cartan.sotofranco.dev

cartan

Riemannian geometry in Rust. Backend-agnostic trait system with const-generic manifolds, correct numerics near singularities, and a discrete exterior calculus layer for covariant PDE solvers.

Cargo.tomlcartan = "0.1"

Pythonpip install cartan

Get Started →GitHub ↗PyPI ↗docs.rs ↗

Documentation

Concepts

Trait hierarchy & math

Manifolds

Formulas & code

Demos

Interactive 3D visualizations

Manifolds

Sphere

$S^{N-1}$

dim = $N-1$

$K = 1$

Manifold Retraction ParallelTransport VectorTransport Connection Curvature GeodesicInterpolation

Euclidean

$\mathbb{R}^N$

dim = $N$

$K = 0$

Manifold Retraction ParallelTransport VectorTransport Connection Curvature GeodesicInterpolation

Special Euclidean

$\mathrm{SE}(N)$

dim = $N(N+1)/2$

Manifold Retraction Connection ParallelTransport GeodesicInterpolation

Correlation

$\mathrm{Corr}(N)$

dim = $N(N-1)/2$

$K = 0$

Manifold Retraction Connection ParallelTransport Curvature GeodesicInterpolation

Special Orthogonal

$\mathrm{SO}(N)$

dim = $N(N-1)/2$

$K \geq 0$

Manifold Retraction ParallelTransport VectorTransport Connection Curvature GeodesicInterpolation

SPD

$SPD(N)$

dim = $N(N+1)/2$

$K \leq 0$

Manifold Retraction ParallelTransport VectorTransport Connection Curvature GeodesicInterpolation

Grassmann

$Gr(N,K)$

dim = $K(N-K)$

$0 \leq K \leq 2$

Manifold Retraction ParallelTransport VectorTransport Connection Curvature GeodesicInterpolation

Coming Soon

Trait Hierarchy

Click any node to view its concept page. Interactive explorer →