Abstract
We consider a generalization of notions of external visibility of simple polygons, namely weak external visibility, weak external visibility from a line and monotonicity, that we call sector visibility. Informally, sector visibility addresses the question of external visibility along rays (or sight lines) whose angles are restricted to a sector (wedge) of specified width u. This provides an interesting measure of the degree of external visibility of a polygon. Our framework also permits a unification and extension of a number of previously unrelated results. Finally, our results uncover a curious complexity discontinuity in this family of problems; algorithms are θ(n) when γ < φ or γ = 2φr, but require ω(n log n) time (at least), when φ < u < 2φ.
| Original language | English (US) |
|---|---|
| Title of host publication | Proceedings of the 5th Annual Symposium on Computational Geometry, SCG 1989 |
| Publisher | Association for Computing Machinery |
| Pages | 247-254 |
| Number of pages | 8 |
| Volume | Part F130124 |
| ISBN (Electronic) | 0897913183 |
| DOIs | |
| State | Published - Jun 5 1989 |
| Event | 5th Annual Symposium on Computational Geometry, SCG 1989 - Saarbruchen, Germany Duration: Jun 5 1989 → Jun 7 1989 |
Other
| Other | 5th Annual Symposium on Computational Geometry, SCG 1989 |
|---|---|
| Country | Germany |
| City | Saarbruchen |
| Period | 6/5/89 → 6/7/89 |
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ASJC Scopus subject areas
- Theoretical Computer Science
- Geometry and Topology
- Computational Mathematics
Cite this
Determining sector visibility of a polygon. / Bhattacharya, B.; Kirkpatrick, D. G.; Toussaint, Godfried.
Proceedings of the 5th Annual Symposium on Computational Geometry, SCG 1989. Vol. Part F130124 Association for Computing Machinery, 1989. p. 247-254.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Determining sector visibility of a polygon
AU - Bhattacharya, B.
AU - Kirkpatrick, D. G.
AU - Toussaint, Godfried
PY - 1989/6/5
Y1 - 1989/6/5
N2 - We consider a generalization of notions of external visibility of simple polygons, namely weak external visibility, weak external visibility from a line and monotonicity, that we call sector visibility. Informally, sector visibility addresses the question of external visibility along rays (or sight lines) whose angles are restricted to a sector (wedge) of specified width u. This provides an interesting measure of the degree of external visibility of a polygon. Our framework also permits a unification and extension of a number of previously unrelated results. Finally, our results uncover a curious complexity discontinuity in this family of problems; algorithms are θ(n) when γ < φ or γ = 2φr, but require ω(n log n) time (at least), when φ < u < 2φ.
AB - We consider a generalization of notions of external visibility of simple polygons, namely weak external visibility, weak external visibility from a line and monotonicity, that we call sector visibility. Informally, sector visibility addresses the question of external visibility along rays (or sight lines) whose angles are restricted to a sector (wedge) of specified width u. This provides an interesting measure of the degree of external visibility of a polygon. Our framework also permits a unification and extension of a number of previously unrelated results. Finally, our results uncover a curious complexity discontinuity in this family of problems; algorithms are θ(n) when γ < φ or γ = 2φr, but require ω(n log n) time (at least), when φ < u < 2φ.
UR - http://www.scopus.com/inward/record.url?scp=0346928759&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0346928759&partnerID=8YFLogxK
U2 - 10.1145/73833.73860
DO - 10.1145/73833.73860
M3 - Conference contribution
AN - SCOPUS:0346928759
VL - Part F130124
SP - 247
EP - 254
BT - Proceedings of the 5th Annual Symposium on Computational Geometry, SCG 1989
PB - Association for Computing Machinery
ER -