Hough techniques for fast optimization of linear constant velocity motion in moving influence fields

Consider a projectile that must be launched at a given time from a given point into linear constant velocity motion, facing possible encounters with other objects moving at known constant speeds. The cost (or utility) of interaction between the projectile and each object is quantified by an essentially arbitrary, possibly object-specific, function of proximity. It is shown that this constrained problem framework allows fast approximation of the globally optimal projectile velocity using Hough-Transform techniques.