Restricted delaunay triangulations and normal cycle
Proceedings of the nineteenth annual symposium on Computational geometry
High-pass quantization for mesh encoding
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Differential Coordinates for Interactive Mesh Editing
SMI '04 Proceedings of the Shape Modeling International 2004
Mathematical Programming: Series A and B
Geometric modeling with conical meshes and developable surfaces
ACM SIGGRAPH 2006 Papers
Geometry of multi-layer freeform structures for architecture
ACM SIGGRAPH 2007 papers
Discrete laplace operators: no free lunch
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Procedural modeling of structurally-sound masonry buildings
ACM SIGGRAPH Asia 2009 papers
Discrete surfaces in isotropic geometry
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
Structural optimization of 3D masonry buildings
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
Computing self-supporting surfaces by regular triangulation
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
On the equilibrium of simplicial masonry structures
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Make it stand: balancing shapes for 3D fabrication
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Designing unreinforced masonry models
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
| Hi-index | 0.00 |
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.