From 74f2f271bc19fb107372b554173e0258036e1ab1 Mon Sep 17 00:00:00 2001
From: Erwan Normand <normand.erwan@protonmail.com>
Date: Wed, 26 Jun 2024 18:56:33 +0200
Subject: [PATCH] Fix xr-perception equation labels

---
 2-perception/xr-perception/3-method.tex | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/2-perception/xr-perception/3-method.tex b/2-perception/xr-perception/3-method.tex
index 062a535..c22efe4 100644
--- a/2-perception/xr-perception/3-method.tex
+++ b/2-perception/xr-perception/3-method.tex
@@ -36,7 +36,7 @@ The visuo-haptic texture rendering system is based on
     \item and a modulation of the signal frequency by the estimated finger speed with a phase matching.
 \end{enumerate*}
 %
-\figref{method/diagram} shows the diagram of the interaction loop and \eqref{signal} the definition of the vibrotactile signal.
+\figref{method/diagram} shows the diagram of the interaction loop and \eqref{xr_perception:signal} the definition of the vibrotactile signal.
 %
 The system is composed of three main components: the pose estimation of the tracked real elements, the visual rendering of the virtual environment, and the vibrotactile signal generation and rendering.
 
@@ -116,10 +116,10 @@ It is generated as a square wave audio signal, sampled at \qty{48}{\kilo\hertz},
 A sample $s_k$ of the audio signal at sampling time $t_k$ is given by:
 %
 \begin{subequations}
-    \label{eq:signal}
+    \label{eq:\labelprefix:signal}
     \begin{align}
-        s(x_{f,j}, t_k) & = A \text{\,sgn} ( \sin (2 \pi \frac{\dot{x}_{f,j}}{\lambda} t_k + \phi_j) ) & \label{eq:signal_speed} \\
-        \phi_j          & = \phi_{j-1} + 2 \pi \frac{x_{f,j} - x_{f,{j-1}}}{\lambda} t_k               & \label{eq:signal_phase}
+        s(x_{f,j}, t_k) & = A \text{\,sgn} ( \sin (2 \pi \frac{\dot{x}_{f,j}}{\lambda} t_k + \phi_j) ) & \label{eq:\labelprefix:signal_speed} \\
+        \phi_j          & = \phi_{j-1} + 2 \pi \frac{x_{f,j} - x_{f,{j-1}}}{\lambda} t_k               & \label{eq:\labelprefix:signal_phase}
     \end{align}
 \end{subequations}
 %
@@ -133,7 +133,7 @@ This is important because it preserves the sensation of a constant spatial frequ
 %
 Note that the finger position and velocity are transformed from the camera frame $\mathcal{F}_c$ to the texture frame $\mathcal{F}_t$, with the $x$ axis aligned with the texture direction.
 %
-However, when a new finger position is estimated at time $t_j$, the phase $\phi_j$ needs to be adjusted as well with the frequency to ensure a continuity in the signal as described in \eqref{signal_phase}.
+However, when a new finger position is estimated at time $t_j$, the phase $\phi_j$ needs to be adjusted as well with the frequency to ensure a continuity in the signal as described in \eqref{xr_perception:signal_phase}.
 %
 This approach avoids sudden changes in the actuator movement thus affecting the texture perception in an uncontrolled way (see \figref{method/phase_adjustment}) and, contrary to previous work~\cite{asano2015vibrotactile,friesen2024perceived}, it enables no constraints a free exploration of the texture by the user with no constraints on the finger speed.
 %