--- _id: '3329' abstract: - lang: eng text: 'We consider the offset-deconstruction problem: Given a polygonal shape Q with n vertices, can it be expressed, up to a tolerance µ 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 shape P; then, P''s offset constitutes an accurate, vertex-reduced, and smoothened approximation of Q. We give an O(n log n)-time exact decision algorithm that handles any polygonal shape, assuming the real-RAM model of computation. An alternative algorithm, based purely on rational arithmetic, answers the same deconstruction problem, up to an uncertainty parameter, and its running time depends on the parameter δ (in addition to the other input parameters: n, δ and the radius of the disk). If the input shape is found to be approximable, the rational-arithmetic algorithm also computes an approximate solution shape for the 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 shape P with at most one more vertex than a vertex-minimal one. Our study is motivated by applications from two different domains. However, since the offset operation has numerous uses, we anticipate that the reverse question that we study here will be still more broadly applicable. We present results obtained with our implementation of the rational-arithmetic algorithm.' author: - first_name: Eric full_name: Berberich, Eric last_name: Berberich - first_name: Dan full_name: Halperin, Dan last_name: Halperin - first_name: Michael full_name: Kerber, Michael id: 36E4574A-F248-11E8-B48F-1D18A9856A87 last_name: Kerber orcid: 0000-0002-8030-9299 - first_name: Roza full_name: Pogalnikova, Roza last_name: Pogalnikova citation: ama: 'Berberich E, Halperin D, Kerber M, Pogalnikova R. Deconstructing approximate offsets. In: Proceedings of the Twenty-Seventh Annual Symposium on Computational Geometry. ACM; 2011:187-196. doi:10.1145/1998196.1998225' apa: 'Berberich, E., Halperin, D., Kerber, M., & Pogalnikova, R. (2011). Deconstructing approximate offsets. In Proceedings of the twenty-seventh annual symposium on Computational geometry (pp. 187–196). Paris, France: ACM. https://doi.org/10.1145/1998196.1998225' chicago: Berberich, Eric, Dan Halperin, Michael Kerber, and Roza Pogalnikova. “Deconstructing Approximate Offsets.” In Proceedings of the Twenty-Seventh Annual Symposium on Computational Geometry, 187–96. ACM, 2011. https://doi.org/10.1145/1998196.1998225. ieee: E. Berberich, D. Halperin, M. Kerber, and R. Pogalnikova, “Deconstructing approximate offsets,” in Proceedings of the twenty-seventh annual symposium on Computational geometry, Paris, France, 2011, pp. 187–196. ista: 'Berberich E, Halperin D, Kerber M, Pogalnikova R. 2011. Deconstructing approximate offsets. Proceedings of the twenty-seventh annual symposium on Computational geometry. SCG: Symposium on Computational Geometry, 187–196.' mla: Berberich, Eric, et al. “Deconstructing Approximate Offsets.” Proceedings of the Twenty-Seventh Annual Symposium on Computational Geometry, ACM, 2011, pp. 187–96, doi:10.1145/1998196.1998225. short: E. Berberich, D. Halperin, M. Kerber, R. Pogalnikova, in:, Proceedings of the Twenty-Seventh Annual Symposium on Computational Geometry, ACM, 2011, pp. 187–196. conference: end_date: 2011-06-15 location: Paris, France name: 'SCG: Symposium on Computational Geometry' start_date: 2011-06-13 date_created: 2018-12-11T12:02:42Z date_published: 2011-06-13T00:00:00Z date_updated: 2023-02-23T11:12:57Z day: '13' department: - _id: HeEd doi: 10.1145/1998196.1998225 language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1109.2158 month: '06' oa: 1 oa_version: Preprint page: 187 - 196 publication: Proceedings of the twenty-seventh annual symposium on Computational geometry publication_status: published publisher: ACM publist_id: '3306' quality_controlled: '1' related_material: record: - id: '3115' relation: later_version status: public scopus_import: 1 status: public title: Deconstructing approximate offsets type: conference user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 year: '2011' ...