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mobius strip


kirk

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I can't find an obvious way to make a continuous mobius.

Here is a kind of clunky workaround. Stand up some NURBS straight lines, rotate 2 of them to make the twist, Then loft them in sequence.

The twist can be formed by on its own (green or brown) and placed with or added to a loft with no twist (pink). Tangency btw the twist and non-twist surfaces is a problem. Add a few more posts to the twist to straighten it out at the ends.

The blue one is lofted starting at the middle of the backstretch - there are two "posts" with a small space btw for start and end of the loft.

Maybe others have a better solution.

-B

ubbthreads.php?ubb=download&Number=8666&filename=MobiusOutline.png

ubbthreads.php?ubb=download&Number=8667&filename=MobiusOGL.png

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Maybe this is a job for a texture of the text or Create Surface Array - v2013 only.

Layer 1 is my setup with "posts" around an oval. No attempt at tangency in backstretch.

Layer 2 has the surface and the array. Text>convert to poly>convert to NURBS. Create Surface Array with the group of NURBS and the Mobius.

To render with color, the letters need some thickness. Otherwise they get interposed in the base surface. I think it requires a lot of work with the NURBS letters and the Shell tool or Project Tool. Let us know if you work out something.

-B

ubbthreads.php?ubb=download&Number=8670&filename=Array%20on%20Mobius.png

Edited by Benson Shaw
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Kirk - this is not as elegant as your example, but it is same idea.

Try lofting NURBS rectangles duplicated around a circle. Then stretch the loft in plan to make the oval. Or duplicate the rectangles around an oval path.

Either case, spread the twist around the whole shape by incrementally rotating each rectangle. My example has the twist in only the "front" 5 at 30? increments. Back stretch has the gap.

Texture is simple Tile choice in the Color shader.

-B ubbthreads.php?ubb=download&Number=8671&filename=Mobius2.png

Edited by Benson Shaw
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Hi, Kirk - Don't get scared off by all this.

My NURBS rectangles are not joined to each other and are not present in the final figure. They are the profile "curves" used to generate a new NURBS surface with the Loft Surface tool. It's in your v2009 Fundamentals 3d Modeling tool set. Read Vectorworks Help about this.

Notes:

1. In plan view the rectangles are each on a plane of a radius, rather than tangent to the circumference. I used Duplicate Along Path to create them.

2. To make the twist, I rotate the whole group of rectangles in plan view around the circle center so the Front view is parallel to the plane of the rectangle I am working on. In Front view, I rotate for the twist with the Modify>Rotate>Rotate 3d - Object Center mode. Then back to plan, rotate the group so next rectangle is on x axis, switch to Front view, rotate the

3. The Gap: I duplicated the starting rectangle (backstretch) and, in plan view, rotated it a fraction of a degree around the circle center (changed is pen color, too). I duplicated the start rectangle again, and rotated it the same amount in the opposite direction (changed pen again). I think I deleted the original one. Zoom in to see the gap and the little 2d line I used as the guide to rotate the duplicates.

4. Engage the Loft Surface tool and click the NURBS rectangles in order. Carefully click the corresponding corner in each one. My loft path starts at the gap eg lower left, and moves around the circle, ending upper right. Then click the green checkmark up in the tool bar (or press Return). In the dialog, choose the option to save the profile curves and click OK. If you need to redo, delete the new Loft (OIP indicate it is a group of 4 NURBS surfaces) and loft again.

This is all on Layer 3 in the attached v2013 and v2009 files. The v2013 texture does not work in v2009, so I made a new one with Checker color shader. I made the shape on the circle, duplicated it and moved the duplicate to the left where I rescaled it to the oval shape.

Post back with questions.

-B

Edited by Benson Shaw
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Sorry to flog this. Kirk and everyone else has probably had enough.

