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COMPGEOM
2005
ACM

The Visibility-Voronoi Complex and Its Applications

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The Visibility-Voronoi Complex and Its Applications
We introduce a new type of diagram called the VV(c)-diagram (the visibility–Voronoi diagram for clearance c), which is a hybrid between the visibility graph and the Voronoi diagram of polygons in the plane. It evolves from the visibility graph to the Voronoi diagram as the parameter c grows from 0 to ∞. This diagram can be used for planning natural-looking paths for a robot translating amidst polygonal obstacles in the plane. A natural-looking path is short, smooth, and keeps—where possible—an amount of clearance c from the obstacles. The VV(c)-diagram contains such paths. We also propose an algorithm that is capable of preprocessing a scene of configuration-space polygonal obstacles and constructs a data structure called the VV-complex. The VV-complex can be used to efficiently plan motion paths for any start and goal configuration and any clearance value c, without having to explicitly construct the VV(c)-diagram for that c-value. The preprocessing time is O(n2 logn), whe...
Ron Wein, Jur P. van den Berg, Dan Halperin
Added 13 Oct 2010
Updated 13 Oct 2010
Type Conference
Year 2005
Where COMPGEOM
Authors Ron Wein, Jur P. van den Berg, Dan Halperin
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