The Mobius Curve Thing

[VIRTUALENVIRONS]

The Mobius Curve thing seems to come up a lot.  I played with it a bit and had limited success, but as I could not see the engineering value, I left it alone.  It came up again a little while ago, so I looked at it again and I think I figured it out, unless what is below is not a Mobius Curve.  The Mobius Curve confuses me.

To make this curve, I used a set of Matched Curves.  Using Matched Curves removes any decision making by Vectorworks on how to interpolate the curves, essentially forcing your will over the interpolation algorithm.

Tomorrow I will post a short tutorial, the file with the Matched curves for anyone to play with.

 

 

[halfcoupler]

I'm not shure, but isn't the Moebius Curve a 180 degree turn ? It seems you made only 90 degrees ?

[VIRTUALENVIRONS]

It is 180 degrees.  It is the view that does not show well, but tomorrow I will post the file and curves if you want to play with this.  This seems to be only possible with single node Matched Curves   The short video below gives a clearer view.

 

 

[Jeff Prince]

This is not a Möbius strip.

It's a squished donut with a twist

aka flattened torus with 180 degree twist.

 

To be a Möbius strip, you have to have an edge.

To be a Mobius bagel, you have to have knife skills...

Something to try at home....

 

 

[VIRTUALENVIRONS]

 

Working file with curves enclosed

Well Jeff, this was more about closing a curve with a half twist than the Mobius, but perhaps we will let the viewers decide.  I can make this again with a squared edge later on.

This is an introduction into single node matched curves.  The enclosed file is VW 2018.

MOBIUS FORUM.vwx

 

 

[Jeff Prince]

27 minutes ago, VIRTUALENVIRONS said:

 

Working file with curves enclosed

Well Jeff, this was more about closing a curve with a half twist than the Mobius, but perhaps we will let the viewers decide.  I can make this again with a squared edge later on.

This is an introduction into single node matched curves.  The enclosed file is VW 2018.

 

I see, using a popular topic for the title (The Mobius Curve Thing)and then the 'ol bait and switch to get people over to your Youtube channel... yet again.

I don't think the Vectorworks community is large enough to sustain your Tim Horton's habit off of ad revenue 🙂

 

 

 

Edited May 15, 2023 by jeff prince

[VIRTUALENVIRONS]

Hi Jeff,

I could care less about my Youtube Channels for money, as I don't monetize them.  Although YouTube does itself, but I can't stop that.  I have three channels, again all non-monetized, but very helpful.  That is how Jonathan Reeves found me.  

 

I have to bring something up here.  Why is it exactly you are on this Forum?  I am here to impart NURBS modelling skills.  The main reason is that Vectorworks itself either cannot or has no interest, but see it as a good thing if others do.

You on the other hand seem to want to drive users to any other software than Vectorworks.  There is literally nothing Rhino could do in terms of Architectural modelling that Vectorworks can't do or do better.  I tell them they can, you tell them they can't.  

[Tom W.]

I thought the whole issue with the original mobius challenge thread was that no-one could achieve the mobius without there being a join where it met itself (seen in hidden line). As far as I can tell @VIRTUALENVIRONS has demonstrated a way to achieve it without the visible join no? Perhaps @line-weight can confirm as I have only been half-following it all

[VIRTUALENVIRONS]

Hi Tom,

Did you download the file and try it.  Pretty easy.  If we can confirm it is a mobius curve, I will explain how in a short tutorial.

 

 

[Jeff Prince]

1 hour ago, VIRTUALENVIRONS said:

Why is it exactly you are on this Forum?

 

I'm here to help people when they have problems and to get help when I have one.  I think my record supports that pretty well.

 

You can have your opinion about Rhino and other softwares, but it is simply wrong.  You do not seem to understand what architects do or require in the course of their work.  Making the claim "there is literally nothing Rhino could do in terms of Architectural modeling that Vectorworks can't do or do better" demonstrates this lack of knowledge.

 

Keep making tutorials and enjoy it, but don't be surprised if people call you out for thing when there are errors.  I'm not hiding behind an avatar and the ananomity of the internet when I make my statements. I think it is important to keep this community honest and as accurate as reasonably possible if it is to remain a valuable resource.

