Encyclopedia of Algorithms

2016 Edition
| Editors: Ming-Yang Kao

Curve Reconstruction

  • Stefan FunkeEmail author
Reference work entry
DOI: https://doi.org/10.1007/978-1-4939-2864-4_712

Years and Authors of Summarized Original Work

  • 1998; Amenta, Bern, Eppstein

  • 1999; Dey, Kumar

  • 1999; Dey, Mehlhorn, Ramos

  • 1999; Giesen

  • 2001; Funke, Ramos

  • 2003; Cheng, Funke, Golin, Kumar, Poon, Ramos

Problem Definition

Given a set S of sample points from a collection Γ of simple (nonintersecting) curves in the Euclidean plane, curve reconstruction is the problem of computing the graph G( S,  Γ), called the correct reconstruction, whose vertex set is S and that has an edge between two vertices if and only if the respective samples are adjacent on a curve in Γ; see Fig.  1.

Keywords

Computational geometry Curve reconstruction 
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Recommended Reading

  1. 1.
    Amenta N, Bern M, Eppstein D (1998) The Crust and the beta-skeleton: combinatorial curve reconstruction. Graph Models Image Process 60/2:2:125–135Google Scholar
  2. 2.
    Althaus E, Mehlhorn K (2000) TSP-based curve reconstruction in polynomial time. In: Proceedings of the 11th annual ACM-SIAM symposium on discrete algorithms, San Francisco, pp 686–695Google Scholar
  3. 3.
    Cheng S-W, Funke S, Golin MJ, Kumar P, Poon S-H, Ramos E A (2003) Curve reconstruction from noisy samples. In: Proceedings of the 19th ACM symposium on computational geometry, San Diego, pp 302–311Google Scholar
  4. 4.
    Dey TK, Kumar P (1999) A simple provable algorithm for curve reconstruction. In: Proceedings of the 10th ACM-SIAM symposium on discrete algorithms, Baltimore, pp 893–894Google Scholar
  5. 5.
    Dey TK, Mehlhorn K, Ramos EA (1999) Curve reconstruction: connecting dots with good reason. In: Proceedings of the 15th annual acm symposium on computational geometry, Miami Beach, pp 197–206Google Scholar
  6. 6.
    Dey TK, Wenger R (2000) Reconstruction curves with sharp corners. In: Proceedings of the 16th annual ACM symposium on computational geometry, Hong Kong, pp 233–241Google Scholar
  7. 7.
    Edelsbrunner H (1998) Shape reconstruction with delaunay complex. In: Proceedings of the 2nd Latin American theoretical informatics symposium, Campinas. LNCS, vol 1380, pp 119–132Google Scholar
  8. 8.
    Funke S, Ramos EA (2001) Reconstructing a collection of curves with corners and endpoints. In: Proceedings of the 12th annual ACM-SIAM symposium on discrete algorithms, Washington, DC, pp 344–353Google Scholar
  9. 9.
    Giesen J (1999) Curve reconstruction, the traveling salesman problem and Menger’s theorem on length. In: Proceedings of the 15th annual ACM symposium on computational geometry, Miami Beach, pp 207–216Google Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Computer Science, Universität StuttgartStuttgartGermany