Crate cartan_geo 

cartan-geo

Geodesic computation and geometric tools for the cartan library.

This crate provides higher-level geometric utilities built on top of the Manifold trait from cartan-core and the concrete manifolds from cartan-manifolds. It focuses on global geometry: geodesic curves, curvature queries, and Jacobi field integration.

Modules

Module	Contents
geodesic	Geodesic<M> – parameterized geodesic, sampling, two-point construction
curvature	CurvatureQuery<M> – sectional, Ricci, scalar curvature at a point
jacobi	integrate_jacobi – RK4 Jacobi field ODE integration

no_std support

cartan-geo is no_std-compatible with default-features = false, features = ["alloc"]. Geodesic, CurvatureQuery, and integrate_jacobi are available unconditionally. Disclination, disclination scanning, and holonomy require std.

References

• do Carmo. “Riemannian Geometry.” Birkhauser, 1992. Chapters 3-5.
• Petersen. “Riemannian Geometry.” Springer, 2016. Chapter 11.

Re-exports

pub use curvature::CurvatureQuery;

pub use curvature::scalar_at;

pub use curvature::sectional_at;

pub use geodesic::Geodesic;

pub use disclination::DisclinationCharge;

pub use disclination::DisclinationSegment;

pub use disclination::DisclinationLine;

pub use disclination::DisclinationEvent;

pub use disclination::EventKind;

pub use disclination::QTensorField3D;

pub use disclination::Sign;

pub use disclination::scan_disclination_lines_3d;

pub use disclination::connect_disclination_lines;

pub use disclination::track_disclination_events;

pub use holonomy::Disclination;

pub use holonomy::edge_transition;

pub use holonomy::holonomy_deviation;

pub use holonomy::is_half_disclination;

pub use holonomy::loop_holonomy;

pub use holonomy::rotation_angle;

pub use holonomy::scan_disclinations;

pub use jacobi::JacobiResult;

pub use jacobi::integrate_jacobi;

Modules

curvature

Curvature queries at a manifold point.

disclination

Disclination line detection and tracking for 3D uniaxial nematics. Charge classification: Z2 (half-integer, ±1/2). Enum designed for Q8 extension.

geodesic

Parameterized geodesics: gamma(t) = Exp_p(t * v).

holonomy

Holonomy-based topological defect detection for discrete Q-tensor fields.

jacobi

Jacobi field integration along a geodesic.