  Avoiding collisions between obstacles and vehicles such as cars, robots or
aircraft is essential to the development of automation and autonomy. To
simplify the problem, many collision avoidance algorithms and proofs consider
vehicles to be a point mass, though the actual vehicles are not points. In this
paper, we consider a convex polygonal vehicle with nonzero area traveling along
a 2-dimensional trajectory. We derive an easily-checkable, quantifier-free
formula to check whether a given obstacle will collide with the vehicle moving
on the planned trajectory. We apply our method to two case studies of aircraft
collision avoidance and study its performance.
