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Duocylinder measures and diagonal slices

In your harness4D geometry toolMIT

Compute the duocylinder's hypervolume, boundary 3-volume and ridge torus area, confirm them by integrating axis and diagonal slices, and write the diagonal slice sweep (stretched Steinmetz bicylinders) as an exact four-strip glTF morph animation.

Render of Duocylinder measures and diagonal slices
The render its check recorded in Godot 4.7.2, 256 by 256 pixels.

What it takes and gives

Entry points
contains, hypervolume, boundary_volume, ridge_area, axis_slice_volume, cavalieri_axis, diagonal_slice_volume, cavalieri_diagonal and 6 more
Outputs
example.gltf
Coordinates
slice x + z = k in its hyperplane basis: ((2x - k)/sqrt 2, y, w), Godot/glTF +Y up

Limits. The slice sweep and the diagonal formulas are for the unit duocylinder (both radii 1); the measure functions take any radii. Slice volumes come from Simpson's rule after a cosine substitution (near 1e-8 relative for the Cavalieri total). Keyframes are morph targets, so between them vertices move along chords.

Details

Kind
4D geometry tool
Engine
Python 3.10 or later
Files
10 files, 224.6 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 duocylinder coarse, preview render
Techniques
duocylinder as a product of two disks, Cavalieri's principle, Steinmetz bicylinder, ruled cylinder surfaces, Chebyshev spacing for quadrature and meshing, Simpson's rule
Tags
4d, duocylinder, steinmetz solid, bicylinder, slice, cavalieri, morph targets, gltf
Identity
library.supply.creative_originals.cf18d470db8995084c1897e4.7261e2a72f34137c
Version
7261e2a72f34137c5a34361bc4c135df500831cd225e32dafadb33cdc346324f

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

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