Packing circles and spheres on surfaces

Handle URI:
http://hdl.handle.net/10754/575744
Title:
Packing circles and spheres on surfaces
Authors:
Schiftner, Alexander; Höbinger, Mathias; Wallner, Johannes; Pottmann, Helmut ( 0000-0002-3195-9316 )
Abstract:
Inspired by freeform designs in architecture which involve circles and spheres, we introduce a new kind of triangle mesh whose faces' incircles form a packing. As it turns out, such meshes have a rich geometry and allow us to cover surfaces with circle patterns, sphere packings, approximate circle packings, hexagonal meshes which carry a torsion-free support structure, hybrid tri-hex meshes, and others. We show how triangle meshes can be optimized so as to have the incircle packing property. We explain their relation to conformal geometry and implications on solvability of optimization. The examples we give confirm that this kind of meshes is a rich source of geometric structures relevant to architectural geometry. © 2009 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 SIGGRAPH Asia 2009 papers on - SIGGRAPH Asia '09
Conference/Event name:
SIGGRAPH Asia 2009
Issue Date:
2009
DOI:
10.1145/1661412.1618485
Type:
Conference Paper
ISSN:
07300301
ISBN:
9781605588582
Appears in Collections:
Conference Papers; Applied Mathematics and Computational Science Program; Applied Mathematics and Computational Science Program; Visual Computing Center (VCC); Visual Computing Center (VCC); Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorSchiftner, Alexanderen
dc.contributor.authorHöbinger, Mathiasen
dc.contributor.authorWallner, Johannesen
dc.contributor.authorPottmann, Helmuten
dc.date.accessioned2015-08-24T09:25:01Zen
dc.date.available2015-08-24T09:25:01Zen
dc.date.issued2009en
dc.identifier.isbn9781605588582en
dc.identifier.issn07300301en
dc.identifier.doi10.1145/1661412.1618485en
dc.identifier.urihttp://hdl.handle.net/10754/575744en
dc.description.abstractInspired by freeform designs in architecture which involve circles and spheres, we introduce a new kind of triangle mesh whose faces' incircles form a packing. As it turns out, such meshes have a rich geometry and allow us to cover surfaces with circle patterns, sphere packings, approximate circle packings, hexagonal meshes which carry a torsion-free support structure, hybrid tri-hex meshes, and others. We show how triangle meshes can be optimized so as to have the incircle packing property. We explain their relation to conformal geometry and implications on solvability of optimization. The examples we give confirm that this kind of meshes is a rich source of geometric structures relevant to architectural geometry. © 2009 ACM.en
dc.publisherAssociation for Computing Machinery (ACM)en
dc.subjectArchitectural geometryen
dc.subjectCircle packingen
dc.subjectComputational conformal geometryen
dc.subjectComputational differential geometryen
dc.subjectFreeform surfaceen
dc.subjectSphere packingen
dc.subjectSupporting structuresen
dc.titlePacking circles and spheres on surfacesen
dc.typeConference Paperen
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 SIGGRAPH Asia 2009 papers on - SIGGRAPH Asia '09en
dc.conference.date2009-12-19en
dc.conference.nameSIGGRAPH Asia 2009en
dc.conference.locationYokohama, Japanen
dc.contributor.institutionEvolute, TU Wien, Austriaen
dc.contributor.institutionTU Wien, Austriaen
dc.contributor.institutionTU Graz, Austriaen
kaust.authorPottmann, Helmuten
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