deletions | additions       diff --git a/Assume_we_are_comparing_two__.tex b/Assume_we_are_comparing_two__.tex  index af3199f..03df2e1 100644  --- a/Assume_we_are_comparing_two__.tex  +++ b/Assume_we_are_comparing_two__.tex 
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Assume we are comparing two intervals $A$ and $B$. Let $$A$ $A$  be the interval stored in-heap, and $B$ the interval we've just encountered the first end-point of. We represent our intervals with a line-segment parametisation. That is, an interval is defined by $\{\mathbf{u} + t\mathbf{v}\mid t\in [0,1]\}$ where in our case $\mathbf{u}$ and $\mathbf{v} \in\mathbb{R}^2$. As such the points of comparison are $B\vert_0$ (the first end-point of B) and the point on $A$ we get by extending the $QB$ segment until intersection.