deletions | additions       diff --git a/Methodology Video Data.tex b/Methodology Video Data.tex  index eabcce2..7a0addc 100644  --- a/Methodology Video Data.tex  +++ b/Methodology Video Data.tex 
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where $m_i$ is the measure of a series of observations $i=1..n$ satisfying the constraint   \begin{equation} \label{eqn:resampling-constraint-map} [(p'_x_i-p_x_j)^2+(p'_y_i-p_y_j)^2 [(p'_{xi}-p_{xj})^2+(p'_{yi}-p_{yj})^2  < (p_x_{j+1}-p_x_j)^2+(p_y_{j+1}-p_y_j)^2] (p_{xj+1}-p_{xj})^2+(p_{yj+1}-p_{yj})^2]  \end{equation} for a grid or hex map and the constraint   \begin{equation} \label{eqn:resampling-constraint-spline} [(p'S_i-pS_j) [(p'_{Si}-p_{Sj})  < (pS_{j+1}-pS_j)] (p_{Sj+1}-p_{Sj})]  \end{equation} for a spline where $S$ is the curvilinear distance along the spline (see section \ref{alignments} for more details on the curvilinear coordinate system employed). This choice of re-sampling will vary from one context to the next.