cartan-core

Core trait definitions for Riemannian geometry.

Part of the cartan workspace.

Overview

cartan-core defines the foundational trait hierarchy that all cartan manifolds, optimizers, and geometric tools depend on. It has minimal dependencies (only rand for RNG trait bounds) and can be used standalone by downstream crates that implement custom manifolds against the cartan trait system.

The trait hierarchy is:

Manifold (exp, log, inner, project, validate)
  |
  +-- Retraction (cheaper exp approximation)
  +-- ParallelTransport -> VectorTransport (blanket impl)
  +-- Connection (Riemannian Hessian)
  |     |
  |     +-- Curvature (Riemann tensor, Ricci, scalar)
  +-- GeodesicInterpolation (gamma(t) sampling)

All floating-point computation uses the Real type alias (currently f64), so that a future generic refactor is mechanical. The crate also provides CartanError for structured error handling across the workspace.

Fiber bundles and rotors

cartan-core also defines associated fiber bundles over simplicial meshes: the Fiber trait (with U1Spin2, TangentFiber, NematicFiber3D), discrete connections (DiscreteConnection, EdgeTransport2D/3D), and the covariant Laplacian CovLaplacian. Parallel transport can be carried either as SO(d) matrices or as geometric-algebra rotors (Rotor2, Rotor3, RotorConnection, CovLaplacian::apply_rotor): a rotor stores the same rotation in fewer floats, composes cheaply, and reverses by conjugation. The matrix and rotor paths agree to floating-point tolerance, so either can be used interchangeably.

Example

use cartan_core::{Manifold, Real};

/// Check that a point lies on the manifold and compute a tangent norm.
fn tangent_norm<M: Manifold>(m: &M, p: &M::Point, v: &M::Tangent) -> Real {
    assert!(m.check(p).is_ok());
    m.inner(p, v, v).sqrt()
}

no_std

Disable default features and enable alloc for embedded targets:

cartan-core = { version = "0.6", default-features = false, features = ["alloc"] }

License