Abstract
Given a set of points P - {p1,p2....Pn} ,n three dimensions, the width of P, W(P)% is defined as the minimum distance between parallel planes of support of P. It is shown that W(P) can be computed in O(n logn time and O(n) space, where / is the number of antipodal pairs? of edges of the convex hull of P, and in the worst case O(n2). [f P is a set of points in the plane, this complexity can be reduced to O(n logn). Finally, for simple polygons linear time suffices.
| Original language | English (US) |
|---|---|
| Title of host publication | Proceedings of the 1st Annual Symposium on Computational Geometry, SCG 1985 |
| Publisher | Association for Computing Machinery, Inc |
| Pages | 1-7 |
| Number of pages | 7 |
| ISBN (Electronic) | 0897911636, 9780897911634 |
| DOIs | |
| State | Published - Jun 1 1985 |
| Event | 1st Annual Symposium on Computational Geometry, SCG 1985 - Baltimore, United States Duration: Jun 5 1985 → Jun 7 1985 |
Other
| Other | 1st Annual Symposium on Computational Geometry, SCG 1985 |
|---|---|
| Country | United States |
| City | Baltimore |
| Period | 6/5/85 → 6/7/85 |
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ASJC Scopus subject areas
- Computational Mathematics
- Geometry and Topology
Cite this
Computing the width of a set. / Houle, Michael B.; Toussaint, Godfried.
Proceedings of the 1st Annual Symposium on Computational Geometry, SCG 1985. Association for Computing Machinery, Inc, 1985. p. 1-7.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
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TY - GEN
T1 - Computing the width of a set
AU - Houle, Michael B.
AU - Toussaint, Godfried
PY - 1985/6/1
Y1 - 1985/6/1
N2 - Given a set of points P - {p1,p2....Pn} ,n three dimensions, the width of P, W(P)% is defined as the minimum distance between parallel planes of support of P. It is shown that W(P) can be computed in O(n logn time and O(n) space, where / is the number of antipodal pairs? of edges of the convex hull of P, and in the worst case O(n2). [f P is a set of points in the plane, this complexity can be reduced to O(n logn). Finally, for simple polygons linear time suffices.
AB - Given a set of points P - {p1,p2....Pn} ,n three dimensions, the width of P, W(P)% is defined as the minimum distance between parallel planes of support of P. It is shown that W(P) can be computed in O(n logn time and O(n) space, where / is the number of antipodal pairs? of edges of the convex hull of P, and in the worst case O(n2). [f P is a set of points in the plane, this complexity can be reduced to O(n logn). Finally, for simple polygons linear time suffices.
UR - http://www.scopus.com/inward/record.url?scp=0002569347&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0002569347&partnerID=8YFLogxK
U2 - 10.1145/323233.323234
DO - 10.1145/323233.323234
M3 - Conference contribution
AN - SCOPUS:0002569347
SP - 1
EP - 7
BT - Proceedings of the 1st Annual Symposium on Computational Geometry, SCG 1985
PB - Association for Computing Machinery, Inc
ER -