https://latex.codecogs.com/eqneditor/editor.php

\\
k := \text{number of spots of a branch}
\\
\vec{s_i} := \text{vector of i}^{th} \text{spot position}
\\
\vec{d_b} := \text{branch movement}
\\
\vec{d_b} = \vec{s_k} - \vec{s_1}
\\
\vec{n_b} := \text{branch movement direction }
\\
\vec{n_b} = \frac{\vec{d_b}}{\left | \vec{d_b} \right |  }
