report : junctions.tex finished

report/subsections/junctions.tex

@@ -45,11 +45,22 @@ X =
  \]
 Then subtract it with the centroid matrix associated.
 \[ 
- X - X_{m}
+ X_{c} = X - X_{m}
 \]
-The normal vector of the best-fitting plane is the left singular vector corresponding to the least singular value of \[ XX^T \]
+The normal vector $N$ of the best-fitting plane will be the cross product of the 2 eigenvectors $v_1,v_2$ corresponding to the two biggest singular values of the covariance matrix of $X_{c}$ : 
+\[
+ X_{c}X_{c}^T
+ \]
+ \[
+ N = v_1 \wedge v_2
+ \]
 
 Then to compute the constant value of the equation we use the centroid.
+\[
+d = -N*X_m
+\]
+
+At the end we have the parameters of the plane in N and d.
 
 \begin{figure}[H]
    \begin{center}