 

20 minutes ago, Tom W. said:

As far as I can tell @VIRTUALENVIRONS has demonstrated a way to achieve it without the visible join no?

 

No, because the object has no edge, which is a requirement of a Möbius strip.  This object is just a squished and twisted torus from a mathematical perspective.

Edited May 15, 2023 by jeff prince

[Tom W.]

Just now, jeff prince said:

No, because the object has no edge, which is a requirement of a Möbius strip.  This object is just a squished and twisted torus from a mathematical perspective.

 

But could the same technique not be used on a thin rectangle or line?

[Jeff Prince]

3 minutes ago, Tom W. said:

But could the same technique not be used on a thin rectangle or line?

 

Try it with a line and see what happens 🙂

 

[Tom W.]

1 minute ago, jeff prince said:

 

Try it with a line and see what happens 🙂

 

 

Can't someone else do it + I just watch? 🙂 

[VIRTUALENVIRONS]

Sorry got lost on this.  Lot of emails coming in.  

This method works for round objects as presented.  I can have a look at doing it with a rectangle or line I suppose, but it would work differently.  Vectorworks sees NURBS lines and Square somewhat different than curves.

 

Anyway, did you see the Twinmotion video.  That is the first thing I have seen in a long time that is impressive.  Most other stuff referred to as new is often twenty years old.

 

[VIRTUALENVIRONS]

Will post curves later this morning.   Got to go cut grass.

 

[Jeff Prince]

1 hour ago, VIRTUALENVIRONS said:

 

Will post curves later this morning.   Got to go cut grass.

 

Looks like the same result that everyone and their uncle came up with on the original Mobius discussion…

 

 

[VIRTUALENVIRONS]

The file below contains a set of "single point matched curves".  As the earlier post, use loft surface, set everything to 100 and use "closed".

MOBIUS SQUARE.vwx

 

[Jeff Prince]

11 minutes ago, VIRTUALENVIRONS said:

The file below contains a set of "single point matched curves".  As the earlier post, use loft surface, set everything to 100 and use "closed".

 

That was an interesting attempt, but it "seams" even further away from the correct solution 🙂

Did you try a line using that method?

[VIRTUALENVIRONS]

Hi Jeff,

This curve inverts 180 degrees and joins using "closed".  I don't know what else you are looking for.  Having said that, I can't be your personal trainer forever.  The curves are there for you and anyone else  to play with.  I think you have enough skills to forensically go through them and understand how it was done. 

 

I noticed you stayed away from the Twinmotion post.

 

 

[line-weight]

On 5/15/2023 at 8:28 PM, Tom W. said:

I thought the whole issue with the original mobius challenge thread was that no-one could achieve the mobius without there being a join where it met itself (seen in hidden line). As far as I can tell @VIRTUALENVIRONS has demonstrated a way to achieve it without the visible join no? Perhaps @line-weight can confirm as I have only been half-following it all

 Have been pre-occupied with other stuff so late coming back to this.

 

I don't think @VIRTUALENVIRONS has yet succeeded in creating a mobius strip using this method.

 

The "square" version posted since still doesn't, because it's not rectangular in section. Look closely at the rectangles used for the loft and they have rounded corners. As a result the generated object has no edges. I'm not a topologist but I think it's a deformed donut really.

 

What Vectorworks has produced using this loft is not clean geometry at all, even if you ignore the "no true edges" issue. This can be seen in hidden line (the only continuous line you can follow isn't even a pretend edge, more like a kind of seam that runs all the way around):

 

 

And in shaded view - the underlying skeleton that appears in orange when I select the object looks fairly clean, but the surface VW has generated from it is a mess:

 

 

 

 

And this is what I get if I take a section through the object:

 

So I would say that although the geometry used to produce the loft object seems very tidy, Vectorworks has completely mangled things when it comes to the resultant object.

 

I wonder what happens trying the same technique but with true rectangles. I think possibly @jeff prince is technically correct when he says that it would only be a true mobius if the cross-section is a line rather than rectangle, but that wasn't a requirement in the original mobius thread. If anyone can create a seamless object with a rectangular cross section then they will have done better than any of the solutions so far... I think.

