On the maximum angle condition for linear tetrahedral elements
SIAM Journal on Numerical Analysis
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Local bisection refinement for N-simplicial grids generated by reflection
SIAM Journal on Scientific Computing
Quality local refinement of tetrahedral meshes based on bisection
SIAM Journal on Scientific Computing
Construction of three-dimensional improved-quality triangulations using local transformations
SIAM Journal on Scientific Computing
Computing
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Surface simplification using quadric error metrics
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Interval volume tetrahedrization
VIS '97 Proceedings of the 8th conference on Visualization '97
Fast and memory efficient polygonal simplification
Proceedings of the conference on Visualization '98
Simplification of tetrahedral meshes
Proceedings of the conference on Visualization '98
Progressive tetrahedralizations
Proceedings of the conference on Visualization '98
Optimal good-aspect-ratio coarsening for unstructured meshes
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Adaptively sampled distance fields: a general representation of shape for computer graphics
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Simplification of Tetrahedral meshes with accurate error evaluation
Proceedings of the conference on Visualization '00
Proceedings of the 2002 ACM SIGGRAPH/Eurographics symposium on Computer animation
A procedural approach to authoring solid models
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Dual contouring of hermite data
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Locally Adapted Tetrahedral Meshes Using Bisection
SIAM Journal on Scientific Computing
TetFusion: an algorithm for rapid tetrahedral mesh simplification
Proceedings of the conference on Visualization '02
Real-time simulation of deformation and fracture of stiff materials
Proceedings of the Eurographic workshop on Computer animation and simulation
GRIN'01 No description on Graphics interface 2001
Delaunay refinement mesh generation
Delaunay refinement mesh generation
Procedural authoring of solid models
Procedural authoring of solid models
Simplification of Three-Dimensional Density Maps
IEEE Transactions on Visualization and Computer Graphics
Large mesh deformation using the volumetric graph Laplacian
ACM SIGGRAPH 2005 Papers
Variational tetrahedral meshing
ACM SIGGRAPH 2005 Papers
Streaming Simplification of Tetrahedral Meshes
IEEE Transactions on Visualization and Computer Graphics
Variational tetrahedral meshing
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Finite volume flow simulations on arbitrary domains
Graphical Models
Stretch-based tetrahedral mesh manipulation
GI '07 Proceedings of Graphics Interface 2007
A decomposition-based representation for 3D simplicial complexes
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
A simplicial complex-based DBMS approach to 3D topographic data modelling
International Journal of Geographical Information Science
Fitting solid meshes to animated surfaces using linear elasticity
ACM Transactions on Graphics (TOG)
SOT: compact representation for tetrahedral meshes
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Technical Section: Fitting 3D garment models onto individual human models
Computers and Graphics
Customizing 3D garments based on volumetric deformation
Computers in Industry
Efficient computation of clipped Voronoi diagram for mesh generation
Computer-Aided Design
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Most 3D mesh generation techniques require simplification and mesh improvement stages to prepare a tetrahedral model for efficient simulation. We have developed an algorithm that both reduces the number of tetrahedra in the model to permit interactive manipulation and removes the most poorly shaped tetrahedra to allow for stable physical simulations such as the finite element method. The initial tetrahedral model may be composed of several different materials representing internal structures. Our approach targets the elimination of poorly-shaped elements while simplifying the model using edge collapses and other mesh operations, such as vertex smoothing, tetrahedral swaps, and vertex addition. We present the results of our algorithm on a variety of inputs, including models with more than a million tetrahedra. In practice, our algorithm reliably reduces meshes to contain only tetrahedra that meet specified shape requirements, such as the minimum solid angle.