lect07-geom-samples.pdf - CMSC 425 Dave Mount Roger Eastman...

CMSC 425 Dave Mount & Roger Eastman
CMSC 425: Lecture 7
Geometric Programming: Sample Solutions
Samples: In the last few lectures, we have been discussing affine and Euclidean geometry, coordi-
nate frames and affine transformations, and rotations. In this lecture, we work through a few
examples of how to apply these concepts to solve a few concrete problems that might arise in
the context of game programming. Caveat : I have not tested the Unity code given here, so
don’t trust it!
Shot-Gun Simulator:
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.
θ
p
r
q
(a)
θ
c
v
p
r
q
(b)
~u
c
u
t t
Fig. 1: Shot gun.
Lecture 7 1 Spring 2018

CMSC 425 Dave Mount & Roger Eastman