Packing circles and spheres on surfaces

Handle URI:
http://hdl.handle.net/10754/575535
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.
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:
1-Dec-2009
DOI:
10.1145/1618452.1618485
Type:
Article
ISSN:
0730-0301
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.authorSchiftner, Alexanderen
dc.contributor.authorHöbinger, Mathiasen
dc.contributor.authorWallner, Johannesen
dc.contributor.authorPottmann, Helmuten
dc.date.accessioned2015-08-24T08:32:02Zen
dc.date.available2015-08-24T08:32:02Zen
dc.date.issued2009-12-01en
dc.identifier.issn0730-0301en
dc.identifier.doi10.1145/1618452.1618485en
dc.identifier.urihttp://hdl.handle.net/10754/575535en
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.en
dc.publisherAssociation for Computing Machinery (ACM)en
dc.titlePacking circles and spheres on surfacesen
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.institutionTU Wien, Evolute, Vienna, Austriaen
dc.contributor.institutionGraz Univ Technol, Graz, Austriaen
kaust.authorPottmann, Helmuten
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.