Using isometries for computational design and fabrication

Caigui Jiang, Hui Wang, Victor Ceballos Inza, Felix Dellinger, Florian Rist, Johannes Wallner, Helmut Pottmann

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Article number42
Number of pages12
JournalACM Transactions on Graphics
Issue number4
Publication statusPublished - 1 Jul 2021


  • architectural geometry
  • computational fabrication
  • computer-aided design
  • discrete differential geometry
  • discrete isometry
  • isometric registration
  • killing vector field

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design


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