{"version":1,"kind":"Article","sha256":"","slug":"302","location":"","dependencies":[],"doi":"10.54294/towi2b","frontmatter":{"title":"Surface Mesh Discrete Curvature Estimators","abstract":"Computing local curvatures of a given surface is important for applications, shape analysis, surface segmentation, meshing, and surface evolution. For a given smooth surface (with a given analytical expression which is sufficiently differentiable) curvatures can be analytically and directly computed. However in real applications, one often deals with a surface mesh which is an insufficiently differentiable approximation, and thus curvatures must be estimated. Based on a surface mesh data structure (\\code{itk::QuadEdgeMesh}~\\cite{itkQE}), we introduce and implement curvature estimators following the approach of Meyer\\etal\\cite{Meyer02}. We show on a sphere that this method results in more stable curvature approximations than the commonly used discrete estimators (as used in VTK: \\code{vtkCurvatures}).","license":"You are licensing your work to Kitware Inc. under the\nCreative Commons Attribution License Version 3.0.\n\nKitware Inc. agrees to the following:\n\nKitware is free\n * to copy, distribute, display, and perform the work\n * to make derivative works\n * to make commercial use of the work\n\nUnder the following conditions:\n\\\"by Attribution\\\" - Kitware must attribute the work in the manner specified by the author or licensor.\n\n * For any reuse or distribution, they must make clear to others the license terms of this work.\n * Any of these conditions can be waived if they get permission from the copyright holder.\n\nYour fair use and other rights are in no way affected by the above.\n\nThis is a human-readable summary of the Legal Code (the full license) available at\nhttp://creativecommons.org/licenses/by/3.0/legalcode","keywords":["curvature","surface mesh"],"authors":[{"name":"Gelas, Arnaud","email":"arnaudgelas@gmail.com","affiliations":[]},{"name":"Gouaillard, Alexandre ","email":"agouaillard@gmail.com","affiliations":[]},{"name":"Megason, Sean ","affiliations":[],"corresponding":true}],"date_submitted":"2008-09-07 17:33:30","external_publication_id":302,"revision_cids":["bafkreibceg64cr64g4pv6agxfov42jmvd4zpemmutoogdhuyonrbp7uihi"],"github":"https://github.com/midas-journal/midas-journal-302.git"},"mdast":{"type":"root"},"downloads":[{"url":"https://pub.desci.com/ipfs/bafkreia7ydkf4pbxug2thys3adtop3t222orrnldeurcgto5f7v2z57vdi","title":"root/code/DiscreteCurvatureEstiimator/CMakeLists.txt","filename":"CMakeLists.txt","extra":{"size_bytes":746,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreieelp4bmmn3uwauuglvjppefplqhdqzq6hofrfufynuxbdkkwy5qq","title":"root/code/DiscreteCurvatureEstiimator/src/itkCross.h","filename":"itkCross.h","extra":{"size_bytes":1148,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreifv5smdcg3sr7yaxhlkxzeqscq6xrm7ngzeuisnj5yfk6lwqrewcq","title":"root/code/DiscreteCurvatureEstiimator/src/itkQEMeshDiscreteCurvatureEstimator.h","filename":"itkQEMeshDiscreteCurvatureEstimator.h","extra":{"size_bytes":3762,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreifvzsa364ngkxdeuwtwjlcotqjjv75x6c4ajhlhu2l3sz6yjaww6i","title":"root/code/DiscreteCurvatureEstiimator/src/itkQEMeshDiscreteCurvatureTensorEstimator.h","filename":"itkQEMeshDiscreteCurvatureTensorEstimator.h","extra":{"size_bytes":1113,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreihoviu76zjbc6iq5xf2h2tttsv2wisv764fmdayt6ntw74jtjrqvu","title":"root/code/DiscreteCurvatureEstiimator/src/itkQEMeshDiscreteGaussianCurvatureEstimator.h","filename":"itkQEMeshDiscreteGaussianCurvatureEstimator.h","extra":{"size_bytes":3499,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreiadxrtuxnjrkpbfm5fopetwyfr3duf6le5p2rfshuixewwqhyr4cu","title":"root/code/DiscreteCurvatureEstiimator/src/itkQEMeshDiscreteMaxCurvatureEstimator.h","filename":"itkQEMeshDiscreteMaxCurvatureEstimator.h","extra":{"size