Adaptive smoothing of spherical trajectories via penalized piecewise geodesic curves: a Python software

Spherical trajectory data arise in many scientific fields, including geophysics, atmospheric sciences, astronomy, and require analysis methods that respect the intrinsic geometry of the sphere. This article introduces spheresmooth , an open-source Python library for intrinsic smoothing of spherical trajectories based on penalized piecewise geodesic curve fitting. The software represents trajectories as sequences of connected geodesic segments on the unit sphere and employs a velocity-based sparsity-inducing penalty to enable automatic selection of control points. By combining this intrinsic formulation with Riemannian optimization techniques, spheresmooth provides adaptive smoothing that captures both global trends and local directional changes while avoiding geometric distortions associated with extrinsic tangent-space approximations. The package offers a modular, user-friendly implementation built on standard scientific Python libraries and supports coordinate transformations, geodesic evaluation, penalized spline fitting, and visualization. The software yields smooth, interpretable spherical curves that remain faithful to the intrinsic geometry of the data. Overall, spheresmooth lowers the barrier to applying intrinsic spherical smoothing methods within modern Python-based scientific workflows.