geodesic

This function computes the value of the geodesic curve connecting two points p and q on the unit sphere at specified time points.

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.

Kwan-Young Bak

spheresmooth

Piecewise Geodesic Smoothing for Spherical Data

Jae-Hwan Jhong

Ja-Yong Koo

Seyoung Lee

geodesic function

<dl><dt>t</dt>
<dd>Numeric vector representing time points for the geodesic path.</dd>
<dt>p</dt>
<dd>Numeric vector representing the starting point on the sphere.</dd>
<dt>q</dt>
<dd>Numeric vector representing the ending point on the sphere.</dd>
<dt>a</dt>
<dd>Start time parameter.</dd>
<dt>b</dt>
<dd>End time parameter.</dd></dl>

Arguments

Compute the value of the geodesic curve connecting two points on the unit sphere for a given set of time points t — geodesic

<dl>

<dt>t</dt>
<dd>Numeric vector representing time points for the geodesic path.</dd>


<dt>p</dt>
<dd>Numeric vector representing the starting point on the sphere.</dd>


<dt>q</dt>
<dd>Numeric vector representing the ending point on the sphere.</dd>


<dt>a</dt>
<dd>Start time parameter.</dd>


<dt>b</dt>
<dd>End time parameter.</dd>

</dl>

geodesic: Compute the value of the geodesic curve connecting two points on the unit sphere for a given set of time points t

Description

Usage

Value

Arguments

Examples