TY - GEN
T1 - Form-finding with polyhedral meshes made simple
AU - Tang, Chengcheng
AU - Sun, Xiang
AU - Gomes, Maria Alexandra
AU - Wallner, Johannes
AU - Pottmann, Helmut
N1 - KAUST Repository Item: Exported on 2020-10-01
PY - 2014/7/27
Y1 - 2014/7/27
N2 - We solve the form-finding problem for polyhedral meshes in a way which combines form, function and fabrication; taking care of user-specified constraints like boundary interpolation, planarity of faces, statics, panel size and shape, enclosed volume, and last, but not least, cost. Our main application is the interactive modeling of meshes for architectural and industrial design. Our approach can be described as guided exploration of the constraint space whose algebraic structure is simplified by introducing auxiliary variables and ensuring that constraints are at most quadratic. Computationally, we perform a projection onto the constraint space which is biased towards low values of an energy which expresses desirable "soft" properties like fairness. We have created a tool which elegantly handles difficult tasks, such as taking boundary-alignment of polyhedral meshes into account, planarization, fairing under planarity side conditions, handling hybrid meshes, and extending the treatment of static equilibrium to shapes which possess overhanging parts.
AB - We solve the form-finding problem for polyhedral meshes in a way which combines form, function and fabrication; taking care of user-specified constraints like boundary interpolation, planarity of faces, statics, panel size and shape, enclosed volume, and last, but not least, cost. Our main application is the interactive modeling of meshes for architectural and industrial design. Our approach can be described as guided exploration of the constraint space whose algebraic structure is simplified by introducing auxiliary variables and ensuring that constraints are at most quadratic. Computationally, we perform a projection onto the constraint space which is biased towards low values of an energy which expresses desirable "soft" properties like fairness. We have created a tool which elegantly handles difficult tasks, such as taking boundary-alignment of polyhedral meshes into account, planarization, fairing under planarity side conditions, handling hybrid meshes, and extending the treatment of static equilibrium to shapes which possess overhanging parts.
UR - http://hdl.handle.net/10754/555978
UR - http://dl.acm.org/citation.cfm?doid=2601097.2601213
UR - http://www.scopus.com/inward/record.url?scp=84905718794&partnerID=8YFLogxK
U2 - 10.1145/2601097.2601213
DO - 10.1145/2601097.2601213
M3 - Conference contribution
SP - 1
EP - 9
BT - ACM Transactions on Graphics
PB - Association for Computing Machinery (ACM)
ER -