Power diagrams: properties, algorithms and applications
SIAM Journal on Computing
Interpolating Subdivision for meshes with arbitrary topology
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Creating models of truss structures with optimization
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Object-oriented software for quadratic programming
ACM Transactions on Mathematical Software (TOMS)
Quality Meshing with Weighted Delaunay Refinement
SIAM Journal on Computing
Variational tetrahedral meshing
ACM SIGGRAPH 2005 Papers
Design exploration through bidirectional modeling of constraints
Design exploration through bidirectional modeling of constraints
Discrete laplace operators: no free lunch
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
On centroidal voronoi tessellation—energy smoothness and fast computation
ACM Transactions on Graphics (TOG)
Procedural modeling of structurally-sound masonry buildings
ACM SIGGRAPH Asia 2009 papers
HOT: Hodge-optimized triangulations
ACM SIGGRAPH 2011 papers
Guided exploration of physically valid shapes for furniture design
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Design of self-supporting surfaces
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Structural optimization of 3D masonry buildings
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
Blue noise through optimal transport
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
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Masonry structures must be compressively self-supporting; designing such surfaces forms an important topic in architecture as well as a challenging problem in geometric modeling. Under certain conditions, a surjective mapping exists between a power diagram, defined by a set of 2D vertices and associated weights, and the reciprocal diagram that characterizes the force diagram of a discrete self-supporting network. This observation lets us define a new and convenient parameterization for the space of self-supporting networks. Based on it and the discrete geometry of this design space, we present novel geometry processing methods including surface smoothing and remeshing which significantly reduce the magnitude of force densities and homogenize their distribution.