Quad-mesh based isometric mappings and developable surfaces

Caigui Jiang, Cheng Wang, Florian Rist, Johannes Wallner, Helmut Pottmann

Research output: Contribution to journalArticlepeer-review

29 Citations (Scopus)

Abstract

We discretize isometric mappings between surfaces as correspondences between checkerboard patterns derived from quad meshes. This method captures the degrees of freedom inherent in smooth isometries and enables a natural definition of discrete developable surfaces. This definition, which is remarkably simple, leads to a class of discrete developables which is much more flexible in applications than previous concepts of discrete developables. In this paper, we employ optimization to efficiently compute isometric mappings, conformal mappings and isometric bending of surfaces. We perform geometric modeling of developables, including cutting, gluing and folding. The discrete mappings presented here have applications in both theory and practice: We propose a theory of curvatures derived from a discrete Gauss map as well as a construction of watertight CAD models consisting of developable spline surfaces.
Original languageEnglish
Article number3392430
JournalACM Transactions on Graphics
Volume39
Issue number4
DOIs
Publication statusPublished - 8 Jul 2020

Keywords

  • computational fabrication
  • computer-aided design
  • developable spline surface
  • developable surface
  • discrete differential geometry
  • discrete isometry
  • shape optimization

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