# Packing circles and spheres on surfaces

- Published in 2009
- Added on

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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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### BibTeX entry

@misc{item8, title = {Packing circles and spheres on surfaces}, author = {Alexander Schiftner and Mathias H{\"{o}}binger and Johannes Wallner and Helmut Pottmann}, url = {http://dl.acm.org/citation.cfm?id=1618485 http://www.geometrie.tugraz.at/wallner/packing.pdf}, urldate = {2011-09-04}, 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.}, comment = {}, year = 2009, collections = {Basically computer science,Geometry} }