Extreme Elevation on a 2-Manifold

Authors:
Pankaj K. Agarwal;Herbert Edelsbrunner;John Harer;Yusu Wang
Affiliations:
Department of Computer Science, Duke University, Durham, NC 27708, USA;Department of Computer Science, Duke University, Durham, NC 27708, USA and Raindrop Geomagic, Research Triangle Park, NC 27709, USA;Department of Mathematics, Duke University, Durham, NC 27708, USA;Department of Computer Science, Duke University, Durham, NC 27708, USA
Venue:
Discrete & Computational Geometry
Year:
2006

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Abstract

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.