期刊
ACM TRANSACTIONS ON GRAPHICS
卷 40, 期 4, 页码 -出版社
ASSOC COMPUTING MACHINERY
DOI: 10.1145/3450626.3459839
关键词
discrete differential geometry; computer-aided design; computational fabrication; architectural geometry; discrete isometry; isometric registration; Killing vector field
资金
- Austrian Science Fund [I2978, W1230, F77]
- KAUST
- Austrian Science Fund (FWF) [F77, I2978] Funding Source: Austrian Science Fund (FWF)
This study successfully represents free forms through precise isometric bending of surfaces made from a small number of molds, solving the paneling task with surfaces of constant Gaussian curvature. The research also explores interesting connections between the paneling problem and the geometry of Killing vector fields, designing and actuating isometries, curved folding in the case of double-curved surfaces, and quad meshes with rigid faces that remain flexible.
We solve the task of representing free forms by an arrangement of panels that are manufacturable by precise isometric bending of surfaces made from a small number of molds. In fact we manage to solve the paneling task with surfaces of constant Gaussian curvature alone. This includes the case of developable surfaces which exhibit zero curvature. Our computations are based on an existing discrete model of isometric mappings between surfaces which for this occasion has been refined to obtain higher numerical accuracy. Further topics are interesting connections of the paneling problem with the geometry of Killing vector fields, designing and actuating isometries, curved folding in the double-curved case, and quad meshes with rigid faces that are nevertheless flexible.
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