A sweepline algorithm for Voronoi diagrams
SCG '86 Proceedings of the second annual symposium on Computational geometry
ACM Transactions on Graphics (TOG)
On the limited memory BFGS method for large scale optimization
Mathematical Programming: Series A and B
Convergence and continuity criteria for discrete approximations of the continuous planar skeleton
CVGIP: Image Understanding
Communications of the ACM
Computational Geometry: Theory and Applications
Interactive geometry remeshing
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Hierarchical mesh decomposition using fuzzy clustering and cuts
ACM SIGGRAPH 2003 Papers
Variational shape approximation
ACM SIGGRAPH 2004 Papers
Variational tetrahedral meshing
ACM SIGGRAPH 2005 Papers
Computing a family of skeletons of volumetric models for shape description
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Curve-Skeleton Properties, Applications, and Algorithms
IEEE Transactions on Visualization and Computer Graphics
Harmonic skeleton for realistic character animation
SCA '07 Proceedings of the 2007 ACM SIGGRAPH/Eurographics symposium on Computer animation
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ACM SIGGRAPH 2007 papers
Defining and computing curve-skeletons with medial geodesic function
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Example-based skeleton extraction
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Generic Remeshing of 3D Triangular Meshes with Metric-Dependent Discrete Voronoi Diagrams
IEEE Transactions on Visualization and Computer Graphics
Skeleton extraction by mesh contraction
ACM SIGGRAPH 2008 papers
Curve-Skeleton Extraction Using Iterative Least Squares Optimization
IEEE Transactions on Visualization and Computer Graphics
Curve skeleton extraction from incomplete point cloud
ACM SIGGRAPH 2009 papers
On centroidal voronoi tessellation—energy smoothness and fast computation
ACM Transactions on Graphics (TOG)
Intersecting quadrics: an efficient and exact implementation
Computational Geometry: Theory and Applications
Lp Centroidal Voronoi Tessellation and its applications
ACM SIGGRAPH 2010 papers
Least squares quantization in PCM
IEEE Transactions on Information Theory
Computer Graphics Forum
L1-medial skeleton of point cloud
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
A shape-aware model for discrete texture synthesis
EGSR '13 Proceedings of the Eurographics Symposium on Rendering
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Centroidal Voronoi Tessellation (CVT) of points has many applications in geometry processing, including re-meshing and segmentation, to name but a few. In this paper, we generalize the CVT concept to graphs via a variational characterization. Given a graph and a 3D polygonal surface, our method optimizes the placement of the vertices of the graph in such a way that the graph segments best approximate the shape of the surface. We formulate the computation of CVT for graphs as a continuous variational problem, and present a simple, approximate method for solving this problem. Our method is robust in the sense that it is independent of degeneracies in the input mesh, such as skinny triangles, T-junctions, small gaps or multiple connected components. We present some applications, to skeleton fitting and to shape segmentation. © 2012 Wiley Periodicals, Inc.