_bytes":2401,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreig6ij5rcdtwnkyi2b73bqfi6t73fjvyppx2at4n3vaitkw46h7joy","title":"root/code/DiscreteCurvatureEstiimator/src/itkQEMeshDiscreteMeanCurvatureEstimator.h","filename":"itkQEMeshDiscreteMeanCurvatureEstimator.h","extra":{"size_bytes":3588,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreigmo446khebstfxscm3lscftd3j5uqw66yzzxl6362mkuy3widclu","title":"root/code/DiscreteCurvatureEstiimator/src/itkQEMeshDiscreteMinCurvatureEstimator.h","filename":"itkQEMeshDiscreteMinCurvatureEstimator.h","extra":{"size_bytes":2401,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreicbo6kddhdy4eoqoqqzmnwof3wv5v5luzpploz7crrikv4ene4nbm","title":"root/code/DiscreteCurvatureEstiimator/src/itkQEMeshDiscretePrincipalCurvaturesEstimator.h","filename":"itkQEMeshDiscretePrincipalCurvaturesEstimator.h","extra":{"size_bytes":3875,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreidgbozhp7lzbbufn7jk23fjmzsdfvxxfbypvizmw6iitvumfri6hy","title":"root/code/DiscreteCurvatureEstiimator/src/itkQEMeshParamMatrixCoefficients.h","filename":"itkQEMeshParamMatrixCoefficients.h","extra":{"size_bytes":12905,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreiezqcd4npvl4rhavhbtreemh4ndvy3cdfvx2wel3goyvy2nh7lmry","title":"root/code/DiscreteCurvatureEstiimator/src/itkQEMeshScalarDataVTKPolyDataWriter.h","filename":"itkQEMeshScalarDataVTKPolyDataWriter.h","extra":{"size_bytes":4609,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreidv44rvxiqc64dgsjfi47idv4y36dt4xiotwuxvpim53ycfepx77m","title":"root/code/DiscreteCurvatureEstiimator/src/itkQuadEdgeMeshExtendedTraits.h","filename":"itkQuadEdgeMeshExtendedTraits.h","extra":{"size_bytes":5338,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreiel55ey6qycok7ykjgynt52jnq4ko3drxmuvhj4ph6qe5npur7tdu","title":"root/code/DiscreteCurvatureEstiimator/src/itkTriangle.h","filename":"itkTriangle.h","extra":{"size_bytes":6621,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreibqqzn4p4o5bordwe5dq4zqnszpevnwlp4c2ejizqk6w65gyum2l4","title":"root/code/DiscreteCurvatureEstiimator/src/itkTriangle.txx","filename":"itkTriangle.txx","extra":{"size_bytes":6837,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreicxhwvfv52eyub367j6uti3pjsubiwyns6fh3hrebf5ogfppxzeu4","title":"root/code/DiscreteCurvatureEstiimator/example/CMakeLists.txt","filename":"CMakeLists.txt","extra":{"size_bytes":480,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreihuz6gsrtt4m6bpffk3q432g7oqcmzmoxmosf44g5urqsiedw5opq","title":"root/code/DiscreteCurvatureEstiimator/example/DiscreteCurvatureEstimator.cxx","filename":"DiscreteCurvatureEstimator.cxx","extra":{"size_bytes":3643,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreie4of7fyac7jqe4lg3ppftykvm7bknaagzbemp7kcxz2ttrzwmfqi","title":"root/code/DiscreteCurvatureEstiimator/doc/InsightArticle.cls","filename":"InsightArticle.cls","extra":{"size_bytes":4240,"type":"file"}},{"url":"https://pub.desci.com/ipfs/bafkreibo4efgrekdmjyh4vo5g2xfr4cxpbyun4kyvj4g65luwqdlbwib7m","title":"root/code/DiscreteCurvatureEstiimator/doc/InsightJournal.sty","filename":"InsightJournal.sty","extra":{"size_bytes":35477,"type":"file"}},{"url":"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Ro¨ssl. Geometric modeling based on polygonal meshes+In SIGGRAPH '07: ACM SIGGRAPH 2007 courses, page 1+2007+2+4+Mario Botsch"},"ref2":{"label":"ref2","enumerator":"2","html":"Triangular meshes delaunay conforming filter+Insight Journal, July-December+1926+Arnaud Gelas+Sean Megason"},"ref3":{"label":"ref3","enumerator":"3","html":"Leonardo Florez-Valencia, and Eric Boix. itkQuadEdgeMesh: A discrete orientable 2-manifold data structure for image processing+Insight Journal, July-December+1926+Alexandre Gouaillard"},"ref4":{"label":"ref4","enumerator":"4","url":"https://doi.org/10.1007/978-3-662-05105-4_2","html":"Discrete differential-geometry operators for triangulated 2-manifolds+2002+1+5+7+Mark Meyer+H. Alan+Barr"}}}}