Journal
ACM TRANSACTIONS ON GRAPHICS
Volume 31, Issue 4, Pages -Publisher
ASSOC COMPUTING MACHINERY
DOI: 10.1145/2185520.2185583
Keywords
Discrete differential geometry; architectural geometry; self-supporting masonry; thrust networks; reciprocal force diagrams; discrete Laplacians; isotropic geometry; mean curvature
Categories
Funding
- NSF [CMMI-11-29917, IIS-11-17257, IIS-10-48948, IIS-09-16129, CCF-06-43268]
- Austrian Science Fund (FWF) [P9206-N12, P23735-N13]
- Austrian Science Fund (FWF) [P 23735] Funding Source: researchfish
- Direct For Computer & Info Scie & Enginr
- Div Of Information & Intelligent Systems [1117257] Funding Source: National Science Foundation
- Austrian Science Fund (FWF) [P23735] Funding Source: Austrian Science Fund (FWF)
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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.
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