Klein bottle figure-eight immersion

In your harnessMesh algorithmMIT

Build the figure-eight immersion of the Klein bottle: a closed, one-sided surface with no edge and Euler characteristic 0. Use it for mathematical sculpture and to test non-orientable meshes.

Render of Klein bottle figure-eight immersion — The render its check recorded in Godot 4.7.2, 256 by 256 pixels.

What it takes and gives

Entry points: figure_eight_point, klein_bottle, main
Parameters: radius, scale, u_segments, v_segments
Complexity: O(u_segments * v_segments)
Axes: +Y up, metres

Limits. The figure-eight immersion passes through itself along one circle, as every Klein bottle in three dimensions must; the mesh does not split faces there. There is no consistent winding, so normals flip across one seam and the surface should be drawn double-sided.

Details

Kind: Mesh algorithm
Engine: Python 3.10 or later
Files: 10 files, 263.4 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: Figure-eight Klein bottle immersion, Grid identification (u + 2 pi, v) ~ (u, -v)
Tags: parametric surface, klein bottle, non-orientable, topology, immersion, sculpture
Identity: library.supply.creative_originals.2a05a0c72fc160c95afdc07b.f0f07047fe7eb326
Version: f0f07047fe7eb3263659a9e2d36f52c2519bf121e70a0795c3fa3a40968167a0

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Klein bottle figure-eight immersion

What it takes and gives

Details

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