Discrete & Computational Geometry

, Volume 36, Issue 4, pp 553–572

Extreme Elevation on a 2-Manifold


DOI: 10.1007/s00454-006-1265-8

Cite this article as:
Agarwal, P., Edelsbrunner, H., Harer, J. et al. Discrete Comput Geom (2006) 36: 553. doi:10.1007/s00454-006-1265-8


Given a smoothly embedded 2-manifold in \({\Bbb R}^3,\) 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.

Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Department of Computer Science, Duke UniversityDurham, NC 27708USA
  2. 2.Raindrop GeomagicResearch Triangle Park, NC 27709USA
  3. 3.Department of Mathematics, Duke UniversityDurham, NC 27708USA