Design of self-supporting surfaces

Etienne Vouga, Mathias Höbinger, Johannes Wallner, Helmut Pottmann

Research output: Contribution to journalArticlepeer-review

98 Scopus citations

Abstract

Self-supporting masonry is one of the most ancient and elegant techniques for building curved shapes. Because of the very geometric nature of their failure, analyzing and modeling such strutures is more a geometry processing problem than one of classical continuum mechanics. This paper uses the thrust network method of analysis and presents an iterative nonlinear optimization algorithm for efficiently approximating freeform shapes by self-supporting ones. The rich geometry of thrust networks leads us to close connections between diverse topics in discrete differential geometry, such as a finite-element discretization of the Airy stress potential, perfect graph Laplacians, and computing admissible loads via curvatures of polyhedral surfaces. This geometric viewpoint allows us, in particular, to remesh self-supporting shapes by self-supporting quad meshes with planar faces, and leads to another application of the theory: steel/glass constructions with low moments in nodes. © 2012 ACM 0730-0301/2012/08-ART87.
Original languageEnglish (US)
Pages (from-to)1-11
Number of pages11
JournalACM Transactions on Graphics
Volume31
Issue number4
DOIs
StatePublished - Jul 1 2012

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design

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