But I kept at it because I was disappointed that this is so difficult in VW and the results were not quite right. The basic problem is that VW loft does not allow reconnecting the loft path to its starting profile curve. I tried again, splitting it into two lofts from new profile curves - a red set and a blue set-twisted uniformly around a circle. For each set, the end instance is an upside down version of the start instance. The endpoints are coincident, so the loft paths can get all the way around the circle.

The surfaces are quite good. The middle one has Draw Edges turned on, so the saved curves show as segments. The two surfaces should have a coincident edge allowing them to add into a single solid and accept uniform texture application.

But, apparently, the edges are not coincident. The two surfaces do not add or Stitch & Trim. And geometric textures cannot be adjusted to match continuously along the seam. Anyone else have this worked out in Vectorworks?

-B

ubbthreads.php?ubb=download&Number=8685&filename=Mobius3%20WF.pngubbthreads.php?ubb=download&Number=8686&filename=Mobius3%20OGL%20DrawEdges.pngubbthreads.php?ubb=download&Number=8687&filename=Mobius3%20Stretch.png

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Benson

Is this what you are looking for?

I just used a loft w/ no rails. The loft tool does allow reconnection to the first profile.

Just click on each nurbs curve in order

Don't click on the first one again at the end. It won't let you anyway.

Click the green checkmark

In the Loft Creation dialog box, check Closed. That will reconnect the final curve to the first curve.

Then use the Select Curve and Select Alignment by Point buttons to line up the "rail" curve (I'm sure that's not what it's called) to the correct vertices. (I cheated and marked them with 3D Loci to make this step easier.)

hth

mk

PS In the unlikely event that kirk is still reading this far down, I'll also post it in VW2009.

PPS The loft object has the tile texture. The other objects are surface extractions created from the loft object and added together. One for each "side" of the strip.

Edited by michaelk
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Thanks, Michael, for checking this out. Several thoughts. And, again, apologies to all for how verbose and esoteric this thread is getting:

Kirk's target example Sample Mobius Render , created in other software, is quite marvelous with a beautiful, Mobius surface hosting an evenly distributed grid over gradient coloration. I thought, maybe, Vectorworks could do that, too. Now I find, maybe not.

A "standard" Mobius strip is a 2d band with ends joined over a 180? twist. This creates a single, continuous 2d surface with a single continuous edge which can only exist in 3 space. A 360? twist creates two parallel surfaces contained within two edges.

The Mobius shape I'm working with is a 180? twist. My profiles are closed rectangular shapes to add thickness to the band - as in Kirk's example image. Ignoring my top & bottom faces for a moment, this still yields a continuous, single Mobius surface.

Closed Loft option pretty much works with a 360 twist, but not with the 180 twist, even after adjusting the contact points of the loft path.

I'm experimenting with rounded rectangles as the profile curves, hoping to produce a single (not group) continuous surface which evenly distributes a checker texture. Tried several ways. Only a couple are close. Both require splitting the profiles into a red half and a blue half (Wire Frame example in my previous post):

1. Duplicate in place the start/end profile. Then make two lofts - go all the way around the Red halves - starts high inside, ends low outside. Move this one to back, thereby exposing both the remaining start/end profiles. Loft the blue ones- start high outside, end low inside. This produces two continuous surfaces, not groups (Blue and Red mobius render in my previous post). They will not add, or stitch/trim, or match up the checker texture along the edge. But together, they represent a very good Mobius shape.

2. Click all the way around the Reds (start High, end Low) and just keep on going around through all the remaining Blues. Loft and pick the Closed option. No need to adjust the contact points. This loft produces a group of surfaces representing the desired continuous Mobius surface (yellow and green example in this post), but the flat "top" & "bottom" are blank. Extracted Curves do not compose and loft without lots of fiddling. Even then they do not stitch & trim.

Any further comment appreciated

-B

ubbthreads.php?ubb=download&Number=8690&filename=Mobius180-group%20of%20surfaces.png

Edited by Benson Shaw
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