Packing circles and spheres on surfaces

Alexander Schiftner, Mathias Höbinger, Johannes Wallner, Helmut Pottmann

Research output: Chapter in Book/Report/Conference proceedingConference contribution

38 Scopus citations

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.
Original languageEnglish (US)
Title of host publicationACM SIGGRAPH Asia 2009 papers on - SIGGRAPH Asia '09
PublisherAssociation for Computing Machinery (ACM)
ISBN (Print)9781605588582
DOIs
StatePublished - 2009

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design

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