| apw_spherical | A polar wander dataset | 
| calculate_loss | Calculate Loss Function | 
| cartesian_to_spherical | Convert Cartesian coordinates to spherical coordinates | 
| cross | Compute the cross product of two vectors | 
| dot | Compute the dot product of two vectors | 
| edp | Compute the equal-distance projection of a point onto the xy plane | 
| exp_map | Compute the exponential map on the unit sphere. | 
| geodesic | Compute the value of the geodesic curve connecting two points on the unit sphere for a given set of time points t | 
| geodesic_lower | Compute the value of the geodesic curve connecting two points on the unit sphere for a given time point t | 
| goni_spherical | A tropical cyclone dataset | 
| knots_quantile | Generate knots for the piecewise geodesic curve based on the quantiles | 
| norm2 | Compute the L2 norm (Euclidean norm) of a vector | 
| normalize | Normalize a matrix row-wise | 
| normalize_lower | This function normalizes the the input vector v by dividing its L2 norm (Euclidean norm). | 
| penalized_linear_spherical_spline | Penalized Linear Spherical Spline | 
| piecewise_geodesic | Piecewise Geodesic | 
| spheresmooth | Piecewise Geodesic Smoothing for Spherical Data | 
| spherical_dist | Calculate spherical distance between two vectors | 
| spherical_to_cartesian | Convert spherical coordinates to Cartesian coordinates |