Let $p$ and $q$ be two imprecise points, given as probability densityfunctions on $mathbb R^2$, and let $cal R$ be a set of $n$ line segments(obstacles) in $mathbb R^2$. We study the problem of approximating theprobability that $p$ and $q$ can see each other; that is, that the segmentconnecting $p$ and $q$ does not cross any segment of $cal R$. To solve thisproblem, we approximate each density function by a weighted set of polygons; anovel approach to dealing with probability density functions in computationalgeometry.
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机译：设$ p $和$ q $为两个不精确点，作为$ mathbb R ^ 2 $上的概率密度函数给出，让$ cal R $为$ mathbb R中的一组$ n $线段（障碍） ^ 2 $。我们研究了近似$ p $和$ q $可以看到彼此的概率的问题；也就是说，连接$ p $和$ q $的线段不会跨越$ cal R $的任何线段。为了解决这个问题，我们用一组加权的多边形来近似每个密度函数。 anovel方法，用于处理计算几何中的概率密度函数。
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