Approximate shortest distances among smooth obstacles in 3D
DOI:
https://doi.org/10.20382/jocg.v10i1a13Abstract
We consider the classic all-pairs-shortest-paths (APSP) problem in a
three-dimensional environment where paths have to avoid a set of
smooth obstacles whose surfaces are represented by discrete point
sets with $n$ sample points in total. We show that if the point sets
represent eps-amples of the underlying surfaces,
$(1+/-O(\sqrt{eps}))$-approximations of the distances between all
pairs of sample points can be computed in $O(n^{5/2} \log^2 n)$ time.
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