Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
The quickhull algorithm for convex hulls
ACM Transactions on Mathematical Software (TOMS)
Fast computation of generalized Voronoi diagrams using graphics hardware
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Communications of the ACM
Variational tetrahedral meshing
ACM SIGGRAPH 2005 Papers
Fast proximity computation among deformable models using discrete Voronoi diagrams
ACM SIGGRAPH 2006 Papers
Real-Time Path Planning in Dynamic Virtual Environments Using Multiagent Navigation Graphs
IEEE Transactions on Visualization and Computer Graphics
On centroidal voronoi tessellation—energy smoothness and fast computation
ACM Transactions on Graphics (TOG)
Isotropic remeshing with fast and exact computation of Restricted Voronoi Diagram
SGP '09 Proceedings of the Symposium on Geometry Processing
Robust modeling of constant mean curvature surfaces
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Modeling cell layers on complex surfaces using constrained Voronoi diagrams
ACM SIGGRAPH 2013 Posters
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The Voronoi diagram is a fundamental geometry structure widely used in various fields, especially in computer graphics and geometry computing. For a set of points in a compact 3D domain (i.e. a finite 3D volume), some Voronoi cells of their Voronoi diagram are infinite, but in practice only the parts of the cells inside the domain are needed, as when computing the centroidal Voronoi tessellation. Such a Voronoi diagram confined to a compact domain is called a clipped Voronoi diagram. We present an efficient algorithm for computing the clipped Voronoi diagram for a set of sites with respect to a compact 3D volume, assuming that the volume is represented as a tetrahedral mesh. We also describe an application of the proposed method to implementing a fast method for optimal tetrahedral mesh generation based on the centroidal Voronoi tessellation.