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
Preserved Fulltext
Other Versions
Deciding whether a family 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. ...
arXiv:2108.12812v2
fatcat:2idlhrqhezenvlrggibbopqzhq
Visibilty: Finding the Staircase Kernel in Orthogonal Polygons
2012
American Journal of Computational and Applied Mathematics
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
Our result is optimal in the case 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. ...
doi:10.5923/j.ajcam.20120202.04
fatcat:qdslfddbe5aqbawxcawmwzdwmy
Open Guard Edges and Edge Guards in Simple Polygons
[chapter]
2012
Lecture Notes in Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2016; you can also visit the original URL.
The file type is application/pdf.
An open edge 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. ...
doi:10.1007/978-3-642-34191-5_5
fatcat:jiw37p64hnah5i6duxmi77all4
Linking disjoint axis-parallel segments into a simple polygon is hard too
[article]
2021
arXiv
pre-print
Preserved Fulltext
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.
Deciding whether a family 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. ...
arXiv:2109.02156v1
fatcat:tp7lx3crpjg7do2dwvn5tvvh6m
Constructing pairwise disjoint paths with few links
[chapter]
1997
Lecture Notes in Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
size 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] .) ...
doi:10.1007/3-540-63307-3_79
fatcat:zovqrixdnvdsldsp3jg5ssdckm
Constructing pairwise disjoint paths with few links
2007
ACM Transactions on Algorithms
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
size 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] .) ...
doi:10.1145/1273340.1273342
fatcat:qnkm7x4e6fdkzjl2cgbugxytse
Page 6972 of Mathematical Reviews Vol. , Issue 95k
[page]
1995
Mathematical Reviews
Preserved Fulltext
The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
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
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
We study 3D 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. ...
doi:10.1007/978-3-642-11805-0_31
fatcat:7qi4s3fmnzcv7gg2bnulsz3emu
Page 3898 of Mathematical Reviews Vol. , Issue 97F
[page]
1997
Mathematical Reviews
Preserved Fulltext
The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
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
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
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. ...
doi:10.1016/0925-7721(95)00032-1
fatcat:zkr23xwcgfdatfj4pftyw325li
Vc-dimension of exterior visibility
2004
IEEE Transactions on Pattern Analysis and Machine Intelligence
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2009; you can also visit the original URL.
The file type is application/pdf.
In this paper, we study the Vapnik-Chervonenkis (VC)-dimension 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] . ...
doi:10.1109/tpami.2004.1273987
pmid:15460289
fatcat:5r22eziegvgtpfsouqk5voe5ui
Circumscribing Polygons and Polygonizations for Disjoint Line Segments
[article]
2021
arXiv
pre-print
Preserved Fulltext
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.
Other Versions
We prove that every arrangement 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 . ...
arXiv:1903.07019v3
fatcat:6dtognj6ofarnjp3aqmqpw27oy
Colouring polygon visibility graphs and their generalizations
[article]
2021
arXiv
pre-print
Preserved Fulltext
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.
Curve pseudo-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. ...
arXiv:2103.07803v1
fatcat:hsfela6gkvc25h5bb5aoivejca
Coverage with k-Transmitters in the Presence of Obstacles
[chapter]
2010
Lecture Notes in Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
We develop lower and upper bounds for the number 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 . ...
doi:10.1007/978-3-642-17461-2_1
fatcat:sz7mdy4sj5bejaeo5yfsykgebm
Growing a Tree from Its Branches
1995
Journal of Algorithms
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Given a set Ä 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. ...
doi:10.1006/jagm.1995.1028
fatcat:ka77vmda2ze2tixjxrmdmquyf4
« Previous
Showing results 1 — 15 out of 6,356 results