Periodic splinets

Periodic splines represent a specific category of splines, defined across a series of knots on a circle, making them particularly suitable for addressing interpolation challenges associated with closed curves and representing functions defined on a circle. Although the term ‘periodic’ suggests temporal context, the periodic splines can represent any data that have a circle as their domain. This paper introduces a method for implementing objects that represent such splines and outlines the derivation of an efficient orthogonal basis. The newly proposed orthonormalized basis, referred to as a periodic splinet, builds upon concepts and tools previously introduced for interval-based splines. Employing this methodology, periodic
splines and splinets have been integrated into an updated version of the R package, Splinets 1.5.0. Additionally, the computational tools developed in this study have been applied to the functional analysis of a prototypical example of circular functional data, namely wind direction and speeds.