Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
On the shape of tetrahedra from bisection
Mathematics of Computation
The quickhull algorithm for convex hulls
ACM Transactions on Mathematical Software (TOMS)
A new Voronoi-based surface reconstruction algorithm
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Fast computation of generalized Voronoi diagrams using graphics hardware
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Output-sensitive construction of polytopes in four dimensions and clipped Voronoi diagrams in three
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Communications of the ACM
Constrained Centroidal Voronoi Tessellations for Surfaces
SIAM Journal on Scientific Computing
Geodesic Voronoi Diagrams on Parametric Surfaces
CGI '97 Proceedings of the 1997 Conference on Computer Graphics International
Simplification and improvement of tetrahedral models for simulation
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Variational tetrahedral meshing
ACM SIGGRAPH 2005 Papers
Geodesic Remeshing Using Front Propagation
International Journal of Computer Vision
Fast proximity computation among deformable models using discrete Voronoi diagrams
ACM SIGGRAPH 2006 Papers
The Medial Scaffold of 3D Unorganized Point Clouds
IEEE Transactions on Pattern Analysis and Machine Intelligence
Mesh Generation: Application to Finite Elements
Mesh Generation: Application to Finite Elements
Voronoi-based variational reconstruction of unoriented point sets
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Variational tetrahedral mesh generation from discrete volume data
The Visual Computer: International Journal of 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
Topological inference via meshing
Proceedings of the twenty-sixth annual symposium on Computational geometry
Computing 2D Periodic Centroidal Voronoi Tessellation
ISVD '11 Proceedings of the 2011 Eighth International Symposium on Voronoi Diagrams in Science and Engineering
SMI 2012: Full Component-aware tensor-product trivariate splines of arbitrary topology
Computers and Graphics
Gap processing for adaptive maximal poisson-disk sampling
ACM Transactions on Graphics (TOG)
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The Voronoi diagram is a fundamental geometric structure widely used in various fields, especially in computer graphics and geometry computing. For a set of points in a compact domain (i.e. a bounded and closed 2D region or a 3D volume), some Voronoi cells of their Voronoi diagram are infinite or partially outside of the domain, 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 to compute the clipped Voronoi diagram for a set of sites with respect to a compact 2D region or a 3D volume. We also apply the proposed method to optimal mesh generation based on the centroidal Voronoi tessellation.