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dc.contributor.authorPELLIS, DAVIDE
dc.contributor.authorWang, Hui
dc.contributor.authorKilian, Martin
dc.contributor.authorRist, Florian
dc.contributor.authorPottmann, Helmut
dc.contributor.authorMüller, Christian
dc.date.accessioned2020-06-02T12:58:50Z
dc.date.available2020-06-02T12:58:50Z
dc.date.issued2020-07
dc.identifier.doi10.1145/3386569.3392446
dc.identifier.urihttp://hdl.handle.net/10754/662972
dc.description.abstractThe isolines of principal symmetric surface parametrizations run symmetrically to the principal directions. We describe two discrete versions of these special nets/quad meshes which are dual to each other and show their usefulness for various applications in the context of fabrication and architectural design. Our discretization of a principal symmetric mesh comes naturally with a family of spheres, the so-called Meusnier and Mannheim spheres. In our representation of principal symmetric meshes, we have direct control over the radii of theses spheres and the intersection angles of the parameter lines. This facilitates tasks such as generating Weingarten surfaces including constant mean curvature surfaces and minimal surfaces. We illustrate the potential of Weingarten surfaces for paneling doubly curved freeform facades by significantly reducing the number of necessary molds. Moreover, we have direct access to curvature adaptive tool paths for cylindrical CNC milling with circular edges as well as flank milling with rotational cones. Furthermore, the construction of curved support structures from congruent circular strips is easily managed by constant sphere radii. The underlying families of spheres are in a natural way discrete curvature spheres in analogy to smooth Möbius and Laguerre geometry which further leads to a novel discrete curvature theory for principal symmetric meshes.
dc.description.sponsorshipThe authors gratefully acknowledge the support by the SFB-Transregio “Discretization in Geometry and Dynamics” through grant I 2978 of the Austrian Science Fund (FWF) as well as by project F77 (SFB “Advanced Computational Design”, subproject SP6), by project P 29981, and by KAUST grant OSR#4009. Furthermore, the authors would like to thank the anonymous reviewers for their valuable comments.
dc.language.isoen
dc.publisherACM
dc.rightsArchived with thanks to ACM Transactions on Graphics
dc.titlePrincipal symmetric meshes
dc.typeArticle
dc.contributor.departmentVisual Computing Center (VCC)
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalACM Transactions on Graphics
dc.eprint.versionPost-print
dc.contributor.institutionTU Wien
dc.contributor.institutionDUT
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)
pubs.publication-statusAccepted
kaust.personRist, Florian
kaust.personPottmann, Helmut
kaust.grant.numberOSR#4009
refterms.dateFOA2020-06-02T12:58:51Z
kaust.acknowledged.supportUnitOSR


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