2010
DOI: 10.1016/j.disc.2010.05.024
|View full text |Cite
|
Sign up to set email alerts
|

On convexification of polygons by pops

Abstract: Given a polygon P in the plane, a pop operation is the reflection of a vertex with respect to the line through its adjacent vertices. We define a family of alternating polygons, and show that any polygon from this family cannot be convexified by pop operations. This family contains simple, as well as non-simple (i.e., self-intersecting) polygons, as desired. We thereby answer in the negative an open problem posed by Demaine and O'Rourke [9, Open Problem 5.3].

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
3
1
1

Citation Types

0
6
0

Year Published

2010
2010
2016
2016

Publication Types

Select...
1
1

Relationship

1
1

Authors

Journals

citations
Cited by 2 publications
(6 citation statements)
references
References 13 publications
0
6
0
Order By: Relevance
“…Until recently, it has remained an open problem whether there exist polygons that cannot be convexified by pops [7,Open Problem 5.3]. We have shown [8] that such polygons do indeed exist, from both classes, simple or self-intersecting, thereby answering the above open problem in its full generality.…”
Section: Introductionmentioning
confidence: 93%
See 1 more Smart Citation
“…Until recently, it has remained an open problem whether there exist polygons that cannot be convexified by pops [7,Open Problem 5.3]. We have shown [8] that such polygons do indeed exist, from both classes, simple or self-intersecting, thereby answering the above open problem in its full generality.…”
Section: Introductionmentioning
confidence: 93%
“…There is an extensive bibliography pertaining to these subjects [7]. See also [6,8] and the references therein. More results on edge-length preserving transformations and chord stretching can be found in [4,12,13,14].…”
Section: Introductionmentioning
confidence: 99%
“…with H 12 (θ 1 , θ 2 ) : (−π, π] → R. The discrete time map (7) describes the change of angles induced by popping bars 1-2. For bars 2-3, it follows on similar lines that…”
Section: Two-dimensional Mapmentioning
confidence: 99%
“…The two-dimensional maps (7) and ( 8) describe the behavior of all four-bar linkages characterized by the lengths l 1 , l 2 , and l 3 . In order to consider the behavior of a unique four-bar linkage, one has to treat the length L of the fixed bar (not used to derive ( 7)-( 8)) as an additional constraint.…”
Section: Invariant Setmentioning
confidence: 99%
See 1 more Smart Citation