---
_id: '1590'
abstract:
- lang: eng
text: 'The straight skeleton of a polygon is the geometric graph obtained by tracing
the vertices during a mitered offsetting process. It is known that the straight
skeleton of a simple polygon is a tree, and one can naturally derive directions
on the edges of the tree from the propagation of the shrinking process. In this
paper, we ask the reverse question: Given a tree with directed edges, can it be
the straight skeleton of a polygon? And if so, can we find a suitable simple polygon?
We answer these questions for all directed trees where the order of edges around
each node is fixed.'
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Oswin
full_name: Aichholzer, Oswin
last_name: Aichholzer
- first_name: Therese
full_name: Biedl, Therese
last_name: Biedl
- first_name: Thomas
full_name: Hackl, Thomas
last_name: Hackl
- first_name: Martin
full_name: Held, Martin
last_name: Held
- first_name: Stefan
full_name: Huber, Stefan
id: 4700A070-F248-11E8-B48F-1D18A9856A87
last_name: Huber
orcid: 0000-0002-8871-5814
- first_name: Peter
full_name: Palfrader, Peter
last_name: Palfrader
- first_name: Birgit
full_name: Vogtenhuber, Birgit
last_name: Vogtenhuber
citation:
ama: 'Aichholzer O, Biedl T, Hackl T, et al. Representing directed trees as straight
skeletons. In: Graph Drawing and Network Visualization. Vol 9411. Springer
Nature; 2015:335-347. doi:10.1007/978-3-319-27261-0_28'
apa: 'Aichholzer, O., Biedl, T., Hackl, T., Held, M., Huber, S., Palfrader, P.,
& Vogtenhuber, B. (2015). Representing directed trees as straight skeletons.
In Graph Drawing and Network Visualization (Vol. 9411, pp. 335–347). Los
Angeles, CA, United States: Springer Nature. https://doi.org/10.1007/978-3-319-27261-0_28'
chicago: Aichholzer, Oswin, Therese Biedl, Thomas Hackl, Martin Held, Stefan Huber,
Peter Palfrader, and Birgit Vogtenhuber. “Representing Directed Trees as Straight
Skeletons.” In Graph Drawing and Network Visualization, 9411:335–47. Springer
Nature, 2015. https://doi.org/10.1007/978-3-319-27261-0_28.
ieee: O. Aichholzer et al., “Representing directed trees as straight skeletons,”
in Graph Drawing and Network Visualization, vol. 9411, Springer Nature,
2015, pp. 335–347.
ista: 'Aichholzer O, Biedl T, Hackl T, Held M, Huber S, Palfrader P, Vogtenhuber
B. 2015.Representing directed trees as straight skeletons. In: Graph Drawing and
Network Visualization. LNCS, vol. 9411, 335–347.'
mla: Aichholzer, Oswin, et al. “Representing Directed Trees as Straight Skeletons.”
Graph Drawing and Network Visualization, vol. 9411, Springer Nature, 2015,
pp. 335–47, doi:10.1007/978-3-319-27261-0_28.
short: O. Aichholzer, T. Biedl, T. Hackl, M. Held, S. Huber, P. Palfrader, B. Vogtenhuber,
in:, Graph Drawing and Network Visualization, Springer Nature, 2015, pp. 335–347.
conference:
end_date: 2015-09-26
location: Los Angeles, CA, United States
name: 'GD: International Symposium on Graph Drawing'
start_date: 2015-09-24
date_created: 2018-12-11T11:52:54Z
date_published: 2015-11-27T00:00:00Z
date_updated: 2022-01-28T09:10:37Z
day: '27'
department:
- _id: HeEd
doi: 10.1007/978-3-319-27261-0_28
intvolume: ' 9411'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1508.01076
month: '11'
oa: 1
oa_version: Preprint
page: 335 - 347
publication: Graph Drawing and Network Visualization
publication_identifier:
eisbn:
- 978-3-319-27261-0
isbn:
- 978-3-319-27260-3
publication_status: published
publisher: Springer Nature
publist_id: '5581'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Representing directed trees as straight skeletons
type: book_chapter
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 9411
year: '2015'
...
