How can I create a Mobius ring?

Question

I may be going about this the wrong way.

I want to create a Mobius ring. I managed to do it by twisting (rotating using proportional editing) then using a curve modifier. But the faces were full of creases no matter how I smoothed them.

I then tried to extrude a plane converted to a curve which was getting there. But I cannot see a way to join two edges of the Mobius ring with a surface. I would appreciate any pointers.

Stephen

Answer 1

• Add a plane in Front view;
• in Object mode, RY90;
• In Edit mode, RZ90 (or RXX90 in this case);
• Add an Array modifier;
• Add an Simple Deform modifier, set type to Twist, set Angle to 180 (or 180*n, depending on how many turns you want).

• Add another Simple Deform modifier, set type to Bend; Create an empty, set it as Origin in the modifier panel, and type 360 as Angle.

• Once the result is expected, AltC -> Mesh from Curve/Meta/Surf/Text to apply all modifiers, then go to Edit mode, W -> Remove Doubles.

Tip: Simple Deform modifiers operate around Local Z Axis. Click to learn more.

example file

Advantages:

• Adjustable subdivision level (by Array);
• Adjustable loop turns (by Bending to 180*n);
• Animatable.

---

A mobius curve can also be generated by the Extra Objects addon.

• Enable it in Addon list;
• ShiftA -> Curve -> Torus Knot Plus;
• F6, set p=2 q=1, then tweak other parameters as you want.

example file

Answer 2

The easiest way (I think) to create a Mobius ring is to use a bezier curve with an extrude value.

1. Add a bezier curve

2. Extrude and move the curve points into a rough circle.

3. Increase the 'Extrude' value on the curve properties to give the curve thickness:

   

4. The trick is to pick one of the middle curve points and press Ctrl+T to start the 'Tilt' tool. This will allow you to rotate the curve point. Type 180 while using this tool to completely flip the curve point.

5. You should end up with something like this:

   

There are actually 4 points in this curve but the last 2 are exactly on top of each other (lower left) to complete the circle.

Convert the curve to a mesh, enter edit mode and merge the start and end vertices using the Alt+M 'Merge' menu.

However, this may cause shading issues as the normals wont know which part of the mesh is 'inside' and which is 'outside'.

Answer 3

I'm not sure what kind of Möbius ring you want, so here is a simple method how you can make the simplest one:

1) Add a circle mesh and extrude all vertices along the z axis.

2) Delete one of the edges.

3) With proportional editing (connected) rotate one loose end 90° and the other -90° around the x axis.

4) Select the 4 vertices at the loose end and press f to create a face.

If you want to create a more complex one with more loops, you could try to start with just a plane and repeatedly extrude and rotate one side.