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by Bettina Speckmann, Csaba D. Toth
http://www.inf.ethz.ch/~hoffmann/pub/hst-pbet-04b.ps.gz
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Abstract:
We show that for any set of disjoint line segments in the plane there exists a pointed binary encompassing tree T, that is, a spanning tree on the segment endpoints that contains all input segments, has maximum degree three, and every vertex v T is pointed, that is, v has an incident angle greater than #. Such a tree can be completed to a minimum pseudo-triangulation. In particular, it follows that every set of disjoint line segments has a minimum pseudo-triangulation of bounded vertex degree. 1
Citations
|
95
|
A combinatorial approach to planar non-colliding robot arm motion planning
– Streinu
- 2000
|
|
78
|
Ray shooting in polygons using geodesic triangulations
– Chazelle, Edelsbrunner, et al.
- 1994
|
|
75
|
Topologically sweeping visibility complexes via pseudotriangulations
– Pocchiola, Vegter
- 1996
|
|
73
|
Deformable free space tilings for kinetic collision detection
– Agarwal, Basch, et al.
|
|
50
|
Finding the intersection of two convex polyhedra
– Muller, Preparata
- 1978
|
|
36
|
Dynamic ray shooting and shortest paths in planar subdivision via balanced geodesic triangulations
– Goodrich, Tamassia
- 1997
|
|
28
|
Tight degree bounds for pseudo-triangulations of points, Comput
– Kettner, Kirkpatrick, et al.
|
|
28
|
Minimal tangent visibility graphs
– Pocchiola, Vegter
- 1996
|
|
23
|
New results on dynamic planar point location
– Cheng, Janardan
- 1992
|
|
23
|
Kinetic maintenance of context-sensitive hierarchical representations for disjoint simple polygons
– Kirkpatrick, Speckmann
|
|
21
|
Computing simple circuits from a set of line segments is NP-complete
– RAPPAPORT
- 1989
|
|
14
|
Growing a tree from its branches
– Bose, Toussaint
- 1995
|
|
13
|
Every set of disjoint line segments admits a binary tree, Discrete Comput Geom
– Bose, Houle, et al.
|
|
11
|
On circumscribing polygons for line segments
– Pach, Rivera-Campo
- 1998
|
|
10
|
Computing homotopic shortest paths in the plane
– Bespamyatnikh
|
|
8
|
Segment endpoint visibility graphs are Hamiltonian
– Tóth
|
|
7
|
Alternating paths through disjoint line segments
– Tóth
|
|
7
|
On the maximum degree of bipartite embeddings of trees in the plane
– Kaneko
- 2000
|
|
7
|
On a counterexample to a conjecture of
– Urabe, Watanabe
- 1992
|
|
6
|
Degree bounds for constrained pseudotriangulations
– Tóth
- 2003
|
|
4
|
Allocating vertex _-guards in simple polygons via pseudotriangulations
– Speckmann, T´oth
- 2005
|
|
3
|
Triangulations without pointed spanning trees
– Aichholzer, Huemer, et al.
- 2004
|
|
2
|
Geometric data structures
– Goodrich, Ramaiyer
- 2000
|
|
2
|
Alternating paths along orthogonal segments
– Toth
- 2003
|
|
1
|
Computing homotopic shortest paths e#ciently
– Efrat, Kobourov, et al.
- 2002
|
