Packing circles and spheres on surfaces

A. Schiftner, M. Höbinger, J. Wallner, H. Pottmann
ACM Transactions on Graphics, volume 28, issue 5, article no. 139, (2009)

Packing circles and spheres on surfaces

Keywords

Computational differential geometry, Architectural ge-ometry, Computational conformal geometry, Freeform surface, Circle packing,  Sphere packing, Supporting structures

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.

Code

DOI:  10.1145/1618452.1618485

Sources

PDF

See all publications 2009