geodesic_lower

This function computes points along the geodesic connecting two points p and q on the unit sphere.

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_lower function

<dl><dt>t</dt>
<dd>Time parameter for the geodesic path.</dd>
<dt>p</dt>
<dd>Numeric vector representing the starting point.</dd>
<dt>q</dt>
<dd>Numeric vector representing the ending point.</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 time point t — geodesic_lower

<dl>

<dt>t</dt>
<dd>Time parameter for the geodesic path.</dd>


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


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


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


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

</dl>

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

Description

Usage

Value

Arguments

Examples