---
_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: 2020-01-21T11:49:01Z
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
status: public
title: Deconstructing approximate offsets
type: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
year: '2011'
...