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Firstly, which might be obvious, am I right to assume that I should disregard data which are in not within the range specified by range_min and range_max, in this case, 0.1000000015 and 1.5 metres, respectively?
Yes, that's the convention.
Also, I am wanting to plot this data, so that I can get a visualization the field of view of the laser (possible wrong terminology). Ie where the laser beams managed to reached in relation to the actual robot.
There is a plugin to view sensor_msgs/LaserScan
in Rviz.