HOMEWORK 1:

DUE: February 2, 2000


(Q1)

Write a simple planar geometry program which
handles points and lines. Use C or C++ or Java.
Implement the operations of Intersect(L,L') and OnLine(P,L)
as defined in the notes.
You must provide for undefined values,
and do not attempt any epsilon-tweaking.

Now conduct some of experiments to
quantify our assertion that for ``many'' choices
of L and L', the expression

	OnLine(Intersect(L,L'), L)

will not evaluate to TRUE.  Express your quantification
in terms of percentages.

(Q2)
We want to understand the ``geometry'' implicit in the epsilon-test

	|ax + by + c| < epsilon

where L::(a,b,c) and P::(x,y).
Assuming that the point $P$ is ideal (i.e., has radius $0$), determine
the geometric shape of the ``fat line'' $L::(a,b,c)$
when $(a,b,c)=(1,1,0)$.  Determine the
exact shape of $L$.  Derive any formula you need.