---
res:
  bibo_abstract:
  - "Inverse design problems in fabrication-aware shape optimization are typically
    solved on discrete representations such as polygonal meshes. This thesis argues
    that there are benefits to treating these problems in the same domain as human
    designers, namely, the parametric one. One reason is that discretizing a parametric
    model usually removes the capability of making further manual changes to the design,
    because the human intent is captured by the shape parameters. Beyond this, knowledge
    about a design problem can sometimes reveal a structure that is present in a smooth
    representation, but is fundamentally altered by discretizing. In this case, working
    in the parametric domain may even simplify the optimization task. We present two
    lines of research that explore both of these aspects of fabrication-aware shape
    optimization on parametric representations.\r\n\r\nThe first project studies the
    design of plane elastic curves and Kirchhoff rods, which are common mathematical
    models for describing the deformation of thin elastic rods such as beams, ribbons,
    cables, and hair. Our main contribution is a characterization of all curved shapes
    that can be attained by bending and twisting elastic rods having a stiffness that
    is allowed to vary across the length. Elements like these can be manufactured
    using digital fabrication devices such as 3d printers and digital cutters, and
    have applications in free-form architecture and soft robotics.\r\n\r\nWe show
    that the family of curved shapes that can be produced this way admits geometric
    description that is concise and computationally convenient. In the case of plane
    curves, the geometric description is intuitive enough to allow a designer to determine
    whether a curved shape is physically achievable by visual inspection alone. We
    also present shape optimization algorithms that convert a user-defined curve in
    the plane or in three dimensions into the geometry of an elastic rod that will
    naturally deform to follow this curve when its endpoints are attached to a support
    structure. Implemented in an interactive software design tool, the rod geometry
    is generated in real time as the user edits a curve and enables fast prototyping.
    \r\n\r\nThe second project tackles the problem of general-purpose shape optimization
    on CAD models using a novel variant of the extended finite element method (XFEM).
    Our goal is the decoupling between the simulation mesh and the CAD model, so no
    geometry-dependent meshing or remeshing needs to be performed when the CAD parameters
    change during optimization. This is achieved by discretizing the embedding space
    of the CAD model, and using a new high-accuracy numerical integration method to
    enable XFEM on free-form elements bounded by the parametric surface patches of
    the model. Our simulation is differentiable from the CAD parameters to the simulation
    output, which enables us to use off-the-shelf gradient-based optimization procedures.
    The result is a method that fits seamlessly into the CAD workflow because it works
    on the same representation as the designer, enabling the alternation of manual
    editing and fabrication-aware optimization at will.@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
  bibo_doi: 10.15479/at:ista:12897
  dct_date: 2023^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/2663-337X
  - http://id.crossref.org/issn/978-3-99078-031-2
  dct_language: eng
  dct_publisher: Institute of Science and Technology Austria@
  dct_title: 'Inverse shape design with parametric representations: Kirchhoff Rods
    and parametric surface models@'
...