TY - JOUR
T1 - Quad-mesh based isometric mappings and developable surfaces
AU - Jiang, Caigui
AU - Wang, Cheng
AU - Rist, Florian
AU - Wallner, Johannes
AU - Pottmann, Helmut
N1 - 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.
PY - 2020/7/8
Y1 - 2020/7/8
N2 - 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.
AB - 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.
KW - computational fabrication
KW - computer-aided design
KW - developable spline surface
KW - developable surface
KW - discrete differential geometry
KW - discrete isometry
KW - shape optimization
UR - http://www.scopus.com/inward/record.url?scp=85090389976&partnerID=8YFLogxK
U2 - 10.1145/3386569.3392430
DO - 10.1145/3386569.3392430
M3 - Article
VL - 39
JO - ACM Transactions on Graphics
JF - ACM Transactions on Graphics
SN - 0730-0301
IS - 4
M1 - 3392430
ER -