Vertex Normals and Face Curvatures of Triangle Meshes

Handle URI:
http://hdl.handle.net/10754/622686
Title:
Vertex Normals and Face Curvatures of Triangle Meshes
Authors:
Sun, Xiang ( 0000-0003-0242-0319 ) ; Jiang, Caigui ( 0000-0002-1342-4094 ) ; Wallner, Johannes; Pottmann, Helmut
Abstract:
This study contributes to the discrete differential geometry of triangle meshes, in combination with discrete line congruences associated with such meshes. In particular we discuss when a congruence defined by linear interpolation of vertex normals deserves to be called a ʼnormal’ congruence. Our main results are a discussion of various definitions of normality, a detailed study of the geometry of such congruences, and a concept of curvatures and shape operators associated with the faces of a triangle mesh. These curvatures are compatible with both normal congruences and the Steiner formula.
KAUST Department:
King Abdullah Univ. of Science and Technology, Thuwal, 23955, Saudi Arabia
Citation:
Sun X, Jiang C, Wallner J, Pottmann H (2016) Vertex Normals and Face Curvatures of Triangle Meshes. Advances in Discrete Differential Geometry: 267–286. Available: http://dx.doi.org/10.1007/978-3-662-50447-5_8.
Publisher:
Springer Nature
Journal:
Advances in Discrete Differential Geometry
Issue Date:
12-Aug-2016
DOI:
10.1007/978-3-662-50447-5_8
Type:
Book Chapter
Sponsors:
The authors are grateful to Alexander Bobenko for fruitful discussions and to the anonymous reviewers for their suggestions. This research was supported by the DFG Collabo- rative Research Center, TRR 109, “Discretization in Geometry and Dynamics” through grants I705 and I706 of the Austrian Science Fund (FWF)
Additional Links:
http://link.springer.com/chapter/10.1007%2F978-3-662-50447-5_8
Appears in Collections:
Book Chapters

Full metadata record

DC FieldValue Language
dc.contributor.authorSun, Xiangen
dc.contributor.authorJiang, Caiguien
dc.contributor.authorWallner, Johannesen
dc.contributor.authorPottmann, Helmuten
dc.date.accessioned2017-01-11T12:20:30Z-
dc.date.available2017-01-11T12:20:30Z-
dc.date.issued2016-08-12en
dc.identifier.citationSun X, Jiang C, Wallner J, Pottmann H (2016) Vertex Normals and Face Curvatures of Triangle Meshes. Advances in Discrete Differential Geometry: 267–286. Available: http://dx.doi.org/10.1007/978-3-662-50447-5_8.en
dc.identifier.doi10.1007/978-3-662-50447-5_8en
dc.identifier.urihttp://hdl.handle.net/10754/622686-
dc.description.abstractThis study contributes to the discrete differential geometry of triangle meshes, in combination with discrete line congruences associated with such meshes. In particular we discuss when a congruence defined by linear interpolation of vertex normals deserves to be called a ʼnormal’ congruence. Our main results are a discussion of various definitions of normality, a detailed study of the geometry of such congruences, and a concept of curvatures and shape operators associated with the faces of a triangle mesh. These curvatures are compatible with both normal congruences and the Steiner formula.en
dc.description.sponsorshipThe authors are grateful to Alexander Bobenko for fruitful discussions and to the anonymous reviewers for their suggestions. This research was supported by the DFG Collabo- rative Research Center, TRR 109, “Discretization in Geometry and Dynamics” through grants I705 and I706 of the Austrian Science Fund (FWF)en
dc.publisherSpringer Natureen
dc.relation.urlhttp://link.springer.com/chapter/10.1007%2F978-3-662-50447-5_8en
dc.rightsThis chapter is distributed under the terms of the Creative Commons Attribution-Noncommercial 2.5 License (http://creativecommons.org/licenses/by-nc/2.5/) which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited. The images or other third party material in this chapter are included in the work’s Creative Commons license, unless indicated otherwise in the credit line; if such material is not included in the work’s Creative Commons license and the respective action is not permitted by statutory regulation, users will need to obtain permission from the license holder to duplicate, adapt or reproduce the material.en
dc.rights.urihttp://creativecommons.org/licenses/by-nc/2.5/en
dc.titleVertex Normals and Face Curvatures of Triangle Meshesen
dc.typeBook Chapteren
dc.contributor.departmentKing Abdullah Univ. of Science and Technology, Thuwal, 23955, Saudi Arabiaen
dc.identifier.journalAdvances in Discrete Differential Geometryen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionGraz University of Technology, Graz, 8010, Austriaen
dc.contributor.institutionVienna University of Technology, Wien, 1040, Australiaen
kaust.authorSun, Xiangen
kaust.authorJiang, Caiguien
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