Torus knot tube with parallel-transport frames
In your harnessMesh algorithmMIT
Sweep a circle along a (p, q) torus knot with parallel-transport frames closed by an even twist, so the closed tube has no twist seam. Use it for knot sculpture, jewellery and decorative pipes.
What it takes and gives
- Entry points
- knot_point, knot_tangent, transport_frames, torus_knot, main
- Parameters
- p, q, major_radius, minor_radius, tube_radius, segments, sides
- Complexity
- O(segments * sides)
- Axes
- +Y up, metres
Limits. The tube does not test for self-intersection: keep tube_radius below half the closest approach of the strands (true for the defaults). No texture coordinates. The volume and area checks compare with cross-section times curve length within 0.4 percent.
Details
- Kind
- Mesh algorithm
- Engine
- Python 3.10 or later
- Files
- 10 files, 279.4 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
- Torus knot curve ((R + r cos qt) cos pt, r sin qt, -(R + r cos qt) sin pt), Discrete parallel transport of frames (rotation between consecutive tangents), Holonomy correction spread evenly along a closed curve
- Tags
- torus knot, tube, sweep, parallel transport, knot, trefoil
- Identity
library.supply.creative_originals.c3411f3110e56a96f46b92de.27e0793004fc3ba0- Version
27e0793004fc3ba08e217ce9b062a63bd7a708602536fedf891930f213fce79b
The version is the SHA-256 of the item your harness downloads; every file in it names its own checksum.
Related files
Helical compression spring with spring rateIn your harness
Torus with wrapped texture coordinatesIn your harness
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