A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2021; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Linking disjoint segments into a simple polygon is hard
[article]

2021
*
arXiv
*
pre-print

Deciding whether a family

arXiv:2108.12812v2
fatcat:2idlhrqhezenvlrggibbopqzhq
*of**disjoint*line segments in the plane can be linked into a simple*polygon*(or a simple*polygonal*chain) by adding segments between their endpoints is NP-hard. ... For each*visibility*edge*of*this*polygon*between two endpoints in V (S), we add a*visibility*edge between the corresponding endpoints in V (S ′ ). ... Then, following the other*visibility*edges*of*the simple*polygon*through S ′ , which are outside and between the gadgets, S can be linked into a simple*polygon*too. ...##
###
Visibilty: Finding the Staircase Kernel in Orthogonal Polygons

2012
*
American Journal of Computational and Applied Mathematics
*

Our result is optimal in the case

doi:10.5923/j.ajcam.20120202.04
fatcat:qdslfddbe5aqbawxcawmwzdwmy
*of*orthogonal*polygon*with holes, since the kernel (as proven) can consist*of*quadratic number*of**disjoint*regions. ... We generalize the notion*of**visibility*in the following way: We say that two points a and b in an orthogonal*polygon*P are*visible*to each other via staircase paths if and only if there exist an orthogonal ... Stefan Pape wants to acknowledge the help*of*Dr. Vassilev during the work on this paper. ...##
###
Open Guard Edges and Edge Guards in Simple Polygons
[chapter]

2012
*
Lecture Notes in Computer Science
*

An open edge

doi:10.1007/978-3-642-34191-5_5
fatcat:jiw37p64hnah5i6duxmi77all4
*of*a simple*polygon*is the set*of*points in the relative interior*of*an edge. ... A guard edge*of*a*polygon*is an edge that sees every point inside the*polygon*. ... Similarly, if q = d, then c is not*visible*from the closed edge ab. We conclude that path(b, c) and path(d, a) are*disjoint*, and Q is a simple*polygon*. ...##
###
Linking disjoint axis-parallel segments into a simple polygon is hard too
[article]

2021
*
arXiv
*
pre-print

Deciding whether a family

arXiv:2109.02156v1
fatcat:tp7lx3crpjg7do2dwvn5tvvh6m
*of**disjoint*axis-parallel line segments in the plane can be linked into a simple*polygon*(or a simple*polygonal*chain) by adding segments between their endpoints is NP-hard. ... Suppose that S can be linked into a simple*polygon*. For each*visibility*edge*of*this*polygon*between two endpoints in V (S), we add a*visibility*edge between the corresponding endpoints in V (S ′ ). ... Then, following the other*visibility*edges*of*the simple*polygon*through S ′ , which are outside and between the gadgets, S can be linked into a simple*polygon*too. ...##
###
Constructing pairwise disjoint paths with few links
[chapter]

1997
*
Lecture Notes in Computer Science
*

size

doi:10.1007/3-540-63307-3_79
fatcat:zovqrixdnvdsldsp3jg5ssdckm
*of*the*polygon*. ... Let P be a simple*polygon*and let {(u 1 , u 1 ), (u 2 , u 2 ), . . . , (um, u m )} be a set*of*m pairs*of*distinct vertices*of*P where for every distinct i, j ≤ m, there exist pairwise*disjoint*(nonintersecting ...*VISIBILITY*The construction*of*pairwise*disjoint*paths uses many*of*the ideas and notation developed in the study*of**polygon**visibility*. (See [Goodman and O'Rourke 1997, Chapter 25] .) ...##
###
Constructing pairwise disjoint paths with few links

2007
*
ACM Transactions on Algorithms
*

size

doi:10.1145/1273340.1273342
fatcat:qnkm7x4e6fdkzjl2cgbugxytse
*of*the*polygon*. ... Let P be a simple*polygon*and let {(u 1 , u 1 ), (u 2 , u 2 ), . . . , (um, u m )} be a set*of*m pairs*of*distinct vertices*of*P where for every distinct i, j ≤ m, there exist pairwise*disjoint*(nonintersecting ...*VISIBILITY*The construction*of*pairwise*disjoint*paths uses many*of*the ideas and notation developed in the study*of**polygon**visibility*. (See [Goodman and O'Rourke 1997, Chapter 25] .) ...##
###
Page 6972 of Mathematical Reviews Vol. , Issue 95k
[page]

1995
*
Mathematical Reviews
*

If the input consists

*of*several*disjoint**polygons*, however, it is often desirable to merge them in prepro- cessing so as to reduce a single*polygon*that retains the geometric characteristics*of*its individual ... We propose an O(n*) time algorithm for finding the maximum independent set*of*the convex*visibility*graph for a restricted class*of*simple*polygons*.” ...##
###
3D Visibility Representations by Regular Polygons
[chapter]

