Learning to segment and unfold polyhedral mesh from failures

Zhonghua Xi, Yun Hyeong Kim, Young J. Kim, Jyh Ming Lien

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


Folding planar sheets to make 3D shapes from is an ancient practice with many new applications, ranging from personal fabrication of customized items to design of surgical instruments for minimally invasive surgery in self-folding machines. Given a polyhedral mesh, unfolding is an operation of cutting and flattening the mesh. The flattened polyhedral nets are then cut out of planar materials and folded back to 3D. Unfolding a polyhedral mesh into planar nets usually require segmentation. Either used as a preprocessing step to simplify the mesh and provide semantics or as the result of unfolding to avoid overlapping, the segmentation and the unfolding operations are decoupled. Consequently, segmented components may not be unfoldable and unfolded nets usually provide no semantic meaning and make folding difficult. In this paper, we propose a strategy that tightly couples unfolding and segmentation. We show that the proposed method produces unfoldable segmentation that resembles carefully designed paper craft. The key idea that enables this capability is an algorithm that learns from failed unfoldings.

Original languageEnglish
Pages (from-to)139-149
Number of pages11
JournalComputers and Graphics (Pergamon)
StatePublished - 1 Aug 2016

Bibliographical note

Funding Information:
This work was supported in part by US NSF EFRI-1240459 , IIS-096053 , CNS-1205260 , and AFOSR FA9550-12-1-0238 . J.-M. Lien was also supported by the Korean Federation of Science and Technology Societies (KOFST) grant funded by the Korean government. Y.-J. Kim and Y.-H. Kim were supported in part by NRF in Korea ( 2014K1A3A1A17073365 , 2015R1A2A1A15055470 ).

Publisher Copyright:
© 2016 Elsevier Ltd.


  • Folding
  • Mesh processing
  • Paper craft
  • Segmentation
  • Shape analysis
  • Unfolding


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