Connect-the-dots: a new heuristic
Computer Vision, Graphics, and Image Processing
Computational Geometry: Theory and Applications
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
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
Reconstruction curves with sharp corners
Proceedings of the sixteenth annual symposium on Computational geometry
Reachability by paths of bounded curvature in convex polygons
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
Shape Reconstruction with Delaunay Complex
LATIN '98 Proceedings of the Third Latin American Symposium on Theoretical Informatics
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A new non-Delaunay-based approach is presented to reconstruct a curve, lying in 2- or 3-space, from a sampling of points. The underlying theory is based on bounding curvature to determine monotone pieces of the curve. Theoretical guarantees are established. The implemented algorithm, based heuristically on the theory, proceeds by iteratively partitioning the sample points using an octree data structure. The strengths of the approach are (a) simple implementation, (b) efficiency - experimental performance compares favorably with Delaunay-based algorithms, (c) robustness - curves with multiple components and sharp corners are reconstructed satisfactorily, and (d) potential extension to surface reconstruction.