---
_id: '3980'
abstract:
- lang: eng
text: Given a smoothly embedded 2-manifold in R-3, we define the elevation of a
point as the height difference to a canonically defined second point on the same
manifold. Our definition is invariant under rigid motions and can be used to define
features such as lines of discontinuous or continuous but non-smooth elevation.
We give an algorithm for finding points of locally maximum elevation, which we
suggest mark cavities and protrusions and are useful in matching shapes as for
example in protein docking.
author:
- first_name: Pankaj
full_name: Agarwal, Pankaj K
last_name: Agarwal
- first_name: Herbert
full_name: Herbert Edelsbrunner
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: John
full_name: Harer, John
last_name: Harer
- first_name: Yusu
full_name: Wang, Yusu
last_name: Wang
citation:
ama: Agarwal P, Edelsbrunner H, Harer J, Wang Y. Extreme elevation on a 2-manifold.
Discrete & Computational Geometry. 2006;36(4):553-572. doi:10.1007/s00454-006-1265-8
apa: Agarwal, P., Edelsbrunner, H., Harer, J., & Wang, Y. (2006). Extreme elevation
on a 2-manifold. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-006-1265-8
chicago: Agarwal, Pankaj, Herbert Edelsbrunner, John Harer, and Yusu Wang. “Extreme
Elevation on a 2-Manifold.” Discrete & Computational Geometry. Springer,
2006. https://doi.org/10.1007/s00454-006-1265-8.
ieee: P. Agarwal, H. Edelsbrunner, J. Harer, and Y. Wang, “Extreme elevation on
a 2-manifold,” Discrete & Computational Geometry, vol. 36, no. 4. Springer,
pp. 553–572, 2006.
ista: Agarwal P, Edelsbrunner H, Harer J, Wang Y. 2006. Extreme elevation on a 2-manifold.
Discrete & Computational Geometry. 36(4), 553–572.
mla: Agarwal, Pankaj, et al. “Extreme Elevation on a 2-Manifold.” Discrete &
Computational Geometry, vol. 36, no. 4, Springer, 2006, pp. 553–72, doi:10.1007/s00454-006-1265-8.
short: P. Agarwal, H. Edelsbrunner, J. Harer, Y. Wang, Discrete & Computational
Geometry 36 (2006) 553–572.
date_created: 2018-12-11T12:06:15Z
date_published: 2006-12-01T00:00:00Z
date_updated: 2021-01-12T07:53:38Z
day: '01'
doi: 10.1007/s00454-006-1265-8
extern: 1
intvolume: ' 36'
issue: '4'
month: '12'
page: 553 - 572
publication: Discrete & Computational Geometry
publication_status: published
publisher: Springer
publist_id: '2148'
quality_controlled: 0
status: public
title: Extreme elevation on a 2-manifold
type: journal_article
volume: 36
year: '2006'
...