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.