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In this paper, we first define a new Voronoi diagram for the endpoints of a set of line segments in the plane which do not intersect (except possibly at their endpoints), which is called a bounded Voronoi diagram. In this Voronoi diagram, the line segments themselves are regarded as obstacles. We present an optimal Θ(n log n) algorithm to construct it, where n is the number of input line segments.
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Wang et al. (1987) studied this question.