Piecewise Geodesic Smoothing for Spherical Data
Calculate Loss Function
Convert Cartesian coordinates to spherical coordinates
Compute the cross product of two vectors
Compute the dot product of two vectors
Compute the equal-distance projection of a point onto the xy plane
Compute the exponential map on the unit sphere.
Compute the value of the geodesic curve connecting two points on the u...
Compute the value of the geodesic curve connecting two points on the u...
Generate knots for the piecewise geodesic curve based on the quantiles
Compute the L2 norm (Euclidean norm) of a vector
This function normalizes the the input vector v by dividing its L2 nor...
Normalize a matrix row-wise
Penalized Linear Spherical Spline
Piecewise Geodesic
Piecewise Geodesic Smoothing for Spherical Data
Calculate spherical distance between two vectors
Convert spherical coordinates to Cartesian coordinates
Fitting a smooth path to a given set of noisy spherical data observed at known time points. It implements a piecewise geodesic curve fitting method on the unit sphere based on a velocity-based penalization scheme. The proposed approach is implemented using the Riemannian block coordinate descent algorithm. To understand the method and algorithm, one can refer to Bak, K. Y., Shin, J. K., & Koo, J. Y. (2023) <doi:10.1080/02664763.2022.2054962> for the case of order 1. Additionally, this package includes various functions necessary for handling spherical data.
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