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Using isometries for computational design and fabrication

Published: 19 July 2021 Publication History

Abstract

We solve the task of representing free forms by an arrangement of panels that are manufacturable by precise isometric bending of surfaces made from a small number of molds. In fact we manage to solve the paneling task with surfaces of constant Gaussian curvature alone. This includes the case of developable surfaces which exhibit zero curvature. Our computations are based on an existing discrete model of isometric mappings between surfaces which for this occasion has been refined to obtain higher numerical accuracy. Further topics are interesting connections of the paneling problem with the geometry of Killing vector fields, designing and actuating isometries, curved folding in the double-curved case, and quad meshes with rigid faces that are nevertheless flexible.

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cover image ACM Transactions on Graphics
ACM Transactions on Graphics  Volume 40, Issue 4
August 2021
2170 pages
ISSN:0730-0301
EISSN:1557-7368
DOI:10.1145/3450626
Issue’s Table of Contents
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

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Publication History

Published: 19 July 2021
Published in TOG Volume 40, Issue 4

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Author Tags

  1. architectural geometry
  2. computational fabrication
  3. computer-aided design
  4. discrete differential geometry
  5. discrete isometry
  6. isometric registration
  7. killing vector field

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