Packing circles and spheres on surfaces

Alexander Schiftner, Mathias Höbinger, Johannes Wallner, Helmut Pottmann

Research output: Contribution to journalArticlepeer-review

3 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.
Original languageEnglish (US)
Pages (from-to)1
JournalACM Transactions on Graphics
Volume28
Issue number5
DOIs
StatePublished - Dec 1 2009

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