2010
*
Lecture Notes in Computer Science
*

We study 3D

doi:10.1007/978-3-642-11805-0_31
fatcat:7qi4s3fmnzcv7gg2bnulsz3emu
*visibility*representations*of*complete graphs where vertices are represented by equal regular*polygons*lying in planes parallel to the xy-plane. ... Edges correspond to the z-parallel*visibility*among these*polygons*. ... We assume that the z-coordinate*of*P i is i but we use it to identify*polygons*that can block*visibility*between other*polygons*only. ...##
###
Page 3898 of Mathematical Reviews Vol. , Issue 97F
[page]

1997
*
Mathematical Reviews
*

Our algorithm also works for a collection

*of**disjoint*simple*polygons*. ... “In the case*of*staircase*polygons*(special convex fans), we define a class*of*graphs called persistent graphs and show that the*visibility*graph*of*a staircase*polygon*is persistent. ...##
###
Finding a shortest diagonal of a simple polygon in linear time

1997
*
Computational geometry
*

*of*vertices satisfying an additional

*visibility*constraint. ... A diagonal

*of*a planar, simple

*polygon*P is an open line segment that connects two nonadjacent vertices and lies in the relative interior

*of*P. ... Theorem 5.5 also implies a linear-time algorithm for computing a closest

*visible*vertex pair

*of*the

*polygon*: a closest

*visible*pair either forms a shortest diagonal or it is an edge

*of*the

*polygon*. ...

##
###
Vc-dimension of exterior visibility

2004
*
IEEE Transactions on Pattern Analysis and Machine Intelligence
*

In this paper, we study the Vapnik-Chervonenkis (VC)-dimension

doi:10.1109/tpami.2004.1273987
pmid:15460289
fatcat:5r22eziegvgtpfsouqk5voe5ui
*of*set systems arising in 2D*polygonal*and 3D polyhedral configurations where a subset consists*of*all points*visible*from one camera. ... Here, we consider the case*of*exterior*visibility*, where the cameras lie on a constrained area outside the*polygon*and have to observe the entire boundary. ...*Polygons*that are entirely*visible*from the viewing circle are called externally*visible**polygons*[29] . ...##
###
Circumscribing Polygons and Polygonizations for Disjoint Line Segments
[article]

2021
*
arXiv
*
pre-print

We prove that every arrangement

arXiv:1903.07019v3
fatcat:6dtognj6ofarnjp3aqmqpw27oy
*of*n*disjoint*line segments in the plane has a subset*of*size Ω(√(n)) that admits a circumscribing*polygon*, which is the first improvement on this bound in 20 years. ... A circumscribing*polygon*is a*polygonization*for G if every edge in E is an edge*of*P. ... We construct a circumscribing*polygon*for a subset Sb2 ⊆ Sb1 incrementally, while maintaining a*polygon*in the segment endpoint*visibility*graph*of*Sb1 . ...##
###
Colouring polygon visibility graphs and their generalizations
[article]

2021
*
arXiv
*
pre-print

Curve pseudo-

arXiv:2103.07803v1
fatcat:hsfela6gkvc25h5bb5aoivejca
*visibility*graphs generalize*polygon*and pseudo-*polygon**visibility*graphs and form a hereditary class*of*graphs. ... The proof is carried through in the setting*of*ordered graphs; we identify two conditions satisfied by every curve pseudo-*visibility*graph (considered as an ordered graph) and prove that they are sufficient ... Acknowledgement We thank Bodhayan Roy for sharing the problem*of*whether*polygon**visibility*graphs are χ-bounded. ...##
###
Coverage with k-Transmitters in the Presence of Obstacles
[chapter]

2010
*
Lecture Notes in Computer Science
*

We develop lower and upper bounds for the number

doi:10.1007/978-3-642-17461-2_1
fatcat:sz7mdy4sj5bejaeo5yfsykgebm
*of*k-transmitters that are necessary and sufficient to cover a given collection*of*line segments,*polygonal*chains and*polygons*. ... We thank Joseph O'Rourke for the pinwheel example from Fig. 6 and for initiating this line*of*work. ... A small enough gap guarantees that the*visibility*regions*of*the points in S are all*disjoint*, as illustrated in Figure 5 . ...##
###
Growing a Tree from Its Branches

1995
*
Journal of Algorithms
*

Given a set Ä

doi:10.1006/jagm.1995.1028
fatcat:ka77vmda2ze2tixjxrmdmquyf4
*of*Ò*disjoint*line segments in the plane, we show that it is always possible to form a spanning tree*of*the endpoints*of*the segments, such that each line segment is an edge*of*the tree and ... Finally, we show that the complexity*of*finding the minimum weight spanning tree is optimal ¢´Ò ÐÓ Òµ when we assume that the endpoints*of*the line segments are in general position. ... The input to the algorithm is a simple*polygon*with collinearities that is weakly-*visible*from an edge ÙÚ. Let the counter-clockwise order*of*the vertices*of*the*polygon*be Ú Ô ¼ Ô ½ Ô Ò ¾ Ù. ...
« Previous

*Showing results 1 — 15 out of 6,356 results*