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mesh algorithms

Klein bottle figure-eight immersion

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.

Recorded render of Klein bottle figure-eight immersion

What this component contains

  • ATTRIBUTION.md
  • LICENSE
  • README.md
  • component.json
  • example.gltf
  • klein_bottle.py
  • meshkit.py
  • preview.png
  • test_package.py
  • verification/native.json

How it works

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

Recorded checks

godot 4.7.2.stable.official.ed1daf0bf

  • generator_runs_system_python
  • generator_runs_verifier_python
  • gltf_strict_structure
  • interpreters_agree
  • example_matches_generator
  • godot_headless_gltf_load
  • godot_compatibility_render

Limits to consider

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.