## Abstract

Consider a collection of disjoint polygons in the plane containing a total of*n* edges. We show how to build, in*O*(*n* ^{2}) time and space, a data structure from which in*O*(*n*) time we can compute the visibility polygon of a given point with respect to the polygon collection. As an application of this structure, the visibility graph of the given polygons can be constructed in*O*(*n* ^{2}) time and space. This implies that the shortest path that connects two points in the plane and avoids the polygons in our collection can be computed in*O*(*n* ^{2}) time, improving earlier*O*(*n* ^{2} log*n*) results.

## Key words

Computational geometry Computer graphics Robotics Visibility Hidden-line Elimination Visibility graph Shortest path## Preview

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© Springer-Verlag New York Inc. 1986