Smooth polyhedral surfaces

Handle URI:
http://hdl.handle.net/10754/626545
Title:
Smooth polyhedral surfaces
Authors:
Günther, Felix; Jiang, Caigui ( 0000-0002-1342-4094 ) ; Pottmann, Helmut
Abstract:
Polyhedral surfaces are fundamental objects in architectural geometry and industrial design. Whereas closeness of a given mesh to a smooth reference surface and its suitability for numerical simulations were already studied extensively, the aim of our work is to find and to discuss suitable assessments of smoothness of polyhedral surfaces that only take the geometry of the polyhedral surface itself into account. Motivated by analogies to classical differential geometry, we propose a theory of smoothness of polyhedral surfaces including suitable notions of normal vectors, tangent planes, asymptotic directions, and parabolic curves that are invariant under projective transformations. It is remarkable that seemingly mild conditions significantly limit the shapes of faces of a smooth polyhedral surface. Besides being of theoretical interest, we believe that smoothness of polyhedral surfaces is of interest in the architectural context, where vertices and edges of polyhedral surfaces are highly visible.
KAUST Department:
Visual Computing Center (VCC)
Publisher:
arXiv
Issue Date:
15-Mar-2017
ARXIV:
arXiv:1703.05318
Type:
Preprint
Additional Links:
http://arxiv.org/abs/1703.05318v1; http://arxiv.org/pdf/1703.05318v1
Appears in Collections:
Other/General Submission; Visual Computing Center (VCC)

Full metadata record

DC FieldValue Language
dc.contributor.authorGünther, Felixen
dc.contributor.authorJiang, Caiguien
dc.contributor.authorPottmann, Helmuten
dc.date.accessioned2017-12-28T07:32:15Z-
dc.date.available2017-12-28T07:32:15Z-
dc.date.issued2017-03-15en
dc.identifier.urihttp://hdl.handle.net/10754/626545-
dc.description.abstractPolyhedral surfaces are fundamental objects in architectural geometry and industrial design. Whereas closeness of a given mesh to a smooth reference surface and its suitability for numerical simulations were already studied extensively, the aim of our work is to find and to discuss suitable assessments of smoothness of polyhedral surfaces that only take the geometry of the polyhedral surface itself into account. Motivated by analogies to classical differential geometry, we propose a theory of smoothness of polyhedral surfaces including suitable notions of normal vectors, tangent planes, asymptotic directions, and parabolic curves that are invariant under projective transformations. It is remarkable that seemingly mild conditions significantly limit the shapes of faces of a smooth polyhedral surface. Besides being of theoretical interest, we believe that smoothness of polyhedral surfaces is of interest in the architectural context, where vertices and edges of polyhedral surfaces are highly visible.en
dc.publisherarXiven
dc.relation.urlhttp://arxiv.org/abs/1703.05318v1en
dc.relation.urlhttp://arxiv.org/pdf/1703.05318v1en
dc.rightsArchived with thanks to arXiven
dc.titleSmooth polyhedral surfacesen
dc.typePreprinten
dc.contributor.departmentVisual Computing Center (VCC)en
dc.eprint.versionPre-printen
dc.contributor.institutionMax Planck Institute for Mathematics, Vivatsgasse 7, 53111 Bonn, Germany.en
dc.contributor.institutionErwin Schrodinger International Institute for Mathematical Physics, Boltzmanngasse 9, 1090 Vienna, Austriaen
dc.contributor.institutionCenter for Geometry and Computational Design, Technische Universitat Wien, Wiedner Hauptstrae 8/104, 1040 Vienna, Austria.en
dc.identifier.arxividarXiv:1703.05318en
kaust.authorJiang, Caiguien
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