On centroidal voronoi tessellation—energy smoothness and fast computation

By Yang Liu, Wenping Wang, Bruno Lévy, Feng Sun, Dong‐Ming Yan, Lin Lu, Chenglei Yang. 2009

387 citations recorded by the source corpus.

How researchers see this paper

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Image-Based Recommendations on Styles and Substitutes (2015, methodology): “We use (hybrid) L-BFGS, a quasi-Newton method for non-linear optimization of problems with many variables [21].”
PolyMesher: a general-purpose mesh generator for polygonal elements written in Matlab (2012, background): “The CVTs corresponding to saddle points of E are called unstable while local and global minimizers (for fixed number of seeds) of the energy functional are known as stable and optimal CVTs, respectively (Du and Wang 2005; Liu et al. 2009).”
Quadratic maximum-entropy serendipity shape functions for arbitrary planar polygons (2013, methodology): “Recently, Ebeida and co-workers [32] proposed an efficient algorithm, which is provably maximal, bias-free unlike centroidal Voronoi tessellation [51, 52]), has a finite stopping-time, and is more efficient than previous algorithms.”
Advances in Studies and Applications of Centroidal Voronoi Tessellations (2010, methodology): “This is achieved in a recent work of [82] based on the preconditioned limited memory BFGS (L-BFGS) method [81].”
Voronoi grids conforming to 3D structural features (2014, methodology): “The function FCVT is C2 [10] but the function FVout is not C1.”
Inferring Networks of Substitutable and Complementary Products (2015, methodology): “We use the Hybrid LBFGS solver of [19], a quasi-Newton method for non-linear optimization of problems with many variables [25].”