---
_id: '12897'
abstract:
- lang: eng
  text: "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."
acknowledged_ssus:
- _id: M-Shop
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Christian
  full_name: Hafner, Christian
  id: 400429CC-F248-11E8-B48F-1D18A9856A87
  last_name: Hafner
citation:
  ama: 'Hafner C. Inverse shape design with parametric representations: Kirchhoff
    Rods and parametric surface models. 2023. doi:<a href="https://doi.org/10.15479/at:ista:12897">10.15479/at:ista:12897</a>'
  apa: 'Hafner, C. (2023). <i>Inverse shape design with parametric representations:
    Kirchhoff Rods and parametric surface models</i>. Institute of Science and Technology
    Austria. <a href="https://doi.org/10.15479/at:ista:12897">https://doi.org/10.15479/at:ista:12897</a>'
  chicago: 'Hafner, Christian. “Inverse Shape Design with Parametric Representations:
    Kirchhoff Rods and Parametric Surface Models.” Institute of Science and Technology
    Austria, 2023. <a href="https://doi.org/10.15479/at:ista:12897">https://doi.org/10.15479/at:ista:12897</a>.'
  ieee: 'C. Hafner, “Inverse shape design with parametric representations: Kirchhoff
    Rods and parametric surface models,” Institute of Science and Technology Austria,
    2023.'
  ista: 'Hafner C. 2023. Inverse shape design with parametric representations: Kirchhoff
    Rods and parametric surface models. Institute of Science and Technology Austria.'
  mla: 'Hafner, Christian. <i>Inverse Shape Design with Parametric Representations:
    Kirchhoff Rods and Parametric Surface Models</i>. Institute of Science and Technology
    Austria, 2023, doi:<a href="https://doi.org/10.15479/at:ista:12897">10.15479/at:ista:12897</a>.'
  short: 'C. Hafner, Inverse Shape Design with Parametric Representations: Kirchhoff
    Rods and Parametric Surface Models, Institute of Science and Technology Austria,
    2023.'
date_created: 2023-05-05T10:40:14Z
date_published: 2023-05-05T00:00:00Z
date_updated: 2024-01-29T10:47:51Z
day: '05'
ddc:
- '516'
- '004'
- '518'
- '531'
degree_awarded: PhD
department:
- _id: GradSch
- _id: BeBi
doi: 10.15479/at:ista:12897
ec_funded: 1
file:
- access_level: open_access
  checksum: cc2094e92fa27000b70eb4bfb76d6b5a
  content_type: application/pdf
  creator: chafner
  date_created: 2023-05-11T10:43:20Z
  date_updated: 2023-12-08T23:30:04Z
  embargo: 2023-12-07
  file_id: '12942'
  file_name: thesis-hafner-2023may11-a2b.pdf
  file_size: 50714445
  relation: main_file
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  checksum: a6b51334be2b81672357b1549afab40c
  content_type: application/pdf
  creator: chafner
  date_created: 2023-05-11T10:43:44Z
  date_updated: 2023-12-08T23:30:04Z
  embargo_to: open_access
  file_id: '12943'
  file_name: thesis-release-form.pdf
  file_size: 265319
  relation: source_file
file_date_updated: 2023-12-08T23:30:04Z
has_accepted_license: '1'
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
page: '180'
project:
- _id: 24F9549A-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '715767'
  name: 'MATERIALIZABLE: Intelligent fabrication-oriented Computational Design and
    Modeling'
publication_identifier:
  isbn:
  - 978-3-99078-031-2
  issn:
  - 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
  record:
  - id: '9817'
    relation: part_of_dissertation
    status: public
  - id: '7117'
    relation: part_of_dissertation
    status: public
  - id: '13188'
    relation: dissertation_contains
    status: public
status: public
supervisor:
- first_name: Bernd
  full_name: Bickel, Bernd
  id: 49876194-F248-11E8-B48F-1D18A9856A87
  last_name: Bickel
  orcid: 0000-0001-6511-9385
title: 'Inverse shape design with parametric representations: Kirchhoff Rods and parametric
  surface models'
type: dissertation
user_id: 400429CC-F248-11E8-B48F-1D18A9856A87
year: '2023'
...