Form-finding with polyhedral meshes made simple

Chengcheng Tang, Xiang Sun, Maria Alexandra Gomes, Johannes Wallner, Helmut Pottmann

Research output: Chapter in Book/Report/Conference proceedingConference contribution

84 Scopus citations


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.
Original languageEnglish (US)
Title of host publicationACM Transactions on Graphics
PublisherAssociation for Computing Machinery (ACM)
Number of pages9
StatePublished - Jul 27 2014

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design


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