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Problem 26: Surface Reconstruction

Statement
Given a sufficiently dense sample of points on a surface (technically, an ε-sample), 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.

Bibliography

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 213-222, 2000.

MO01
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.



The Open Problems Project - December 04, 2015