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Torus knot tube without a twist seam

Generate a closed tube along a (p, q) torus knot, with section frames carried by parallel transport and the leftover twist spread evenly so the tube closes without a seam, plus the curve length and crossing number. Use it for jewellery, logos, abstract art and math visuals.

Recorded render of Torus knot tube without a twist seam

What this component contains

  • ATTRIBUTION.md
  • LICENSE
  • README.md
  • component.json
  • graphcheck.py
  • meshcheck.py
  • preview.png
  • test_package.py
  • test_torus_knot.py
  • torus_knot.py
  • verification/native.json

How it works

Operator
baltor.torus_knot
Parameters
p, q, major_radius, minor_radius, tube_radius, samples, sides
Result
One smooth-shaded closed mesh named Torus Knot, genus one.
Blender
4.2 or later
Axes
Blender Z up, -Y forward
Units
metres

Recorded checks

blender 5.2.1 LTS (hash 9e2066aef7ef built 2026-08-25 02:12:34)

  • addon_install_and_enable
  • operator_runs_with_defaults
  • blender_data_matches_core
  • addon_disable_unregisters
  • script_mode_runs
  • clean_reopen_addon_file
  • clean_reopen_script_file
  • gltf_separate_export
  • engine_output_clean

Limits to consider

Coprime p and q only, since other pairs give links of several loops. The tube can intersect itself when the tube radius is large compared with the gaps between strands; nothing checks or prevents this. Parallel transport is discrete, so very few samples give a visibly faceted tube. Verified in Blender 5.2.1; written for the 4.2 API.