TY - JOUR
T1 - Using isometries for computational design and fabrication
AU - Jiang, Caigui
AU - Wang, Hui
AU - Ceballos Inza, Victor
AU - Dellinger, Felix
AU - Rist, Florian
AU - Wallner, Johannes
AU - Pottmann, Helmut
PY - 2021/7/1
Y1 - 2021/7/1
N2 - 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.
AB - 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.
KW - architectural geometry
KW - computational fabrication
KW - computer-aided design
KW - discrete differential geometry
KW - discrete isometry
KW - isometric registration
KW - killing vector field
UR - http://www.scopus.com/inward/record.url?scp=85111301110&partnerID=8YFLogxK
U2 - 10.1145/3450626.3459839
DO - 10.1145/3450626.3459839
M3 - Article
SN - 0730-0301
VL - 40
JO - ACM Transactions on Graphics
JF - ACM Transactions on Graphics
IS - 4
M1 - 42
ER -