chore: documentation fixes (#6)

remove unused dependencies

docs/notations.typ

@@ -1,9 +1,6 @@
 #set page(width: 16cm, margin: 0.5em, height: auto)
 #let definition(content) = box(fill: luma(92%), width: 100%, inset: 0.5em, stroke: black)[#content]
 
-#import "@preview/lovelace:0.2.0": *
-#show: setup-lovelace.with(body-inset: 0pt)
-
 #let pr = $nu$
 #let time = $t$
 == Notations

docs/position_modeling.typ

@@ -1,17 +1,13 @@
 #set page(width: 16cm, margin: 0.5em, height: auto)
 #let definition(content) = box(fill: luma(92%), width: 100%, inset: 0.5em, stroke: black)[#content]
 
-#import "@preview/lovelace:0.2.0": *
-#show: setup-lovelace.with(body-inset: 0pt)
-
 #let pr = $nu$
 #let time = $t$
 
-
 == Position modeling
 
 #definition[The raw input is processed as follow
-   
+
   raw input $->$ wobble smoother $->$ upsampled $->$ position modeling]
 
 #definition[
@@ -44,7 +40,7 @@ the output
   - Output : smoothed stream ${(p_f [k],v_f [k],a_f [k]), 0 <= k <=n}$
   We define $Phi[k] = p[k]$. An euler scheme integration scheme is used with the initial conditions being $v[0] = 0$ and $p_f [0] = p[0]$ (same
   initial conditions)
-   
+
   Update rule is simply
   $
     a_f [j] = (p[j]- p_f [j-1]) / k_"spring" - k_"drag" v_f [j-1]\

docs/resampling.typ

@@ -1,39 +1,34 @@
 #set page(width: 16cm, margin: 0.5em, height: auto)
 #let definition(content) = box(fill: luma(92%), width: 100%, inset: 0.5em, stroke: black)[#content]
 
-#import "@preview/lovelace:0.2.0": *
-#show: setup-lovelace.with(body-inset: 0pt)
-
 #let pr = $nu$
 #let time = $t$
 
-
 == Resampling
 #let inv = $v$
 
 *Algorithm* : Upsampling\
-*Input* : ${inv[k] = (x[k],y[k],t[k]), 0 <= k <= n}$ and a target rate `sampling_min_output_rate`\,
-    Interpolate time and position between each $k$ by linearly adding interpolated values
-  \
-  This is done by adding linearly interpolated values so that the output stream is
-    $
-      {
-      inv[0], underbrace(u_0[1]\, dots\, u_0[n_0-1], "interpolated"), inv[
-      1
-      ], underbrace(u_1[1]\, dots\, u_1[n_1 - 1 ], "interpolated"),inv[2], dots
-      }
-    $
-    Each $n_i$ is the minimum integer such that
-    $
-            & (t[i]-t[i-1]) / n_i < Delta_"target"\
-      <=> & n_i = ceil((t[i+1]-t[i])/Delta_"target")
-    $
-    and the linear interpolation means
-    $
-      u_j [k] = (1 - k / n_j) inv[j] + k / n_i inv[j+1]
-    $\
-  *Output* : ${(x'[k'],y'[k'],t'[k']), 0 <= k; <= n'}$ the upsampled position and times. This verifies $
-    forall k', t'[k'] - t'[k'-1] < Delta_"target" = 1/#text[`sampling_min_output_rate`]
-  $\
+*Input* : ${inv[k] = (x[k],y[k],t[k]), 0 <= k <= n}$ and a target rate `sampling_min_output_rate`\, Interpolate time and
+position between each $k$ by linearly adding interpolated values\
+This is done by adding linearly interpolated values so that the output stream is
+$
+  {
+  inv[0], underbrace(u_0[1]\, dots\, u_0[n_0-1], "interpolated"), inv[
+  1
+  ], underbrace(u_1[1]\, dots\, u_1[n_1 - 1 ], "interpolated"),inv[2], dots
+  }
+$
+Each $n_i$ is the minimum integer such that
+$
+        & (t[i]-t[i-1]) / n_i < Delta_"target"\
+  <=> & n_i = ceil((t[i+1]-t[i])/Delta_"target")
+$
+and the linear interpolation means
+$
+  u_j [k] = (1 - k / n_j) inv[j] + k / n_i inv[j+1]
+$\
+*Output* : ${(x'[k'],y'[k'],t'[k']), 0 <= k; <= n'}$ the upsampled position and times. This verifies $
+  forall k', t'[k'] - t'[k'-1] < Delta_"target" = 1/#text[`sampling_min_output_rate`]
+$\
 *Remark* : As this is a streaming algorithm, we only calculate this interpolation with respect to the latest stroke
 position.

docs/wobble.typ

@@ -1,9 +1,6 @@
 #set page(width: 16cm, margin: 0.5em, height: auto)
 #let definition(content) = box(fill: luma(92%), width: 100%, inset: 0.5em, stroke: black)[#content]
 
-#import "@preview/lovelace:0.2.0": *
-#show: setup-lovelace.with(body-inset: 0pt)
-
 #let pr = $nu$
 #let time = $t$
 
@@ -49,4 +46,4 @@ $
 where $p'[j] = (x'[j],y'[j])$\
 *Output*: ${(x'[k],y'[k]) in RR^2, 0<= k <=n}$ the filtered positions.\ Hence for low local speeds, the smoothing is
 maximum (we take exactly the average position over the time $Delta T$) and for high speed there is no smoothing. We also
-note that the first position is thus never filtered.
+note that the first position is thus never filtered.