Connect-the-dots: a new heuristic
Computer Vision, Graphics, and Image Processing
Piecewise smooth surface reconstruction
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
r-regular shape reconstruction from unorganized points
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
A-shapes of a finite point set
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
The crust and the &Bgr;-Skeleton: combinatorial curve reconstruction
Graphical Models and Image Processing
Curve reconstruction, the traveling salesman problem and Menger's theorem on length
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
A simple provable algorithm for curve reconstruction
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
A simple algorithm for homeomorphic surface reconstruction
Proceedings of the sixteenth annual symposium on Computational geometry
TSP-based curve reconstruction in polynomial time
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Curve reconstruction: connecting dots with good reason
Computational Geometry: Theory and Applications
Reconstructing curves with sharp corners
Computational Geometry: Theory and Applications
Regular and non-regular point sets: Properties and reconstruction
Computational Geometry: Theory and Applications
Computational topology for isotopic surface reconstruction
Theoretical Computer Science - Spatial representation: Discrete vs. continous computational models
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The goals of this paper are twofold. The first is to present a new sampling theory for curves, based on a new notion of local feature size. The properties of this new feature size are investigated, and are compared with the standard feature size definitions. The second goal is to revisit an existing algorithm for combinatorial curve reconstruction in spaces of arbitrary dimension, the Nearest Neighbour Crust of Dey and Kumar [Proc. ACMSIAM Sympos. Discrete Algorithms, 1999, pp. 893-894], and to prove its validity under the new sampling conditions. Because the new sampling theory can imply less dense sampling, the new proof is, in some cases, stronger than that presented in [Proc. ACM-SIAM Sympos. Discrete Algorithms, 1999, pp. 893-894]. Also of interest are the techniques used to prove the theorem, as they are unlike those used used in the curve reconstruction literature to date.