Years and Authors of Summarized Original Work
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2001; Althaus, Mehlhorn
Problem Definition
An instance of the curve reconstruction problem is a finite set of sample points V in the plane, which are assumed to be taken from an unknown planar curve γ. The task is to construct a geometric graph G on V such that two points in V are connected by an edge in G if and only if the points are adjacent on γ. The curve γ may consist of one or more connected components, and each of them may be closed or open (with endpoints), and may be smooth everywhere (tangent defined at every point) or not.
Many heuristic approaches have been proposed to solve this problem. This work continues a line of reconstruction algorithms with guaranteed performance, i.e., algorithms which probably solve the reconstruction problem under certain assumptions of γ and V. Previous proposed solutions with guaranteed performances were mostly local: a subgraph of the complete geometric graph defined by the points is considered...
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Recommended Reading
Althaus E, Mehlhorn K (2001) Traveling salesman-based curve reconstruction in polynomial time. SIAM J Comput 31:27–66
Althaus E, Mehlhorn K, Näher S, Schirra S (2000) Experiments on curve reconstruction. In: ALENEX, pp 103–114
Amenta N, Bern M (1999) Surface reconstruction by Voronoi filtering. Discrete Comput Geom 22:481–504
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Giesen J (2000) Curve reconstruction, the TSP, and Menger's theorem on length. Discrete Comput Geom 24:577–603
Schrijver A (1986) Theory of linear and integer programming. Wiley, New York
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Ramos, E. (2016). TSP-Based Curve Reconstruction. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_440
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