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The Power of RULESURF

1) Draw the outline shape.

2) Draw a '3D polyline' to create the curve profile that twists.
Repeat the '3D polyline' but mirror around 180 degs.

3) Set 'SURFTAB1' to 20, it will create a smoother surface, with 20 segments.

4) RULESURF the 2 3D polylines together.

NB The source is not an ellipse but could be if you wish.

Hey presto, a couple of minutes and a MOBIUS thingymijig !!

Nick

http://www.eezylearn.pwp.blueyonder....mages/mob1.jpg
http://www.eezylearn.pwp.blueyonder....mages/mob2.jpg

2. "Draw a '3D polyline' to create the curve profile that twists."

Hmm... sounds easy when you say it like that but I reckon I'll be sticking with fuccaro's LISP routine should I ever need to draw a Mobius strip.

By the way, in case you were wondering, the strip was named after August Mobius (1790-186, German mathematician who invented it.

3. If you look at the polyline I have drawn it snapping to an end point then a midpoint then another end point then mirrored it. That was pretty easy. Only three points to draw !

Nick

4. Nick
I was sure you will find a way to do it. But let me ask you: there is a surface or are two surfaces with two common edges creating the ilusion of a single one?

5. Originally Posted by fuccaro
Nick
I was sure you will find a way to do it. But let me ask you: there is a surface or are two surfaces with two common edges creating the ilusion of a single one?
It's a single twisted rulesurf. Since the two polylines twist when you then create a surface between them the surface is twisted also. A RULESURF is a surface between any two entities

Curve to curve, line to line circle to circle, rectangle to rectangle etc etc. The best thing is it works easily across planes. Unlike the dreaded REGIONs which only work co-planar (same plane ie same XY plane)

Anyway covering a MATHS lesson on mortgages, boring !. Not teaching graphics just now.

Nick

PS I'll do a detailed RULESURF tutorial soon, good weather for rock climbing inthe evenings just now, here in Scotland.

6. Originally Posted by johnfulwyler
The mobius thread was interesting to see. I didn't even know what the term meant before now
Just out of curiousity, what exactly would a mobius be used for?
The Mobius strip is a funny object: it has a single surface. Create a Mobius strip from a paper ribbon and put it on the table. Move a pencil along it. You will end up with a continuous closed line. Cut the strip and examine the ribbon: on both of sides you have lines!
On the ancient times I used a printer with an inked ribbon. That ribbon was twisted. In this way it was used on both of sides (longer life).
Other utilities of the Mobius strip? Somebody else?

7. I suppose you could design a double edged V belt used in car engines for drive belts etc and have it twisted as above to improve the life.

Nick

8. How about endless toilet paper

Rob.

9. Rob
This is an ... interesting way to... save paper. Saving paper we will save the trees. We will have more oxygen for our planet and we will live longer. I am sure that your paper saving invention has nothing to do with the fact that you are Scottish!

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Originally Posted by fuccaro
I am sure that your paper saving invention has nothing to do with the fact that you are Scottish!
oh no not the scottish jokes pleeese.

Nick
(Scottish n proud of it)

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