Hyperbolic centroidal Voronoi tessellation
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Centroidal Voronoi tessellation in universal covering space of manifold surfaces
Computer Aided Geometric Design
Computing Voronoi Treemaps: Faster, Simpler, and Resolution-independent
Computer Graphics Forum
Generalized edge-weighted centroidal Voronoi tessellations for geometry processing
Computers & Mathematics with Applications
Parallel computing 2D Voronoi diagrams using untransformed sweepcircles
Computer-Aided Design
Cartogram visualization for nonlinear manifold learning models
Data Mining and Knowledge Discovery
PixelPie: maximal Poisson-disk sampling with rasterization
Proceedings of the 5th High-Performance Graphics Conference
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Centroidal Voronoi tessellations (CVT) are widely used in computational science and engineering. The most commonly used method is Lloyd's method, and recently the L-BFGS method is shown to be faster than Lloyd's method for computing the CVT. However, these methods run on the CPU and are still too slow for many practical applications. We present techniques to implement these methods on the GPU for computing the CVT on 2D planes and on surfaces, and demonstrate significant speedup of these GPU-based methods over their CPU counterparts. For CVT computation on a surface, we use a geometry image stored in the GPU to represent the surface for computing the Voronoi diagram on it. In our implementation a new technique is proposed for parallel regional reduction on the GPU for evaluating integrals over Voronoi cells.