Power diagrams: properties, algorithms and applications
SIAM Journal on Computing
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Algorithm 772: STRIPACK: Delaunay triangulation and Voronoi diagram on the surface of a sphere
ACM Transactions on Mathematical Software (TOMS)
Constrained Centroidal Voronoi Tessellations for Surfaces
SIAM Journal on Scientific Computing
Variational shape approximation
ACM SIGGRAPH 2004 Papers
Surface Segmentation Using Geodesic Centroidal Tesselation
3DPVT '04 Proceedings of the 3D Data Processing, Visualization, and Transmission, 2nd International Symposium
Centroidal Voronoi diagrams for isotropic surface remeshing
Graphical Models - Special issue on SMI 2003
Finite Volume Methods on Spheres and Spherical Centroidal Voronoi Meshes
SIAM Journal on Numerical Analysis
Convergence of the Lloyd Algorithm for Computing Centroidal Voronoi Tessellations
SIAM Journal on Numerical Analysis
Computing surface hyperbolic structure and real projective structure
Proceedings of the 2006 ACM symposium on Solid and physical modeling
Recent progress in robust and quality Delaunay mesh generation
Journal of Computational and Applied Mathematics - Special issue: The international symposium on computing and information (ISCI2004)
Generic Remeshing of 3D Triangular Meshes with Metric-Dependent Discrete Voronoi Diagrams
IEEE Transactions on Visualization and Computer Graphics
IEEE Transactions on Visualization and Computer Graphics
ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing
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
Hyperbolic Voronoi Diagrams Made Easy
ICCSA '10 Proceedings of the 2010 International Conference on Computational Science and Its Applications
Hyperbolic centroidal Voronoi tessellation
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
GPU-Assisted Computation of Centroidal Voronoi Tessellation
IEEE Transactions on Visualization and Computer Graphics
Delaunay triangulations of point sets in closed euclidean d-manifolds
Proceedings of the twenty-seventh annual symposium on Computational geometry
ICCSA'06 Proceedings of the 2006 international conference on Computational Science and Its Applications - Volume Part V
Asymptotically optimal block quantization
IEEE Transactions on Information Theory
Least squares quantization in PCM
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Graphics Interaction: 5-6-7 Meshes: Remeshing and analysis
Computers and Graphics
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The centroidal Voronoi tessellation (CVT) has found versatile applications in geometric modeling, computer graphics, and visualization, etc. In this paper, we first extend the concept of CVT from Euclidean space to spherical space and hyperbolic space, and then combine all of them into a unified framework - the CVT in universal covering space. The novel spherical and hyperbolic CVT energy functions are defined, and the relationship between minimizing the energy and the CVT is proved. We also show by our experimental results that both spherical and hyperbolic CVTs have the similar property as their Euclidean counterpart where the sites are uniformly distributed with respect to given density values. As an example of the application, we utilize the CVT in universal covering space to compute uniform partitions and high-quality remeshing results for genus-0, genus-1, and high-genus (genus1) surfaces.