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Cl(4,0) rotors and bivector decomposition

In your harness4D geometry toolMIT

A 4D geometric algebra: geometric and outer products, reversion, rotors exp(-B/2), the split of any bivector into two commuting simple parts, reflections, and the torus knot a double rotation traces, written as a glTF tube on the Clifford torus.

Render of Cl(4,0) rotors and bivector decomposition
The render its check recorded in Godot 4.7.2, 256 by 256 pixels.

What it takes and gives

Entry points
blade, vector, bivector, product, wedge, grade, reverse, add and 18 more
Outputs
example.gltf
Coordinates
x, y, z, w = e1, e2, e3, e4; knot stereographically projected from (0, 0, 0, 1) to Godot/glTF +Y up

Limits. Multivectors are dense lists of 16 floats and products loop over all blade pairs, so the module suits exploration and tests, not bulk transforms. exp_multivector uses a truncated Taylor series after scaling and squaring (about 1e-12 for moderate bivectors). split_bivector refuses isoclinic bivectors, whose planes are not unique. The torus shell uses alpha blending, whose sorting depends on the viewer.

Details

Kind
4D geometry tool
Engine
Python 3.10 or later
Files
10 files, 288.2 KB
Licence
MIT
Declared effects
reads files, runs commands, writes files
Checked with
Godot 4.7.2, gl_compatibility (opengl3, Mesa llvmpipe under Xvfb)
Checks
cli rebuilds example, gltf structure example, cli example runs, cli example gltf structure, godot loads example, godot loads cli knot 3 5, preview render
Techniques
Clifford algebra Cl(4,0) with blade bitmasks, rotors exp(-B/2) and the sandwich product, invariant decomposition of a 4D bivector into commuting simple bivectors, Cartan-Dieudonne: rotations as products of reflections, torus knots on the Clifford torus, Gauss linking integral
Tags
4d, geometric algebra, clifford algebra, rotor, bivector, torus knot, clifford torus, gltf
Identity
library.supply.creative_originals.eee3e5bc840dc323d0b5044e.abeb37ca99ebbe0e
Version
abeb37ca99ebbe0e34be3d448f09c2208034aa65cc9e6c918a29314530377792

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

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