Quad-mesh based isometric mappings and developable surfaces

Jiang, Caigui, Wang, Cheng, Rist, Florian, Wallner, Johannes and Pottmann, Helmut (2020) Quad-mesh based isometric mappings and developable surfaces. ACM Transactions on Graphics, 39 (4). ISSN 0730-0301

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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.

Item Type: Article
Additional Information: Funding Information: This work was supported by the SFB-Transregio programme Dis-cretization in geometry and dynamics, through grant I2978 of the Austrian Science Fund. Caigui Jiang, Florian Rist, and Cheng Wang were supported by KAUST baseline funding. The authors wish to thank Jonathan Schrodt for his contribution in the project’s initial phase.
Uncontrolled Keywords: computational fabrication,computer-aided design,developable spline surface,developable surface,discrete differential geometry,discrete isometry,shape optimization,computer graphics and computer-aided design ,/dk/atira/pure/subjectarea/asjc/1700/1704
Faculty \ School: Faculty of Science > School of Computing Sciences
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Depositing User: LivePure Connector
Date Deposited: 23 Jan 2024 01:40
Last Modified: 30 Jan 2024 03:47
URI: https://ueaeprints.uea.ac.uk/id/eprint/94228
DOI: 10.1145/3386569.3392430

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