Centroidal Voronoi Tessellation of Line Segments and Graphs

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.

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