Nonobtuse triangulation of polygons
Discrete & Computational Geometry
On the limited memory BFGS method for large scale optimization
Mathematical Programming: Series A and B
Long and thin triangles can be good for linear interpolation
SIAM Journal on Numerical Analysis
Anisotropic mesh transformations and optimal error control
Proceedings of the third ARO workshop on Adaptive methods for partial differential equations
Delaunay triangulations and Voronoi diagrams for Riemannian manifolds
Proceedings of the sixteenth annual symposium on Computational geometry
Optimizing 3D triangulations using discrete curvature analysis
Mathematical Methods for Curves and Surfaces
Anisotropic voronoi diagrams and guaranteed-quality anisotropic mesh generation
Proceedings of the nineteenth annual symposium on Computational geometry
Variational shape approximation
ACM SIGGRAPH 2004 Papers
Anisotropic Centroidal Voronoi Tessellations and Their Applications
SIAM Journal on Scientific Computing
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Nonobtuse remeshing and mesh decimation
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
A Delaunay Simplification Algorithm for Vector Fields
PG '07 Proceedings of the 15th Pacific Conference on Computer Graphics and Applications
Generic Remeshing of 3D Triangular Meshes with Metric-Dependent Discrete Voronoi Diagrams
IEEE Transactions on Visualization and Computer Graphics
Locally uniform anisotropic meshing
Proceedings of the twenty-fourth annual symposium on Computational geometry
On centroidal voronoi tessellation—energy smoothness and fast computation
ACM Transactions on Graphics (TOG)
On Nonobtuse Simplicial Partitions
SIAM Review
Asymptotically optimal block quantization
IEEE Transactions on Information Theory
Particle-based anisotropic surface meshing
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
(OBIFS) isotropic image analysis for improving a predicting agent based systems
Expert Systems with Applications: An International Journal
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Anisotropic triangle meshes are used for efficient approximation of surfaces and flow data in finite element analysis, and in these applications it is desirable to have as few obtuse triangles as possible to reduce the discretization error. We present a variational approach to suppressing obtuse triangles in anisotropic meshes. Specifically, we introduce a hexagonal Minkowski metric, which is sensitive to triangle orientation, to give a new formulation of the centroidal Voronoi tessellation (CVT) method. Furthermore, we prove several relevant properties of the CVT method with the newly introduced metric. Experiments show that our algorithm produces anisotropic meshes with much fewer obtuse triangles than using existing methods while maintaining mesh anisotropy.