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    Packing circles and spheres on surfaces

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    Type
    Conference Paper
    Authors
    Schiftner, Alexander
    Höbinger, Mathias
    Wallner, Johannes
    Pottmann, Helmut cc
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Applied Mathematics and Computational Science Program
    Visual Computing Center (VCC)
    Date
    2009
    Permanent link to this record
    http://hdl.handle.net/10754/575744
    
    Metadata
    Show full item record
    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.
    Citation
    Schiftner, A., Höbinger, M., Wallner, J., & Pottmann, H. (2009). Packing circles and spheres on surfaces. ACM SIGGRAPH Asia 2009 Papers on - SIGGRAPH Asia ’09. doi:10.1145/1661412.1618485
    Publisher
    Association for Computing Machinery (ACM)
    Journal
    ACM SIGGRAPH Asia 2009 papers on - SIGGRAPH Asia '09
    Conference/Event name
    SIGGRAPH Asia 2009
    ISBN
    9781605588582
    DOI
    10.1145/1661412.1618485
    ae974a485f413a2113503eed53cd6c53
    10.1145/1661412.1618485
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