Moebius strip and twisted bands

In your harnessMesh algorithmMIT

Build a band around a circle with any number of half twists: one gives a one-sided Moebius strip with a single edge, even counts give two-sided bands. Use it for sculpture, puzzles and topology tests.

Render of Moebius strip and twisted bands — The render its check recorded in Godot 4.7.2, 256 by 256 pixels.

What it takes and gives

Entry points: band_point, mobius_strip, main
Parameters: radius, width, half_twists, segments, strips
Complexity: O(segments * strips)
Axes: +Y up, metres

Limits. A one-sided surface has no consistent winding: faces disagree across one seam column and the normals there flip, so render it double-sided (the material is marked so). Very wide bands (width near twice the radius) self-intersect. The area check tolerance covers the flat-quad approximation.

Details

Kind: Mesh algorithm
Engine: Python 3.10 or later
Files: 10 files, 205.5 KB
Licence: MIT
Declared effects: reads files, runs commands, writes files
Checked with: Godot 4.7.2, gl_compatibility, OpenGL 3 driver, Mesa llvmpipe under Xvfb
Checks: generator runs system python, generator runs verifier python, gltf strict structure, interpreters agree, example matches generator, godot headless gltf load, godot compatibility render
Techniques: Parametric band ((R + s cos(k u / 2)) cos u, s sin(k u / 2), -(R + s cos(k u / 2)) sin u), Seam identification with reversal for odd half twists
Tags: primitive, moebius strip, non-orientable, twisted band, topology, parametric surface
Identity: library.supply.creative_originals.54ead8bd0d771da1292b5cfc.a8f1d6839e841620
Version: a8f1d6839e8416206db039cddd8afa3c465b9019274d34ffad95f285ab421d5b

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Moebius strip and twisted bands

What it takes and gives

Details

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