Quadtree Decomposition, Steiner Triangulation, and Ray Shooting

@inproceedings{Cheng1998QuadtreeDS,
  title={Quadtree Decomposition, Steiner Triangulation, and Ray Shooting},
  author={Siu-Wing Cheng and Kam-Hing Lee},
  booktitle={ISAAC},
  year={1998}
}
We present a new quadtree-based decomposition of a polygon possibly with holes. For a polygon of n vertices, a truncated decomposition can be computed in O(n log n) time which yields a Steiner triangulation of the interior of the polygon that has O(n log n) size and approximates the minimum weight Steiner triangulation (MWST) to within a constant factor. An approximate MWST is good for ray shooting in the average case as defined by Aronov and Fortune. The untruncated decomposition also yields… 

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Theorem 3. Given a polygon of n vertices, there is an approximate MWST of

  • Theorem 3. Given a polygon of n vertices, there is an approximate MWST of

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  • Proc. 14th ACM Symposium on Computational Geometry
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