A geometry and physics substrate for spaces that are not flat 3D: higher dimensions and curved manifolds, real-time, in Rust on wgpu.
What works today:
- 4D rigid-body physics. First-party geometric algebra (
Bivector4/Rotor4with invariant-decomposition exponential), GJK and EPA lifted to R⁴ (EPA validated against analytical penetration depths), persistent contact manifolds, a warm-started projected Gauss-Seidel solver. - Exact polychoral cross-sections. All six regular convex 4-polytopes with exact topology at unit circumradius; sections are computed as geometry, not mesh approximations, alongside raymarched-SDF and wireframe render modes.
- Geometry as a type parameter. The same scene renders in Euclidean, hyperbolic, and spherical 3-space through one
Spacetrait, and both render paths (SDF raymarch, rasterizer) run on the same implementations. - Determinism. Simulation is bit-reproducible: same binary, same inputs, same bits. Pinned by tests that run in CI.
cargo run --release -p polytope_playground # native
cd crates/polytope_playground && trunk serve --release # browser (local)
Stable Rust 1.95 or newer; any wgpu backend (Vulkan, DX12, Metal, WebGPU). The browser build needs trunk. Controls live in the on-screen panels; backtick opens the debug console (trace summary prints per-section frame timings).
- A geometry is anything implementing
Space(exp, log, distance, parallel transport, isometries). Everything downstream is an opt-in capability trait (WgslSpace,RasterizableSpace,SectionableSpace,PhysicsSpace), so a new geometry is wired in by implementing what it actually supports. - Scenes are typed SDF trees that emit WGSL on demand; the emit chain combines scene code with the selected space's shader prelude.
- Correctness is enforced by an invariant test suite, not by inspecting rendered output: Gauss-Bonnet on geodesic triangles, isometry invariance of distance, transport length preservation, loop holonomy.
- Apart from
glamandbytemuck, the math layer is first-party. The crate-by-crate map lives in docs/ARCHITECTURE.md. - A variable-curvature
BlendedSpace(a single Riemannian metric interpolating E³ to H³) exists as a validated reference implementation; its numerical geodesics do not yet meet a gameplay frame budget.
Marc ten Bosch's 4D Toys is the direct conceptual ancestor of the polytope playground: four-dimensional objects as inhabitants of a 4D space whose 3D slices the viewer inspects. Zeno Rogue's HyperRogue, CodeParade's HyperEngine/Hyperbolica, and Michael Walczyk's polychora shaped the non-Euclidean and 4D rendering choices. Textbook citations (Coxeter, Hestenes and Sobczyk, do Carmo, Foley et al., Knuth) live in the rustdocs at each use site.
I use AI coding tools, primarily Claude Code, heavily; invariant tests gate every primitive regardless of authorship, and responsibility for what ships is mine. Single-maintainer project: reach out before starting anything at humesze@proton.me.
Dual-licensed under MIT OR Apache-2.0. See LICENSE-MIT and LICENSE-APACHE.