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Approximation of Normal Cycles

David Cohen-Steiner 1 Jean-Marie Morvan
1 PRISME - Geometry, Algorithms and Robotics
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : This report deals with approximations of geometric data defined on a hypersurf- ace of the Euclidean space E^n. Using geometric measure theory, we evaluate an upper bound on the flat norm of the difference of the normal cycle of a compact subset of E^n whose boundary is a smooth (closed oriented embedded) hypersurface, and the normal cycle of a compact geometric subset of E^n "close to it". We deduce bounds between the difference of the curvature measures of the smooth hypersurface and the curvature measures of the geometric compact subset.
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https://hal.inria.fr/inria-00071863
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Submitted on : Tuesday, May 23, 2006 - 7:02:48 PM
Last modification on : Friday, February 4, 2022 - 3:16:09 AM
Long-term archiving on: : Sunday, April 4, 2010 - 10:41:45 PM

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  • HAL Id : inria-00071863, version 1

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David Cohen-Steiner, Jean-Marie Morvan. Approximation of Normal Cycles. RR-4723, INRIA. 2003. ⟨inria-00071863⟩

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