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

[Peter Neufeld.]

Thanks Jeff but I can't work out the crucial part of bending the twisted extrude using the circle?

 

Cheers,

Peter

[line-weight]

10 hours ago, jeff prince said:

 

 

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

 

I think what I posted above shows that it does, unless anyone can show me where it fails.

[Benson Shaw]

@jeff prince Nice sample!  I'm not fulling understanding the need for the circle.  It seems length of your "bar" is just shy of the circle circumference? Bend click at ends of the line segment under the bar, then #3 at top of circle causes bend angle just shy of 180" without data entry?  

 

Re logical definition: I think in one sense, the definition infers a join.  Many Mobius Strip definitions start with suggestion to imagine joining the ends of a strip of twisted paper. We agree ignore the thickness of the paper, the effects of the glue, etc. and just accept the paper as a surface.  All very reasonable.   In another sense, though, most of these definitions go on to suggest the construction process alludes to a single surface with only one face and one continuous edge.  No thickness, no start or end, no A side or B side.  But doesn't really matter.  Vectorworks is making an approximation. Very good ones are shown in this thread. Any facets, gaps, join lines, uncertain tangency, etc. can be minimized to acceptable value by employing various strategies.

 

@line-weight Nice sample!   Seems you cut things into 8 segments at some point? Can you reveal a bit about your process?

 

No fail in your sample. Very nice.  Hidden line does reveal the underlying segmentation.

 

 

Thanks @Peter Neufeld. for pushing this out!

 

-B

[line-weight]

1 hour ago, Benson Shaw said:

@line-weight Nice sample!   Seems you cut things into 8 segments at some point? Can you reveal a bit about your process?

 

No fail in your sample. Very nice.  Hidden line does reveal the underlying segmentation.

 

I did it with the subdivision tool. I was a little surprised when it worked. I didn't cut anything (other than within the subdivision edit)

 

Start with torus primitive, fiddle around a bit making breaks so as to make some faces to rotate, then stick back together using the "bridge" function.

 

My next project was to see if I could make it as a true single "surface" (rather than a solid) using the subdivision tool. However, so far I've not managed. It doesn't want to let me stick it back together with a twist in it (if I rotate things then stick back together, it adds another twist to turn it into a simple loop).

 

It's disappointing that it leaves those seam lines as revealed in hidden line. Didn't notice that. It seems I can extract the two edges each to a series of NURBs curves. Then I can "compose" these to single NURBs curves. Then I can loft between them but the "seams" reappear. Closer inspection of the composed NURBs reveals some doubled-up nodes and removing these means that it won't let me loft. There's also a kind of doubled node at the start/end point, and if I delete this, I get a break in the loop, although it will let me loft between them, producing this (in hidden line):

 

(but even if I'd managed to join that gap, the object produced wouldn't be a mobius strip)

 

 

 

 

 

 

 

Edited January 3, 2023 by line-weight

[Benson Shaw]

3 hours ago, line-weight said:

There's also a kind of doubled node at the start/end point

AFIK NURBS curves are never closed.  Start and end points can be coincident, but a segment does not manifest between them.

? Or can other software close them?

 

Anyone know of a closed NURBS curve?

 

 

 

3 hours ago, line-weight said:

I did it with the subdivision tool.

SubD! Super!

 

-B

[Pat Stanford]

Isn't a closed NURBS curve actually a NURBS surface?

[Peter Vandewalle]

24 minutes ago, Pat Stanford said:

Isn't a closed NURBS curve actually a NURBS surface?

No. In a nurbs surface each vertex is more like a crosspoint of 2 nurbs curves, 1 in U direction, 1 in V direction.

[line-weight]

10 hours ago, Peter Vandewalle said:

No. In a nurbs surface each vertex is more like a crosspoint of 2 nurbs curves, 1 in U direction, 1 in V direction.

Can a NURBs surface be "closed" in one or both directions ... eg like the outside of a cylinder, or a sphere?

[line-weight]

By the way, is a seam line appearing in "hidden line" actually evidence that there's a non-smooth transition between two faces?

 

For example if I draw this shape where I know the arc of the curved end meets the adjacent flat face exactly at a tangent, and set the hidden line smoothing angle to zero, I get a line at that point.

 

[Peter Neufeld.]

Hi All,

So the conclusion as far as I can see is that twisting and bending solids is easy. However to close upon itself is nigh on impossible unless you cheat as I did with the 359.999º  method or by using some other notable and creative methods posted here by such esteemed users. I am still intrigued by Jeff's circle method. I tried everything I could think of before returning to the Deform tool, for this solid object.

 

In the end it boils down to why can't you bend an object more that 360º with the deform tool?!! Thanks to everyone and please continue if you can add more to this thread.

 

Cheers,

Peter

[Benson Shaw]

On 1/4/2023 at 2:11 AM, line-weight said:

By the way, is a seam line appearing in "hidden line" actually evidence that there's a non-smooth transition between two faces?

Good question.  I think the "seams" can represent at least a couple different things:

• Discontinuity  - point or surface region with more than one definition, eg an edge/corner or other intangency.
• Some form of Vectorworks surface interpretation, but not necessarily a discontinuity.

Changing the smoothing angle (hidden line) or the crease angle (shaded) causes different configuration of the seams.

Different methods of attaining the shape produce different interpretations of seams.

 

I think the mobius techniques involving bend shy of the full rotation produce a gap which will definitely produce a line in HL.

No apparent gaps or intangency via Lineweight's SubD or Tobias' cut with separate bends at full 180°.  Even though they have the HL lines.

 

Attached video shows a test sequence with the smoothing angle on same(?) shape made with different methods.  Not proof of anything, but shows differences.

-B

Edited January 5, 2023 by Benson Shaw
Lunch at desk

[line-weight]

3 hours ago, Benson Shaw said:

Changing the smoothing angle (hidden line) or the crease angle (shaded) causes different configuration of the seams.

Different methods of attaining the shape produce different interpretations of seams

 

Of course, the smoothing / crease angle settings are very useful in the real world and I often tweak them to get acceptable results from imperfect models.

 

Somehow it feels like cheating though - like, if the geometry is mathematically correct, then it should be possible to set it to 0 degrees and have no lines where there shouldn't be. And when there's a line there I want to know whether it's me or VW that's lacking in precision 😬

[Kevin K]

You guys are having wayyyy to much fun !

For my next challenge.....I have to try to create a 'Bowline' knot.  ....or maybe 'knot' 🙂

 

[Peter Neufeld.]

Hi Kevin,

Have a look at this thread a few posts earlier:

 

 

@AlanWAlan Woodwell has tied the knot beautifully!

 

Cheers,

Peter

 

[Kevin K]

Peter

Man...that was beautiful!! Way above my pay grade 🙂

Thank you for the inspirational link!