 

[VIRTUALENVIRONS]

Hi Line - weight

You have given this a lot of thought.  Based on your original emails to me, the problem was getting curves to rotate 180 degrees and then close.  That was the issue I was solving here.  If the curve did not close as some of the earlier example I played with, extracting a iso-parms would give a twisting curve.  If you notice on this model it extract a iso-parm the curve is uniform.

 

If a Mobius curve needs to be a strip as Jeff suggests or have sharp corners, etc., then it is not a mobius curve.  But, this issue of closing a curve with 180 twist is solved.

[line-weight]

12 minutes ago, VIRTUALENVIRONS said:

Hi Line - weight

You have given this a lot of thought.  Based on your original emails to me, the problem was getting curves to rotate 180 degrees and then close.  That was the issue I was solving here.  If the curve did not close as some of the earlier example I played with, extracting a iso-parms would give a twisting curve.  If you notice on this model it extract a iso-parm the curve is uniform.

 

Can you explain what an iso-parm is, and how you extract one in Vectorworks?

 

I think when you talk about "closing" a curve you mean the same thing as what we have been calling a "seamless" join (without having a very precise definition of that).

 

We'd been sort-of using hidden line view as a test - if a "seam" shows up in hidden line then it suggests the surfaces each side of it don't transition smoothly. However, I think I pointed out that hidden line will still show a seam in some cases where there ought to be a perfect transition.

 

It would be useful to understand what you mean by isoparm and whether this provides a precise method of checking for non-smooth joins in vectorworks.

 

 

[VIRTUALENVIRONS]

If you go to Extract in the 3D NURBS menu and to the upper left corner.  You will see four options, point, line, Iso-parametric (Isoparm) and surface.  Choose Iso-parametric.  There is a little tool icon to the right. Have them all checked off for simplicity.

 

With these parameters selected, hold the mouse over the "object that rotates on itself 180 degrees and joins with "Closed in the Loft Menu".    You will see both a red horizontal and vertical line appear.  Click once to select, copy them out somewhere else to look at them.

 

I the earlier trial version of that curve, the curve would not be joined and would also have a screw thread appearance as it was not closed or seamless.

[line-weight]

2 hours ago, VIRTUALENVIRONS said:

If you go to Extract in the 3D NURBS menu and to the upper left corner.  You will see four options, point, line, Iso-parametric (Isoparm) and surface.  Choose Iso-parametric.  There is a little tool icon to the right. Have them all checked off for simplicity.

 

With these parameters selected, hold the mouse over the "object that rotates on itself 180 degrees and joins with "Closed in the Loft Menu".    You will see both a red horizontal and vertical line appear.  Click once to select, copy them out somewhere else to look at them.

 

I the earlier trial version of that curve, the curve would not be joined and would also have a screw thread appearance as it was not closed or seamless.

Ok, thanks for the explanation.

 

My question though is do we have something with any special properties that a simple donut doesn't. The one on the left I've just done as a EAP. It offers a continuous/closed path around the ring, and also a continuous one around the ring's cross section. Yours I think is topologically the same, except that it's actually two surfaces joined together (highlighting the isoparm reveals the seam between them). I found that extracting surfaces allows me to to dis-assemble into those two surfaces.

 

So VW has created two "closed" strips, but neither has the special property of a mobius strip, which only has one surface, rather than a front and a back.

 

 

 

 

 

 

Edited June 8, 2023 by line-weight

[VIRTUALENVIRONS]

Hi Line weight,

Mine is a single object as far as I can tell.  If the curves join with "closed" in the dialogue box, then it is a single object.  Try cutting it is half or sections. etc.  

 

As I stated earlier, I was trying to address your issue with curves that turn 180 degrees and then will close in the loft NURBS dialogue box.  Although this is interesting, there is no engineering value in the "Curve that turns on itself 180 degrees and then closes in the Loft Dialogue box".

 

The Ladies Ring on the other hand has great engineering value.  I would be happy to talk about that some more.

regards....Paul