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 language | English |
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Article number | 128 |
Number of pages | 13 |
Journal | ACM Transactions on Graphics |
Volume | 39 |
Issue number | 4 |
DOIs | |
Publication status | Published - 8 Jul 2020 |
Keywords
- computational fabrication
- computer-aided design
- developable spline surface
- developable surface
- discrete differential geometry
- discrete isometry
- shape optimization
ASJC Scopus subject areas
- Computer Graphics and Computer-Aided Design