--- _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' ...