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Problem 25: Polyhedral Surface Approximation
- How efficiently can one compute a polyhedral surface
that is an
ε-approximation of a given triangulated surface in
- Mitchell [?]
- Partial and Related Results
- It is NP-hard to obtain the minimum-facet surface
separating two nested convex polytopes [DG97],
polynomial-time approximation algorithms are known
for this case, and for separating two terrain surfaces,
achieving factors within O(1) or O(log n) of optimal.
However, no polynomial-time approximation results
are known for general surfaces.
- Entry Revision History
- J. O'Rourke, 2 Aug. 2001.
P. K. Agarwal and S. Suri.
Surface approximation and geometric partitions.
SIAM J. Comput., 27:1016-1035, 1998.
H. Brönnimann and M. T. Goodrich.
Almost optimal set covers in finite VC-dimension.
Discrete Comput. Geom., 14:263-279, 1995.
G. Das and M. T. Goodrich.
On the complexity of optimization problems for 3-dimensional convex
polyhedra and decision trees.
Comput. Geom. Theory Appl., 8:123-137, 1997.
J. S. B. Mitchell and Joseph O'Rourke.
Computational geometry column 42.
Internat. J. Comput. Geom. Appl., 11(5):573-582, 2001.
Also in SIGACT News 32(3):63-72 (2001), Issue 120.
Joseph S. B. Mitchell and Subhash Suri.
Separation and approximation of polyhedral objects.
Comput. Geom. Theory Appl., 5:95-114, 1995.
The Open Problems Project - September 19, 2017