Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Polygonization of implicit surfaces
Computer Aided Geometric Design
A singly exponential stratification scheme for real semi-algebraic varieties and its applications
Theoretical Computer Science
Delaunay triangulations and Voronoi diagrams for Riemannian manifolds
Proceedings of the sixteenth annual symposium on Computational geometry
Curvature-Dependent Triangulation of Implicit Surfaces
IEEE Computer Graphics and Applications
Anisotropic voronoi diagrams and guaranteed-quality anisotropic mesh generation
Proceedings of the nineteenth annual symposium on Computational geometry
Anisotropic polygonal remeshing
ACM SIGGRAPH 2003 Papers
Provably good surface sampling and approximation
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Sampling and meshing a surface with guaranteed topology and geometry
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Isotopic implicit surface meshing
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Natural neighbor coordinates of points on a surface
Computational Geometry: Theory and Applications
Locally uniform anisotropic meshing
Proceedings of the twenty-fourth annual symposium on Computational geometry
Anisotropic diagrams: Labelle Shewchuk approach revisited
Theoretical Computer Science
From Segmented Images to Good Quality Meshes Using Delaunay Refinement
Emerging Trends in Visual Computing
Obtuse triangle suppression in anisotropic meshes
Computer Aided Geometric Design
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We study the problem of triangulating a smooth closed implicit surface Σ endowed with a 2D metric tensor that varies over Σ. This is commonly known as the anisotropic surface meshing problem. We extend the 2D metric tensor naturally to 3D and employ the 3D anisotropic Voronoi diagram of a set P of samples on Σ to triangulate Σ. We prove that a restricted dual, Mesh P, is a valid triangulation homeomorphic to Σ under appropriate conditions. We also develop an algorithm for constructing P and Mesh P. In addition to being homeomorphic to Σ, each triangle in Mesh P is well-shaped when measured using the 3D metric tensors of its vertices. Users can set upper bounds on the anisotropic edge lengths and the angles between the surface normals at vertices and the normals of incident triangles (measured both isotropically and anisotropically).