the challenge. 

-B 

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OK - Here is a passable NURBS mobius using the concept of joining two separate lofts.  Not great compared to @Tobias Kern method, but at least proves that one can get very close with lofting.  Problems are many: fussy setup, potential for miss during rubberband clicks. Then, the finished solid has those signature vwx edge facets and a very slight intangency at the vertical join.  Likely there are other mathematical inconsistencies, too.

 

Reason for lofting an extra station on each side of the "keeper" volume is that NURBS bow more "easily" at center of curve, similar to bending a strip of wood or metal. So ends of the rubberbands are straighter than they should be for perfectly tangent solid addition. Creating the longer loft and cutting off the straighter ends captures a better approximation of the intended curvature in the retained volume. More stations would allow a longer volume and a better keeper, at expense of more involved setup.  I could go on.  Ask if this is not making sense.  Or, just use the deform tool!

 

Enjoy!

 

-B

Edited by Benson Shaw
A trip to the lobby
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  • Vectorworks, Inc Employee

Hi Benson,

That is absolutely wonderful top notch Lofting! Excellent work although as you attest, alas, there is a visible join.

I wish there was a command that could rotate objects as they are duplicated along a path like how we can already for linear arrays. Somewhat fiddly getting the profiles at the correct angle in your example but beautifully done like Tobi. Also why is it that the Deform tool can not bend something >360º? And, also that once bent the objects become Generic Solids and therefore are unable to be edited?

My solution using the Deform tool will probably really annoy any CAD purists, but unless someone can suss it beforehand I won't post the movie until someone tries again!

 

Cheers,

Peter

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Hi,

 

great Nurbs-Loft, like that solution.

 

Yesterday I also play around with a Möbius Nurbs Loft

and came close to Bensons solution.

 

A combination of two lofts is needed to fulfill the challenge.

A full 360 is not possible with any solution, I guess.

 

In November, I bought a Rhino license to learn it a bit

and to do some Nurbs things, which are not possible in VW.

 

I will write a wish for a better Loft-Tool in the following days.

 

 

Happy New Year!

Tobi

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@Benson Shaw as I'm sure you're fully aware the difficulty with your method is getting the two halves to join mathematically exactly, that is with all the curves meeting each other at a properly tangential transition. And you can get pretty close by telling each loft to pass through the same profile at the same point, but the lines leading in from each side don't arrive at that profile at exactly right angles.

 

I'm often posting a link to this thread and particularly the contributions from @axhake because it addresses problems that always arise whenever you're attempting this sort of thing with NURBs and lofts or extrude-along-paths. And the solution there is basically to accept that the object will be faceted rather than truly curved. But you have some control over the number of facets and can make sure things do actually meet exactly.

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On 12/29/2022 at 10:05 AM, Peter Neufeld. said:

It's actually quite hard to bend so that there is no visible join

 

I'm not seeing the difficulty in this task, am I missing something?

Draw a rectangular solid with your desired dimensions.

Twist axially 180 degrees.

Bend symmetrically using some helper geometry, notably a circle with the circumference = the length of the twisted rectangle.

Viewing from the bottom makes this a little easier to pick.

42942217_ScreenShot2023-01-02at11_08_49.thumb.png.f506aad9da1f4809de961341d75f7375.png

 

1218429878_ScreenShot2023-01-02at11_05_29.thumb.png.e1e67367c6fecae39d1ca69e861c17c5.png

 

1575098415_ScreenShot2023-01-02at10_35_03.thumb.png.4e2d9497f71f3c9cb29a21d4b5cc1a9d.png

 

 

 

 

 

 

Edited by jeff prince
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  • Vectorworks, Inc Employee

Oh no Jeff - we're missing something! Excellent stuff.

You have solved the riddle most likely more accurately than my feeble attempt. However I can't work out your method as much as I try so can you please send a quick movie? This is exactly what I was hoping for as I couldn't believe how tricky this was to model. My attempt (please don't flame me!) which you can see below is not a purist CAD answer so it is inherently false/inaccurate/a workaround, but it works!. I look forward to seeing the better answer!

 

 

 

 

Cheers,

Peter

 

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OK, Nicely done!

 

And, this is observation rather than complaint . . .  Buuuuut . . . Hidden line render shows the seam at the join.  Tobias' shows seams at initial cut and at join.  My loft shows seams at the cuts, too.

 

Anyway, the surface renders are wonderful!

 

Thanks all!!!

 

-B

Edited by Benson Shaw
looking into the pool of darkness
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  • Vectorworks, Inc Employee

Hi Benson,

I never thought of doing a HLR and you are absolutely right. No way to get rid of it. It's like a lie detector - no smoothing angle erases it. Yes a good observation but still the point of this exercise was that:

 

1: Once the Deform tool is used object changes to Generic Solid so no going back.

2. Not using anything other than itself to snap to, Deform can't go past 360º (until Jeff shows how it's done).

3. Using NURBS afterwards from extracting curves and Bi-Rail Lofting produces hollow solid.

4. Shelling NURBS surface never seemed to work.

 

Hence my quest for an answer. 

 

Cheers,

Peter

 

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4 hours ago, Benson Shaw said:

And, this is observation rather than complaint . . .  Buuuuut . . . Hidden line render shows the seam at the join.

 

Doesn't the logical definition of a Möbius strip feature a single join? 

 

4 hours ago, Peter Neufeld. said:

Not using anything other than itself to snap to, Deform can't go past 360º (until Jeff shows how it's done).

It also can't go past 180, depending on the mode you select and type of geometry you are creating 😉

 

Here's my file with the construction method in steps.  You'll find some curious things occurred, even when using geometry for construction.

I don't think Vectorworks is capable of resolving the curve without a seam because it apparently can't be drawn as a closed curve to begin with.

 

Blender is probably the actual correct answer because it can define a closed Bezier circle 😉

I haven't used Rhino in a very long time, but I imagine there is a method there too.

Does Vectorworks even have the correct tools to do a truly closed solid like this?

It's easy enough to make it visually passable with thickness, developable with a single surface.

 

1068292194_ScreenShot2023-01-02at16_53_47.thumb.png.da0893c24a78c5b9be307d58f669950c.png

Mobyish Strip

mobius strip.vwx

Edited by jeff prince
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