### Abstract

Let $p$ and $q$ be two imprecise points, given as probability density functions 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 the probability that $p$ and $q$ can see each other; that is, that the segment connecting $p$ and $q$ does not cross any segment of $\cal R$. To solve this problem, we approximate each density function by a weighted set of polygons; a novel approach to dealing with probability density functions in computational geometry.

Original language | English |
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Publisher | s.n. |

Number of pages | 13 |

Publication status | Published - 2014 |

### Publication series

Name | arXiv.org |
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Volume | 1402.5681 [cs.CG] |

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## Cite this

Buchin, K., Kostitsyna, I., Löffler, M., & Silveira, R. I. (2014).

*Region-based approximation of probability distributions (for visibility between imprecise points among obstacles)*. (arXiv.org; Vol. 1402.5681 [cs.CG]). s.n.