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Problem 26: Surface Reconstruction
 Statement
 Given a sufficiently dense sample of
points on a surface (technically, an
εsample),
reconstruct a surface homeomorphic to the original.
 Origin
 Amenta and Bern [?]
 Status/Conjectures
 Open.
 Partial and Related Results
 This has recently been accomplished for
smooth surfaces [ACDL00],
but remains open for surfaces
with sharp edges and corners.
 Appearances
 [MO01]
 Categories
 reconstruction; point sets
 Entry Revision History
 J. O'Rourke, 2 Aug. 2001.
 ACDL00

N. Amenta, S. Choi, T. K. Dey, and N. Leekha.
A simple algorithm for homeomorphic surface reconstruction.
In Proc. 16th Annu. ACM Sympos. Comput. Geom., pages 213222,
2000.
 MO01

J. S. B. Mitchell and Joseph O'Rourke.
Computational geometry column 42.
Internat. J. Comput. Geom. Appl., 11(5):573582, 2001.
Also in SIGACT News 32(3):6372 (2001), Issue 120.
The Open Problems Project  September 19, 2017