Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Surface simplification using quadric error metrics
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Topology-reducing surface simplification using a discrete solid representation
ACM Transactions on Graphics (TOG)
Geomodeling
Constrained Centroidal Voronoi Tessellations for Surfaces
SIAM Journal on Scientific Computing
Centroidal Voronoi diagrams for isotropic surface remeshing
Graphical Models - Special issue on SMI 2003
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)
Isotropic remeshing with fast and exact computation of Restricted Voronoi Diagram
SGP '09 Proceedings of the Symposium on Geometry Processing
Lp Centroidal Voronoi Tessellation and its applications
ACM SIGGRAPH 2010 papers
Multinerves and helly numbers of acyclic families
Proceedings of the twenty-eighth annual symposium on Computational geometry
Least squares quantization in PCM
IEEE Transactions on Information Theory
Isotropic Surface Remeshing Using Constrained Centroidal Delaunay Mesh
Computer Graphics Forum
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We propose a method to remesh the surfaces of 3D sealed geological structural models for subsequent volumetric meshing. The input of the method is a set of triangulated surfaces that are in contact along given lines and at given points. The output is a set of surfaces meshed with triangles as equilateral as possible. The method relies on a global Centroidal Voronoi optimization to place the vertices of the final surfaces combined with combinatorial considerations to either recover or simplify the surfaces, lines and points of the input model. When the final resolution is sufficient, the input contact lines and points are also contact lines and points of the final model. However, when dealing with models with complex contacts, resolution may be insufficient and instead of a refinement strategy that may lead to too many points, we propose to locally merge some features of the input model. This ability to simplify the input model is particularly interesting when the model is to be volumetrically meshed. The method is demonstrated on twelve structural models, including seven models built with an implicit modeling method, and one folded layer model affected by a discrete fracture network.