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Arbitrary order principal directions and how to compute them

Julie Digne 1 Sebastien Valette Raphaëlle Chaine Yohann Béarzi
1 Origami - Origami
LIRIS - Laboratoire d'InfoRmatique en Image et Systèmes d'information
Abstract : Curvature principal directions on geometric surfaces are a ubiquitous concept of Geometry Processing techniques. However they only account for order 2 differential quantities, oblivious of higher order differential behaviors. In this paper, we extend the concept of principal directions to higher orders for surfaces in R 3 by considering symmetric differential tensors. We further show how they can be explicitly approximated on point set surfaces and that they convey valuable geometric information, that can help the analysis of 3D surfaces.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03431258
Contributor : Julie Digne Connect in order to contact the contributor
Submitted on : Tuesday, November 16, 2021 - 3:41:30 PM
Last modification on : Friday, November 19, 2021 - 3:49:09 AM

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2111.05800.pdf
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  • HAL Id : hal-03431258, version 1

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Julie Digne, Sebastien Valette, Raphaëlle Chaine, Yohann Béarzi. Arbitrary order principal directions and how to compute them. 2021. ⟨hal-03431258⟩

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