Use the Extension

To download and install the extension follow the steps on the Sketchup page.

To open the Loop/Ring Parameters click Extensions and Draw Ring.

The ring has a diameter which is twice the radius. It has an integer number of loops so that the start and the end meet seamlessly.

The basic cross section is a rectangle, which may be smoothed to an ellipse (circle if width = thickness). It has two levels of rotation, one around its own center and one around an external point.

Strip width

Cross section in the x direction

Strip thickness

Cross section in the y direction

Offset x

From the outer twist rotation point

Offset y

From the outer twist rotation point

Radius

Ring radius

Loops

Must be an integer to close the ring

Inner twists

Number of inner rotations of the strip

Outer twists

Number of outer rotations of the strip

Strip type

Rectangular or elliptical

Detail

The number of polygons are multiplied by 4 when the level of detail is increased one step

Strip color

Color applied to all polygons

Edges

Soft smoothes all, hard shows all edges.

Notes

If your design has multiple loops then start producing a ring with Detail set to Coarse.  Increase the level of detail when the overall design looks fine.

The inner rotation is 0.5 for the classical Möbius strip. It may also be any multiple of 0.25 for a quadratic cross section.

Method

The creation process involves the following steps for each segment of the ring:

1. Rotate (z-axis) the cross section around its center by the amount corresponding to the segment
2. Offset the rotated cross section according to the offset values from the outer rotation point
3. Rotate (z-axis) the cross section around the outer twist rotation point
4. Offset the cross section by the radius along the x-axis
5. Rotate the (y-axis) the cross section to the location of the segment
6. Draw triangles between the current segment and the previous segment.

Questions

If you have any questions, comments or suggestions please don’t hesitate to contact me.