Quadtree Decomposition, Steiner Triangulation, and Ray Shooting [chapter]

Siu-Wing Cheng, Kam-Hing Lee
1998 Lecture Notes in Computer Science  
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(nlog 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 de ned by Aronov and Fortune. The untruncated decomposition also yields an
more » ... pproximate MWST. Moreover, we show that this triangulation supports query-sensitive ray shooting as de ned by Mitchell, Mount, and Suri. Hence, there exists a Steiner triangulation that is simultaneously good for ray shooting in the query-sensitive sense and in the average case.
doi:10.1007/3-540-49381-6_39 fatcat:facad6j7t5carbw77tvedtsrpq