期刊
ACM TRANSACTIONS ON GRAPHICS
卷 39, 期 4, 页码 -出版社
ASSOC COMPUTING MACHINERY
DOI: 10.1145/3386569.3392430
关键词
discrete differential geometry; computer-aided design; computational fabrication; shape optimization; discrete isometry; developable surface; developable spline surface
资金
- SFB-Transregio programme Discretization in geometry and dynamics through Austrian Science Fund [I2978]
- KAUST baseline funding
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 isometrics 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.
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