Geodesic patterns

Handle URI:
http://hdl.handle.net/10754/575542
Title:
Geodesic patterns
Authors:
Pottmann, Helmut ( 0000-0002-3195-9316 ) ; Huang, Qixing; Deng, Bailin; Schiftner, Alexander; Kilian, Martin; Guibas, Leonidas J.; Wallner, Johannes
Abstract:
Geodesic curves in surfaces are not only minimizers of distance, but they are also the curves of zero geodesic (sideways) curvature. It turns out that this property makes patterns of geodesics the basic geometric entity when dealing with the cladding of a freeform surface with wooden panels which do not bend sideways. Likewise a geodesic is the favored shape of timber support elements in freeform architecture, for reasons of manufacturing and statics. Both problem areas are fundamental in freeform architecture, but so far only experimental solutions have been available. This paper provides a systematic treatment and shows how to design geodesic patterns in different ways: The evolution of geodesic curves is good for local studies and simple patterns; the level set formulation can deal with the global layout of multiple patterns of geodesics; finally geodesic vector fields allow us to interactively model geodesic patterns and perform surface segmentation into panelizable parts. © 2010 ACM.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program; Visual Computing Center (VCC)
Publisher:
Association for Computing Machinery (ACM)
Journal:
ACM Transactions on Graphics
Issue Date:
26-Jul-2010
DOI:
10.1145/1778765.1778780
Type:
Article
ISSN:
07300301
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Visual Computing Center (VCC); Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorPottmann, Helmuten
dc.contributor.authorHuang, Qixingen
dc.contributor.authorDeng, Bailinen
dc.contributor.authorSchiftner, Alexanderen
dc.contributor.authorKilian, Martinen
dc.contributor.authorGuibas, Leonidas J.en
dc.contributor.authorWallner, Johannesen
dc.date.accessioned2015-08-24T08:32:23Zen
dc.date.available2015-08-24T08:32:23Zen
dc.date.issued2010-07-26en
dc.identifier.issn07300301en
dc.identifier.doi10.1145/1778765.1778780en
dc.identifier.urihttp://hdl.handle.net/10754/575542en
dc.description.abstractGeodesic curves in surfaces are not only minimizers of distance, but they are also the curves of zero geodesic (sideways) curvature. It turns out that this property makes patterns of geodesics the basic geometric entity when dealing with the cladding of a freeform surface with wooden panels which do not bend sideways. Likewise a geodesic is the favored shape of timber support elements in freeform architecture, for reasons of manufacturing and statics. Both problem areas are fundamental in freeform architecture, but so far only experimental solutions have been available. This paper provides a systematic treatment and shows how to design geodesic patterns in different ways: The evolution of geodesic curves is good for local studies and simple patterns; the level set formulation can deal with the global layout of multiple patterns of geodesics; finally geodesic vector fields allow us to interactively model geodesic patterns and perform surface segmentation into panelizable parts. © 2010 ACM.en
dc.publisherAssociation for Computing Machinery (ACM)en
dc.subjectArchitectural geometryen
dc.subjectCladdingen
dc.subjectComputational differential geometryen
dc.subjectFreeform surfaceen
dc.subjectGeodesicen
dc.subjectGeometry of websen
dc.subjectJacobi fielden
dc.subjectPatternen
dc.subjectTimber rib shellen
dc.titleGeodesic patternsen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentVisual Computing Center (VCC)en
dc.identifier.journalACM Transactions on Graphicsen
dc.contributor.institutionStanford University, United Statesen
dc.contributor.institutionEvolute GmbH, TU Wien, Austriaen
dc.contributor.institutionTU Graz, TU Wien, Austriaen
kaust.authorPottmann, Helmuten
kaust.authorDeng, Bailinen
kaust.authorKilian, Martinen
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