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“Centroidal Voronoi Tessellations for Line Segments and Graphs”
Lin Lu, Bruno Lévy and Wenping Wang
Computer Graphics Forum (Eurographics conf. proc.), 2012

Abstract: Centroidal Voronoi Tesselation (CVT) of points has many applications in geometry processing, including re-meshing and segmentation to name but a few. In this paper, we propose a new extension of CVT, generalized to graphs. 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 approximated method to solve 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.

BibTex reference 

@ARTICLE{lu:cvtgraph_eg:12,
   AUTHOR     = "Lin Lu and Bruno Lévy and Wenping Wang",
   TITLE      = "Centroidal Voronoi Tessellations for Line Segments and Graphs",
   JOURNAL    = "Computer Graphics Forum (Eurographics conf. proc.)",
   YEAR       = "2012",
}