Form-finding with Polyhedral Meshes Made Simple

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

Research output: Contribution to journalArticlepeer-review

Abstract

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
Article number70
Pages (from-to)1-9
JournalACM Transactions on Graphics
Volume33
Issue number4
DOIs
Publication statusPublished - 2014

Fields of Expertise

  • Sonstiges

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