As you just verified, except for the rods that touch the floor of the bin,
every rod in the stack is supported by exactly two other rods. Choose one rod
from the stack and locate the two rods that support it. Let's consider just
those three rods for a moment.
This diagram illustrates the situation of
three rods in the stack. The three circles in the diagram are the cross
sections of rods. The circle at the top of the figure is being supported by
the other two circles. The center positions of the two supporting rods are
known and fixed.
Intuitively, you should realize that the position of the supported rod is
determined by the positions of the two rods that support it. Mathematically,
the position of the supported rod is a function of:
- the X-Y positions of the centers of the supporting rods,
- the radii of the supporting rods, and
- the radius of the supported rod.
Suppose that this function were actually available to you. That is, suppose
you had some computational device that allowed you to choose any rod in the
stack, input the above information, and then determine the X-Y center position
of the rod you chose. How would that help you solve the rod stacking problem?
Click here for an answer.
You might have noticed that we haven't gone into much detail about how our
function would work inside. We've talked about what the function would
do, but not how it would do it. But that's okay--as you should know
from your experience with Maple, you don't have to know how a function works
inside in order to use it. We'll come back to this point again later in this
lesson.
In fact, we wouldn't have to discuss the insides of the three-rod function at
all, except for one thing. Can you guess what that thing is?
Click here for the answer.
Eric N. Eide
Hamlet Project
Department of Computer Science
University of Utah