Power diagrams: properties, algorithms and applications
SIAM Journal on Computing
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
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
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
GPU-Assisted Computation of Centroidal Voronoi Tessellation
IEEE Transactions on Visualization and Computer Graphics
ICCSA'06 Proceedings of the 2006 international conference on Computational Science and Its Applications - Volume Part V
Delaunay triangulations of point sets in closed euclidean d-manifolds
Proceedings of the twenty-seventh annual symposium on Computational geometry
Centroidal Voronoi tessellation in universal covering space of manifold surfaces
Computer Aided Geometric Design
Transactions on Computational Science XIV
Graphics Interaction: 5-6-7 Meshes: Remeshing and analysis
Computers and Graphics
Hyperbolic delaunay complexes and voronoi diagrams made practical
Proceedings of the twenty-ninth annual symposium on Computational geometry
| Hi-index | 0.00 |
The centroidal Voronoi tessellation (CVT) has found versatile applications in geometric modeling, computer graphics, and visualization. In this paper, we extend the concept of the CVT from Euclidean space to hyperbolic space. A novel hyperbolic CVT energy is defined, and the relationship between minimizing this energy and the hyperbolic CVT is proved. We also show by our experimental results that the hyperbolic CVT has the similar property as its Euclidean counterpart where the sites are uniformly distributed according to given density values. Two algorithms -- Lloyd's algorithm and the L-BFGS algorithm -- are adopted to compute the hyperbolic CVT, and the convergence of Lloyd's algorithm is proved. As an example of the application, we utilize the hyperbolic CVT to compute uniform partitions and high-quality remeshing results for high-genus (genus1) surfaces.