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