= Poisson line process
{c}
{title2=$\Pi\subset\{L(p,\theta):p>0,\ 0\leq\theta<2\pi\}$}
Identify an unoriented line not through the origin by $L(p,\theta)=\{z:z\cdot(\cos\theta,\sin\theta)=p\}$, with $p>0$. A <Poisson point process> on this parameter space is a random collection of lines. The <measure> $c\,dp\,d\theta$ is invariant under rotations and translations; signed coordinates $t\in\mathbb R$, $0\leq\theta<\pi$ give the same <measure> $c\,dt\,d\theta$. The number of lines meeting a disk of radius $r$ is <Poisson> with <mean> $2\pi cr$.
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