Deconstructing approximate offsets

E. Berberich, D. Halperin, M. Kerber, R. Pogalnikova, Discrete & Computational Geometry 48 (2012) 964–989.


Journal Article | Published | English
Author
; ; ;
Department
Abstract
We consider the offset-deconstruction problem: Given a polygonal shape Q with n vertices, can it be expressed, up to a tolerance ε in Hausdorff distance, as the Minkowski sum of another polygonal shape P with a disk of fixed radius? If it does, we also seek a preferably simple-looking solution P; then, P's offset constitutes an accurate, vertex-reduced, and smoothened approximation of Q. We give an O(nlogn)-time exact decision algorithm that handles any polygonal shape, assuming the real-RAM model of computation. A variant of the algorithm, which we have implemented using the cgal library, is based on rational arithmetic and answers the same deconstruction problem up to an uncertainty parameter δ its running time additionally depends on δ. If the input shape is found to be approximable, this algorithm also computes an approximate solution for the problem. It also allows us to solve parameter-optimization problems induced by the offset-deconstruction problem. For convex shapes, the complexity of the exact decision algorithm drops to O(n), which is also the time required to compute a solution P with at most one more vertex than a vertex-minimal one.
Publishing Year
Date Published
2012-12-01
Journal Title
Discrete & Computational Geometry
Acknowledgement
We thank Eyal Flato (Plataine Ltd.) for raising the offset-deconstruction problem in connection with wood cutting. We also thank Tim Bretl (UIUC) for suggesting the digital-pen offset-deconstruction problem. This work has been supported in part by the Israel Science Foundation (grant no. 1102/11), by the German–Israeli Foundation (grant no. 969/07), by the Hermann Minkowski–Minerva Center for Geometry at Tel Aviv University, and by the EU Project under Contract No. 255827 (CGL—Computational Geometry Learning).
Volume
48
Issue
4
Page
964 - 989
IST-REx-ID

Cite this

Berberich E, Halperin D, Kerber M, Pogalnikova R. Deconstructing approximate offsets. Discrete & Computational Geometry. 2012;48(4):964-989. doi:10.1007/s00454-012-9441-5
Berberich, E., Halperin, D., Kerber, M., & Pogalnikova, R. (2012). Deconstructing approximate offsets. Discrete & Computational Geometry, 48(4), 964–989. https://doi.org/10.1007/s00454-012-9441-5
Berberich, Eric, Dan Halperin, Michael Kerber, and Roza Pogalnikova. “Deconstructing Approximate Offsets.” Discrete & Computational Geometry 48, no. 4 (2012): 964–89. https://doi.org/10.1007/s00454-012-9441-5.
E. Berberich, D. Halperin, M. Kerber, and R. Pogalnikova, “Deconstructing approximate offsets,” Discrete & Computational Geometry, vol. 48, no. 4, pp. 964–989, 2012.
Berberich E, Halperin D, Kerber M, Pogalnikova R. 2012. Deconstructing approximate offsets. Discrete & Computational Geometry. 48(4), 964–989.
Berberich, Eric, et al. “Deconstructing Approximate Offsets.” Discrete & Computational Geometry, vol. 48, no. 4, Springer, 2012, pp. 964–89, doi:10.1007/s00454-012-9441-5.

Link(s) to Main File(s)
Access Level
OA Open Access
Material in IST:
Earlier Version

Export

Marked Publications

Open Data IST Research Explorer

Sources

arXiv 1109.2158

Search this title in

Google Scholar