---
_id: '1596'
abstract:
- lang: eng
text: Let C={C1,...,Cn} denote a collection of translates of a regular convex k-gon
in the plane with the stacking order. The collection C forms a visibility clique
if for everyi < j the intersection Ci and (Ci ∩ Cj)\⋃i<l<jCl =∅.elements
that are stacked between them, i.e., We show that if C forms a visibility clique
its size is bounded from above by O(k4) thereby improving the upper bound of 22k
from the aforementioned paper. We also obtain an upper bound of 22(k/2)+2 on the
size of a visibility clique for homothetes of a convex (not necessarily regular)
k-gon.
alternative_title:
- LNCS
article_processing_charge: No
author:
- first_name: Radoslav
full_name: Fulek, Radoslav
id: 39F3FFE4-F248-11E8-B48F-1D18A9856A87
last_name: Fulek
orcid: 0000-0001-8485-1774
- first_name: Radoš
full_name: Radoičić, Radoš
last_name: Radoičić
citation:
ama: 'Fulek R, Radoičić R. Vertical visibility among parallel polygons in three
dimensions. In: Graph Drawing and Network Visualization. Vol 9411. Springer
Nature; 2015:373-379. doi:10.1007/978-3-319-27261-0_31'
apa: 'Fulek, R., & Radoičić, R. (2015). Vertical visibility among parallel polygons
in three dimensions. In Graph Drawing and Network Visualization (Vol. 9411,
pp. 373–379). Los Angeles, CA, United States: Springer Nature. https://doi.org/10.1007/978-3-319-27261-0_31'
chicago: Fulek, Radoslav, and Radoš Radoičić. “Vertical Visibility among Parallel
Polygons in Three Dimensions.” In Graph Drawing and Network Visualization,
9411:373–79. Springer Nature, 2015. https://doi.org/10.1007/978-3-319-27261-0_31.
ieee: R. Fulek and R. Radoičić, “Vertical visibility among parallel polygons in
three dimensions,” in Graph Drawing and Network Visualization, vol. 9411,
Springer Nature, 2015, pp. 373–379.
ista: 'Fulek R, Radoičić R. 2015.Vertical visibility among parallel polygons in
three dimensions. In: Graph Drawing and Network Visualization. LNCS, vol. 9411,
373–379.'
mla: Fulek, Radoslav, and Radoš Radoičić. “Vertical Visibility among Parallel Polygons
in Three Dimensions.” Graph Drawing and Network Visualization, vol. 9411,
Springer Nature, 2015, pp. 373–79, doi:10.1007/978-3-319-27261-0_31.
short: R. Fulek, R. Radoičić, in:, Graph Drawing and Network Visualization, Springer
Nature, 2015, pp. 373–379.
conference:
end_date: 2015-09-26
location: Los Angeles, CA, United States
name: 'GD: Graph Drawing and Network Visualization'
start_date: 2015-09-24
date_created: 2018-12-11T11:52:56Z
date_published: 2015-11-27T00:00:00Z
date_updated: 2022-01-28T09:20:50Z
day: '27'
ddc:
- '510'
department:
- _id: UlWa
doi: 10.1007/978-3-319-27261-0_31
ec_funded: 1
file:
- access_level: open_access
checksum: eec04f86c5921d04f025d5791db9b965
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:17:06Z
date_updated: 2020-07-14T12:45:04Z
file_id: '5258'
file_name: IST-2016-595-v1+1_VerticalVisibilityGDRevision.pdf
file_size: 312992
relation: main_file
file_date_updated: 2020-07-14T12:45:04Z
has_accepted_license: '1'
intvolume: ' 9411'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Submitted Version
page: 373 - 379
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Graph Drawing and Network Visualization
publication_identifier:
isbn:
- 978-3-319-27260-3
publication_status: published
publisher: Springer Nature
publist_id: '5575'
pubrep_id: '595'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Vertical visibility among parallel polygons in three dimensions
type: book_chapter
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 9411
year: '2015'
...