Convex partitions of polyhedra: a lower bound and worst-case optimal algorithm
SIAM Journal on Computing
Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms
ACM Transactions on Graphics (TOG)
Triangulating a nonconvex polytope
Discrete & Computational Geometry - Selected papers from the fifth annual ACM symposium on computational geometry, Saarbrücken, Germany, June 5-11, 1989
On the difficulty of triangulating three-dimensional nonconvex polyhedra.
Discrete & Computational Geometry
Automatic mesh generator with specified boundary
Computer Methods in Applied Mechanics and Engineering
Approximating constrained tetrahedrizations
Computer Aided Geometric Design
Adaptive finite element methods in computational mechanics
Computer Methods in Applied Mechanics and Engineering - Special issue on reliability in computational mechanics
A convergent adaptive algorithm for Poisson's equation
SIAM Journal on Numerical Analysis
Guaranteed-quality Delaunay meshing in 3D (short version)
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
A condition guaranteeing the existence of higher-dimensional constrained Delaunay triangulations
Proceedings of the fourteenth annual symposium on Computational geometry
Tetrahedral mesh generation by Delaunay refinement
Proceedings of the fourteenth annual symposium on Computational geometry
Sweep algorithms for constructing higher-dimensional constrained Delaunay triangulations
Proceedings of the sixteenth annual symposium on Computational geometry
A point-placement strategy for conforming Delaunay tetrahedralization
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Quality Mesh Generation in Higher Dimensions
SIAM Journal on Computing
Geometry and topology for mesh generation
Geometry and topology for mesh generation
Conforming Delaunay triangulations in 3D
Proceedings of the eighteenth annual symposium on Computational geometry
Updating and constructing constrained delaunay and constrained regular triangulations by flips
Proceedings of the nineteenth annual symposium on Computational geometry
An efficient algorithm for 3D adaptive meshing
Advances in Engineering Software - Engineering computational technology
UNSTRUCTURED MESH GENERATION AND ADAPTIVITY
UNSTRUCTURED MESH GENERATION AND ADAPTIVITY
Mesh Generation: Application to Finite Elements
Mesh Generation: Application to Finite Elements
Discrete & Computational Geometry
Three-dimensional constrained boundary recovery with an enhanced Steiner point suppression procedure
Computers and Structures
High quality real-time image-to-mesh conversion for finite element simulations
Proceedings of the 27th international ACM conference on International conference on supercomputing
High quality real-time Image-to-Mesh conversion for finite element simulations
Journal of Parallel and Distributed Computing
Guaranteed quality tetrahedral Delaunay meshing for medical images
Computational Geometry: Theory and Applications
Fracture and impulse based finite-discrete element modeling of fragmentation
Computational Mechanics
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A constrained Delaunay tetrahedralization of a domain in R^3 is a tetrahedralization such that it respects the boundaries of this domain, and it has properties similar to those of a Delaunay tetrahedralization. Such objects have various applications such as finite element analysis, computer graphics rendering, geometric modeling, and shape analysis. This article is devoted to presenting recent developments on constrained Delaunay tetrahedralizations of piecewise linear domains. The focus is on the application of numerically solving partial differential equations using finite element or finite volume methods. We survey various related results and detail two core algorithms that have provable guarantees and are amenable to practical implementation. We end this article by listing a set of open questions.