From c0dba60334fb7e966a6328581446b73a55b10b23 Mon Sep 17 00:00:00 2001 From: Erwan Normand Date: Tue, 12 Nov 2024 21:15:34 +0100 Subject: [PATCH] Typo --- 3-perception/vhar-system/2-method.tex | 12 ++++++------ 3-perception/vhar-system/figures/diagram.odg | Bin 28379 -> 28484 bytes 3-perception/vhar-system/figures/diagram.pdf | Bin 51772 -> 52040 bytes 3 files changed, 6 insertions(+), 6 deletions(-) diff --git a/3-perception/vhar-system/2-method.tex b/3-perception/vhar-system/2-method.tex index ea945a5..33e3d68 100644 --- a/3-perception/vhar-system/2-method.tex +++ b/3-perception/vhar-system/2-method.tex @@ -46,9 +46,9 @@ To reduce the noise in the pose estimation while maintaining good responsiveness The filtered pose is denoted as $\pose{c}{\hat{T}}{i}$. The optimal filter parameters were determined using the method of \textcite{casiez2012filter}, with a minimum cut-off frequency of \qty{10}{\hertz} and a slope of \num{0.01}. -The velocity (without angular velocity) of the finger marker, denoted as $\pose{c}{\dot{T}}{f}$, is estimated using the discrete derivative of the position. -It is then filtered with another 1€ filter with the same parameters, and denoted as $\pose{c}{\hat{\dot{T}}}{f}$. -Finally, this filtered finger velocity is transformed into the augmented surface frame $\poseFrame{s}$ to be used in the vibrotactile signal generation, such as $\pose{s}{\hat{\dot{T}}}{f} = \pose{c}{T}{s} \, \pose{c}{\hat{\dot{T}}}{f}$. +The velocity (without angular velocity) of the finger marker, denoted as $\pose{c}{\dot{X}}{f}$, is estimated using the discrete derivative of the position. +It is then filtered with another 1€ filter with the same parameters, and denoted as $\pose{c}{\hat{\dot{X}}}{f}$. +Finally, this filtered finger velocity is transformed into the augmented surface frame $\poseFrame{s}$ to be used in the vibrotactile signal generation, such as $\pose{s}{\hat{\dot{X}}}{f} = \pose{s}{T}{c} \, \pose{c}{\hat{\dot{X}}}{f}$. \subsection{Virtual Environment Alignment} \label{virtual_real_alignment} @@ -74,7 +74,7 @@ The amplifier is connected to the audio output of a computer that generates the The represented haptic texture is a 1D series of parallels virtual grooves and ridges, similar to the real linear grating textures manufactured for psychophysical roughness perception studies \secref[related_work]{roughness}. %\cite{friesen2024perceived,klatzky2003feeling,unger2011roughness}. It is generated as a square wave audio signal $r$, sampled at \qty{48}{\kilo\hertz}, with a texture period $\lambda$ and an amplitude $A$, similar to \eqref[related_work]{grating_rendering}. -Its frequency is a ratio of the absolute finger filtered (scalar) velocity $x_f = \pose{s}{|\hat{\dot{T}}|}{f}$, and the texture period $\lambda$ \cite{friesen2024perceived}. +Its frequency is a ratio of the absolute finger filtered (scalar) velocity $x_f = \poseX{s}{|\hat{\dot{X}}|}{f}$, and the texture period $\lambda$ \cite{friesen2024perceived}. As the finger is moving horizontally on the texture, only the $X$ component of the velocity is used. This velocity modulation strategy is necessary as the finger position is estimated at a far lower rate (\qty{60}{\hertz}) than the audio signal (unlike high-fidelity force-feedback devices \cite{unger2011roughness}). @@ -82,14 +82,14 @@ This velocity modulation strategy is necessary as the finger position is estimat % %The best strategy instead is to modulate the frequency of the signal as a ratio of the filtered finger velocity ${}^t\hat{\dot{\mathbf{X}}}_f$ and the texture period $\lambda$ \cite{friesen2024perceived}. % -When a new finger velocity $x_f\,(t_j)$ is estimated at time $t_j$, the phase $\phi$ of the signal $r$ needs also to be adjusted to ensure a continuity in the signal. +When a new finger velocity $x_f\,(t_j)$ is estimated at time $t_j$, the phase $\phi\,(t_j)$ of the signal $r$ needs also to be adjusted to ensure a continuity in the signal. In other words, the sampling of the audio signal runs at \qty{48}{\kilo\hertz}, and its frequency and phase is updated at a far lower rate of \qty{60}{\hertz} when a new finger velocity is estimated. A sample $r(x_f, t_j, t_k)$ of the audio signal at sampling time $t_k$, with $t_k >= t_j$, is thus given by: \begin{subequations} \label{eq:signal} \begin{align} r(x_f, t_j, t_k) & = A\, \text{sgn} ( \sin (2 \pi \frac{x_f\,(t_j)}{\lambda} t_k + \phi(t_j) ) ) & \label{eq:signal_speed} \\ - \phi(t_j) & = \phi(t_{j-1}) + 2 \pi \frac{x_f\,(t_j) - x_f\,(t_j - 1)}{\lambda} t_k & \label{eq:signal_phase} + \phi(t_j) & = \phi(t_{j-1}) + 2 \pi \frac{x_f\,(t_j) - x_f\,(t_j - 1)}{\lambda} t_k & \label{eq:signal_phase} \end{align} \end{subequations} diff --git a/3-perception/vhar-system/figures/diagram.odg b/3-perception/vhar-system/figures/diagram.odg index 23d398cd5d85dfa7d3c52ac58db5a3f86e961937..50da868a2e3dc6841dc70dd0431be077006c5a9a 100644 GIT binary patch delta 25111 zcmYiNV|1oXv^9+0v7L0(v2EKObexWD+qi;G$5zL-ZQHhO8=ZX5-tRtRocd9<)|zY7 zpQxod~)fJn^n#un#A|bbeUGpQBidKbYu#MZxuKuw>)Q_ zNa0V0mDHYU;WyLSWmv%8l9%|k6&I>_FqD{W5|k^!mAY1}--o4Q*%&ikA=zdidB=)0 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