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Calculate how far a line travels through each square in a grid created using the meshm function

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Hi, I have plotted a grid using the meshm function over a map with earthquakes and seismic stations plotted. Between each earthquake and each seismic station which recorded it is a travel path (a line).
I want to determine how far each travel path crosses through each square in the grid created using meshm.
The data I have is the earthquake latitude, earthquake longitude, station latitude and station longitude, and the lines were drawn simply using plotm, so I'm aware I'll have to determine the y = mx + c form of each line.
If anyone could help, or at least provide some pointers that would be much appreciated.
Thanks
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Rik
Rik 2018-8-15
It looks like this question is made obsolete by your new question. If this is not the case, you can edit this question (clarifying the difference) to re-open it.

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