Discrete & Computational Geometry

, Volume 36, Issue 4, pp 553–572 | Cite as

Extreme Elevation on a 2-Manifold

  • Pankaj K. AgarwalEmail author
  • Herbert EdelsbrunnerEmail author
  • John HarerEmail author
  • Yusu WangEmail author


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.


Triple Point Tangent Plane Height Function Morse Function Protein Docking 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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

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