CMSC 425 : Lecture 7 Geometric Programming : Sample Solutions

Problem: You have been asked to implement a new weapon that behaves something like a shot gun. It has a wide ange of effectiveness, but it is only effective at relatively small distances. Suppose that the end of the muzzle of the gun is located at a point p (in 3-dimensional space), and it has been aimed at a target point t (see Fig. 1(a)). The gun shoots a spray of pellets within angle θ the central axis between p and t, but bullets are only effective up to a distance of r from the end of the muzzle. (Let’s assume that θ is given in degrees and is strictly smaller than 90◦.) Given a point q, write a procedure to determine whether the point q will be hit when the gun is fired.