An On Log N Algorithm for the Voronoi Diagram of a Set of Simple Curve Segment
An On Log N Algorithm for the Voronoi Diagram of a Set of Simple Curve Segment
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In the Shamos-Hoey algorithm, the merge curve is a connected set (we can view this as a kind of 'separability' property of the two sets X^ and X/(). The work of Drysdale and Lee attempts to recover this separability property. As they reported, finding such a separability property that is computationally simple remained elusive despite considerable effort. Accepting the fact that C will have many connected components in general, the technical issue is to t"md at least one pomt (called a 'starter...') in eacli compwnent of C. The innovation of Kirkpatrick is to show that no notion of separability is needed (ie. X^ and X^ can be arbitrary). His idea is to subdivide each Voronoi cell (by introducing 'spokes') into simpler subcells, and to use the fact that a certain minimum spanning tree of X intersects the Voronoi edges and spokes of X^ and X^ in a fashion that allows one to find the starters. This idea appeared again in Sharir's work on intersection circles. In some sense, our new idea is to reintroduce the separability condition in a radical way ('by simply imposing it').
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To quickly assess the difficulty of the text, read a short excerpt:
In the Shamos-Hoey algorithm, the merge curve is a connected set (we can view this as a kind of 'separability' property of the two sets X^ and X/(). The work of Drysdale and Lee attempts to recover this separability property. As they reported, finding such a separability property that is computationally simple remained elusive despite considerable effort. Accepting the fact that C will have many connected components in general, the technical issue is to t"md at least one pomt (called a 'starter...') in eacli compwnent of C. The innovation of Kirkpatrick is to show that no notion of separability is needed (ie. X^ and X^ can be arbitrary). His idea is to subdivide each Voronoi cell (by introducing 'spokes') into simpler subcells, and to use the fact that a certain minimum spanning tree of X intersects the Voronoi edges and spokes of X^ and X^ in a fashion that allows one to find the starters. This idea appeared again in Sharir's work on intersection circles. In some sense, our new idea is to reintroduce the separability condition in a radical way ('by simply imposing it').
What to read after An On Log N Algorithm for the Voronoi Diagram of a Set of Simple Curve Segment?
You can find similar books in the "Read Also" column, or choose other free books by Chee K Yap to read onlineMoreLess
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