On the limited memory BFGS method for large scale optimization
Mathematical Programming: Series A and B
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
A new Voronoi-based surface reconstruction algorithm
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Communications of the ACM
Interactive geometry remeshing
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
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
Variational tetrahedral meshing
ACM SIGGRAPH 2005 Papers
Centroidal Voronoi diagrams for isotropic surface remeshing
Graphical Models - Special issue on SMI 2003
Geodesic Remeshing Using Front Propagation
International Journal of Computer Vision
Provably good sampling and meshing of Lipschitz surfaces
Proceedings of the twenty-second annual symposium on Computational geometry
Delaunay refinement for piecewise smooth complexes
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Generic Remeshing of 3D Triangular Meshes with Metric-Dependent Discrete Voronoi Diagrams
IEEE Transactions on Visualization and Computer Graphics
On centroidal voronoi tessellation—energy smoothness and fast computation
ACM Transactions on Graphics (TOG)
On Mesh Geometry and Stiffness Matrix Conditioning for General Finite Element Spaces
SIAM Journal on Numerical Analysis
On centroidal voronoi tessellation—energy smoothness and fast computation
ACM Transactions on Graphics (TOG)
Technical Section: Fiedler trees for multiscale surface analysis
Computers and Graphics
Hyperbolic centroidal Voronoi tessellation
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Spectral sampling of manifolds
ACM SIGGRAPH Asia 2010 papers
Centroidal Voronoi tessellation in universal covering space of manifold surfaces
Computer Aided Geometric Design
Efficient computation of 3d clipped voronoi diagram
GMP'10 Proceedings of the 6th international conference on Advances in Geometric Modeling and Processing
Beady: interactive beadwork design and construction
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Robust modeling of constant mean curvature surfaces
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Vertex location optimisation for improved remeshing
Graphical Models
Adaptive surface splatting for facial rendering
Computer Animation and Virtual Worlds
Rationalization of Triangle-Based Point-Folding Structures
Computer Graphics Forum
Parallel computing 2D Voronoi diagrams using untransformed sweepcircles
Computer-Aided Design
Isotropic Surface Remeshing Using Constrained Centroidal Delaunay Mesh
Computer Graphics Forum
Adaptive maximal Poisson-disk sampling on surfaces
SIGGRAPH Asia 2012 Technical Briefs
Efficient computation of clipped Voronoi diagram for mesh generation
Computer-Aided Design
Particle-based anisotropic surface meshing
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Cost-effective printing of 3D objects with skin-frame structures
ACM Transactions on Graphics (TOG)
Sphere-Meshes: shape approximation using spherical quadric error metrics
ACM Transactions on Graphics (TOG)
Gap processing for adaptive maximal poisson-disk sampling
ACM Transactions on Graphics (TOG)
New software developments for quality mesh generation and optimization from biomedical imaging data
Computer Methods and Programs in Biomedicine
Approximating functions on a mesh with restricted Voronoï diagrams
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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We propose a new isotropic remeshing method, based on Centroidal Voronoi Tessellation (CVT). Constructing CVT requires to repeatedly compute Restricted Voronoi Diagram (RVD), defined as the intersection between a 3D Voronoi diagram and an input mesh surface. Existing methods use some approximations of RVD. In this paper, we introduce an efficient algorithm that computes RVD exactly and robustly. As a consequence, we achieve better remeshing quality than approximation-based approaches, without sacrificing efficiency. Our method for RVD computation uses a simple procedure and a kd-tree to quickly identify and compute the intersection of each triangle face with its incident Voronoi cells. Its time complexity is O(mlogn), where n is the number of seed points and m is the number of triangles of the input mesh. Fast convergence of CVT is achieved using a quasi-Newton method, which proved much faster than Lloyd's iteration. Examples are presented to demonstrate the better quality of remeshing results with our method than with the state-of-art approaches.