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 language||English (US)|
|Journal||ACM Transactions on Graphics|
|State||Published - 2020|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: This work was supported by the SFB-Transregio programme Discretization 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. We wish to thank
Jonathan Schrodt for his contribution in the project’s initial phase.