---
res:
  bibo_abstract:
  - "The behavior of a rigid body primarily depends on its mass moments, which consist
    of the mass, center of mass, and moments of inertia. It is possible to manipulate
    these quantities without altering the geometric appearance of an object by introducing
    cavities in its interior. Algorithms that find cavities of suitable shapes and
    sizes have enabled the computational design of spinning tops, yo-yos, wheels,
    buoys, and statically balanced objects. Previous work is based, for example, on
    topology optimization on voxel grids, which introduces a large number of optimization
    variables and box constraints, or offset surface computation, which cannot guarantee
    that solutions to a feasible problem will always be found.\r\n\r\nIn this work,
    we provide a mathematical analysis of constrained topology optimization problems
    that depend only on mass moments. This class of problems covers, among others,
    all applications mentioned above. Our main result is to show that no matter the
    outer shape of the rigid body to be optimized or the optimization objective and
    constraints considered, the optimal solution always features a quadric-shaped
    interface between material and cavities. This proves that optimal interfaces are
    always ellipsoids, hyperboloids, paraboloids, or one of a few degenerate cases,
    such as planes.\r\n\r\nThis insight lets us replace a difficult topology optimization
    problem with a provably equivalent non-linear equation system in a small number
    (<10) of variables, which represent the coefficients of the quadric. This system
    can be solved in a few seconds for most examples, provides insights into the geometric
    structure of many specific applications, and lets us describe their solution properties.
    Finally, our method integrates seamlessly into modern fabrication workflows because
    our solutions are analytical surfaces that are native to the CAD domain.@eng"
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Christian
      foaf_name: Hafner, Christian
      foaf_surname: Hafner
      foaf_workInfoHomepage: http://www.librecat.org/personId=400429CC-F248-11E8-B48F-1D18A9856A87
  - foaf_Person:
      foaf_givenName: Mickaël
      foaf_name: Ly, Mickaël
      foaf_surname: Ly
      foaf_workInfoHomepage: http://www.librecat.org/personId=6340d7f0-b48d-11eb-b10d-b7487e71d9f1
  - foaf_Person:
      foaf_givenName: Christopher J
      foaf_name: Wojtan, Christopher J
      foaf_surname: Wojtan
      foaf_workInfoHomepage: http://www.librecat.org/personId=3C61F1D2-F248-11E8-B48F-1D18A9856A87
    orcid: 0000-0001-6646-5546
  bibo_doi: 10.1145/3658194
  bibo_issue: '4'
  bibo_volume: 43
  dct_date: 2024^xs_gYear
  dct_identifier:
  - UT:001289270900045
  dct_isPartOf:
  - http://id.crossref.org/issn/0730-0301
  - http://id.crossref.org/issn/1557-7368
  dct_language: eng
  dct_publisher: Association for Computing Machinery@
  dct_subject:
  - Topology Optimization
  - Mass Moments
  - Computational Geometry
  dct_title: 'Spin-it faster: Quadrics solve all topology optimization problems that
    depend only on mass moments@'
...