Article

Normal Based Estimation of the Curvature Tensor for Triangular Meshes

Authors:

Holger Theisel,

Christian Rossl,

Rhaleb Zayer,

Hans-Peter SeidelAuthors Info & Claims

PG '04: Proceedings of the Computer Graphics and Applications, 12th Pacific Conference

Pages 288 - 297

Published: 06 October 2004 Publication History

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Abstract

We introduce a new technique for estimating the curvature tensor of a triangular mesh. The input of the algorithm is only a single triangle equipped with its (exact or estimated) vertex normals. This way we get a smooth function of the curvature tensor inside each triangle of the mesh. We show that the error of the new method is comparable with the error of a cubic fitting approach if the incorporated normals are estimated. If the exact normals of the underlying surface are available at the vertices, the error drops significantly. We demonstrate the applicability of the new estimation at a rather complex data set.

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Di Angelo LDi Stefano P(2018)C1 continuities detection in triangular meshesComputer-Aided Design10.1016/j.cad.2010.05.00542:9(828-839)Online publication date: 30-Dec-2018
https://dl.acm.org/doi/10.1016/j.cad.2010.05.005
Razdan ABae M(2018)Curvature estimation scheme for triangle meshes using biquadratic Bézier patchesComputer-Aided Design10.1016/j.cad.2005.03.00337:14(1481-1491)Online publication date: 29-Dec-2018
https://dl.acm.org/doi/10.1016/j.cad.2005.03.003
Tang YLi HSun XMorvan JChen L(2017)Principal Curvature Measures Estimation and Application to 3D Face RecognitionJournal of Mathematical Imaging and Vision10.1007/s10851-017-0728-259:2(211-233)Online publication date: 1-Oct-2017
https://dl.acm.org/doi/10.1007/s10851-017-0728-2
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PG '04: Proceedings of the Computer Graphics and Applications, 12th Pacific Conference

October 2004

376 pages

ISBN:0769522343

Publisher

IEEE Computer Society

United States

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Published: 06 October 2004

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Di Angelo LDi Stefano P(2018)C1 continuities detection in triangular meshesComputer-Aided Design10.1016/j.cad.2010.05.00542:9(828-839)Online publication date: 30-Dec-2018
https://dl.acm.org/doi/10.1016/j.cad.2010.05.005
Razdan ABae M(2018)Curvature estimation scheme for triangle meshes using biquadratic Bézier patchesComputer-Aided Design10.1016/j.cad.2005.03.00337:14(1481-1491)Online publication date: 29-Dec-2018
https://dl.acm.org/doi/10.1016/j.cad.2005.03.003
Tang YLi HSun XMorvan JChen L(2017)Principal Curvature Measures Estimation and Application to 3D Face RecognitionJournal of Mathematical Imaging and Vision10.1007/s10851-017-0728-259:2(211-233)Online publication date: 1-Oct-2017
https://dl.acm.org/doi/10.1007/s10851-017-0728-2
Schmitt OSteinmann P(2017)On curvature approximation in 2D and 3D parameter---free shape optimizationStructural and Multidisciplinary Optimization10.1007/s00158-016-1595-y55:5(1655-1669)Online publication date: 1-May-2017
https://dl.acm.org/doi/10.1007/s00158-016-1595-y
Lehmann NReif U(2012)Notes on the curvature tensorGraphical Models10.1016/j.gmod.2012.04.00374:6(321-325)Online publication date: 1-Nov-2012
https://dl.acm.org/doi/10.1016/j.gmod.2012.04.003
Griffin WWang YBerrios DOlano MGarland MWang R(2011)GPU curvature estimation on deformable meshesSymposium on Interactive 3D Graphics and Games10.1145/1944745.1944772(159-166)Online publication date: 18-Feb-2011
https://dl.acm.org/doi/10.1145/1944745.1944772
Jiao XZha HHaines EMcGuire M(2008)Consistent computation of first- and second-order differential quantities for surface meshesProceedings of the 2008 ACM symposium on Solid and physical modeling10.1145/1364901.1364924(159-170)Online publication date: 2-Jun-2008
https://dl.acm.org/doi/10.1145/1364901.1364924
Yu JYin XGu XMcMillan LGortler SBelyaev AGarland M(2007)Focal surfaces of discrete geometryProceedings of the fifth Eurographics symposium on Geometry processing10.5555/1281991.1281994(23-32)Online publication date: 4-Jul-2007
https://dl.acm.org/doi/10.5555/1281991.1281994
Kalogerakis ESimari PNowrouzezahrai DSingh KBelyaev AGarland M(2007)Robust statistical estimation of curvature on discretized surfacesProceedings of the fifth Eurographics symposium on Geometry processing10.5555/1281991.1281993(13-22)Online publication date: 4-Jul-2007
https://dl.acm.org/doi/10.5555/1281991.1281993
Botsch MPauly MKobbelt LAlliez PLévy BBischoff SRössl CMcMains SSloan P(2007)Geometric modeling based on polygonal meshes Video files associated with this course are available from the citation pageACM SIGGRAPH 2007 courses10.1145/1281500.1281640(1-es)Online publication date: 5-Aug-2007
https://dl.acm.org/doi/10.1145/1281500.1281640
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