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Torus knot tube without a twist seam

In your harnessBlender toolMIT

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.

Render of Torus knot tube without a twist seam
The render its check recorded in Blender 5.2.1, 192 by 192 pixels.

What it takes and gives

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

Limits. 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.

Details

Kind
Blender tool
Engine
Blender 4.2 or later
Files
11 files, 119.9 KB
Licence
MIT
Declared effects
runs commands
Checked with
Blender 5.2.1, background (Cycles CPU for previews)
Checks
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
Techniques
Torus knot parametrisation ((R + a cos qt) cos pt, (R + a cos qt) sin pt, a sin qt), Parallel transport of a normal along a closed curve and its holonomy angle, Crossing number of a torus knot min(p(q - 1), q(p - 1))
Tags
blender, procedural, knot, torus knot, math, mesh generator, abstract
Identity
library.supply.creative_originals.3e0f6904628eddea507e6785.0b746d5f7cf69802
Version
0b746d5f7cf69802727d87b22ea4932272d2820c09a5bb2b0fa3ea601a66b564

The version is the SHA-256 of the item your harness downloads; every file in it names its own checksum.

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