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Packing circles and spheres on surfaces

Published: 01 December 2009 Publication History

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.

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Published In

cover image ACM Transactions on Graphics
ACM Transactions on Graphics  Volume 28, Issue 5
December 2009
646 pages
ISSN:0730-0301
EISSN:1557-7368
DOI:10.1145/1618452
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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 December 2009
Published in TOG Volume 28, Issue 5

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Author Tags

  1. architectural geometry
  2. circle packing
  3. computational conformal geometry
  4. computational differential geometry
  5. freeform surface
  6. sphere packing
  7. supporting structures

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