Exact hyperplane slice sweep as glTF morph targets
In your harness4D geometry toolMIT
Sweep a hyperplane through the 5-cell, tesseract, 16-cell or 24-cell and write one glTF mesh whose morph-target animation plays the exact sequence of 3D cross-sections (for example tetrahedron, truncated tetrahedron, octahedron).
What it takes and gives
- Entry points
- make_polytope, direction_vector, tetrahedra, build, positions_at, mesh_measures, exact_measures, morph_error and 6 more
- Outputs
- example.gltf
- Coordinates
- slice points in the hyperplane's own x, y, z (fourd.hyperplane_basis; for the normal (0,0,0,1) these are x, y, z), Godot/glTF +Y up
Limits. Convex polytopes with planar cells only (the four built in). Where vertex heights tie, a slice corner jumps between two coincident positions inside a 1 ms keyframe pair; the drawn shape does not change there. The mesh holds degenerate zero-area triangles for parts of cells the hyperplane has not reached. The slice frame (hyperplane basis) is fixed for the whole sweep.
Details
- Kind
- 4D geometry tool
- Engine
- Python 3.10 or later
- Files
- 10 files, 172.2 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 16cell slices, preview render
- Techniques
- cross-sections of convex polytopes by hyperplanes, tetrahedral decomposition of polyhedral cells, piecewise-linear vertex motion between critical heights, glTF 2.0 morph targets with linear weight interpolation
- Tags
- 4d, slice, cross-section, hyperplane, morph targets, blend shapes, animation, gltf
- Identity
library.supply.creative_originals.6a0aa38c2a34de5172c8101e.d1f4507910233768- Version
d1f45079102337689f07d4ec36105146b379e6cd6a1eb26dcb831e4b751081fd
The version is the SHA-256 of the item your harness downloads; every file in it names its own checksum.
Related files
Tesseract from 4-bit vertex labelsIn your harness
Something wrong with this item, its rights or its safety? Report it on the support page, or from your harness after a download.