Why are curves shifted by their centroid?

[glegarda]

Hello,

I am trying to use the SRVF framework to align a set of 2-dimensional, single-valued surfaces, all of which are defined for $x \in [0,1]$ (and $y \in \mathbb{R}$) and are exactly 0 both at $x=0$ and at $x=1$. The goal is to then compute distances between them. I am able to compute and extract the aligned values by encoding my data as an fdacurve object; however, I expected them to remain equal to 0 at $x \in [0,1]$, which is not the case. I noticed in the source code that an offset is applied to every curve equal to its centroid, which is shifting every curve prior to alignment, causing the observed result.

What is the reason behind this offset? Would it be possible to skip it? If not, would it be sound to shift the curves back to their original position before computing distances between them?

Thanks in advance for your help!