I'm trying to calculate the relative velocity ($V_R$) between an exact velocity ($V_0$) and a velocity range ($V_1$).
The exact velocity ($V_0$) is represented simply by ($course$, $speed$).
The velocity range ($V_1$) is represented by a range of courses and a range of speeds, like so: $([course_{min}, course_{max}], [speed_{min}, speed_{max}])$
I'd like to obtain the relative velocity ($V_R = V_1 - V_0$), which would also be represented by $([course_{min}, course_{max}], [speed_{min}, speed_{max}])$.
Note that $(course, speed)$ is very similar to polar coordinates, with the only difference being that $course$ is zero when facing up (north) and increases clockwise.
I built a spreadsheet to see what patterns would emerge for different ranges of courses and speeds, and I came to the conclusion that the minimum and maximum relative courses & speeds often occur at the "corners" of course/speed space ($(course_{min}, speed_{min})$, $(course_{min}, speed_{max})$, $(course_{max}, speed_{min})$, $(course_{max}, speed_{min})$), but not always.
I'm wondering if there's a relatively simple equation to find $V_R$, or if I'll just need to perform a "brute force" calculation, where I loop through the courses and speeds (at some level of precision) and pick out the min/max values.