Delaunay mesh generation

Content: Introduction Meshes and the goals of mesh generation Delaunay triangulations and Delaunay refinement algorithms A brief history of mesh generation A personal history of working in mesh generation Simplices, complexes, and polyhedra Metric space topology How to measure an element Two-Dimensional Delaunay Triangulations Triangulations of a planar point set The Delaunay triangulation The parabolic lifting map The Delaunay Lemma The flip algorithm The optimality of the Delaunay triangulation The uniqueness of the Delaunay triangulation The weighted Delaunay triangulation Symbolic weight perturbations Constrained Delaunay triangulations in the plane Algorithms for Constructing Delaunay Triangulations The orientation and incircle predicates A dictionary data structure for triangulations Inserting a vertex into a Delaunay triangulation Inserting a vertex outside a Delaunay triangulation The running time of vertex insertion Optimal point location by a conflict graph The incremental insertion algorithm Deleting a vertex from a Delaunay triangulation Inserting or deleting a vertex in a CDT Inserting a segment into a CDT The gift-wrapping algorithm Three-Dimensional Delaunay Triangulations Triangulations of a point set in Rd The Delaunay triangulation in Rd The optimality of the Delaunay triangulation in Rd Bistellar flips and the flip algorithm Three-dimensional constrained Delaunay triangulations Algorithms for Constructing Delaunay Triangulations in R3 A dictionary data structure for tetrahedralizations Delaunay vertex insertion in R3 Biased randomized insertion orders Optimal point location by a conflict graph in R3 Point location by walking The gift-wrapping algorithm in R3 Inserting a vertex into a CDT in R3 Inserting a polygon into a CDT Delaunay Refinement in the Plane A generic Delaunay refinement algorithm Ruppert's Delaunay refinement algorithm Implementation and running time A proof of termination A proof of size optimality and optimal grading Meshing domains with small angles Constrained Delaunay refinement Voronoi Diagrams and Weighted Complexes Voronoi diagrams Weighted Voronoi and weighted Delaunay Quarantined complexes Tetrahedral Meshing of PLCs A tetrahedral Delaunay refinement algorithm Implementation and running time A proof of termination and good grading Refining slivers away Constrained Delaunay tetrahedral refinement Weighted Delaunay Refinement for PLCs with Small Angles The ideas behind weighted Delaunay refinement Protecting vertices and segments The refinement stage A proof of termination and good grading Sliver Exudation The main idea and the algorithm Implementing sliver exudation Properties of the union of weighted Delaunay triangulations The Sliver Theorem Refinement for Sliver Exudation Enforcing domain conformity with uncertain vertex weights A refinement algorithm for sliver exudation A guarantee of domain conformity during sliver exudation A proof of termination, good quality, and good grading Finite triangulations and the Sliver Theorem Smooth Surfaces and Point Samples Topological spaces Maps, homeomorphisms, and isotopies Manifolds Smooth manifolds The medial axis and local feature size of a smooth manifold The variation in normal vectors on smooth surfaces Approximations of tangents by simplices Restricted Delaunay Triangulations of Surface Samples Restricted Voronoi diagrams and Delaunay triangulations The Topological Ball Theorem Distances and angles in epsilon-samples Local properties of restricted Voronoi faces Global properties of restricted Voronoi faces The fidelity of the restricted Delaunay triangulation Meshing Smooth Surfaces and Volumes Delaunay surface meshing with a known local feature size Topology-driven surface meshing A practical surface meshing algorithm Extensions: quality, smoothness, and polyhedral surfaces Tetrahedral meshing of volumes bounded by smooth surfaces Meshing Piecewise Smooth Complexes Piecewise smooth complexes and their triangulations An algorithm for meshing PSCs The ball properties and the PSC Lemma A proof of termination Manifold patch triangulations and homeomorphism Extensions: polygonal surfaces, quality, and tetrahedral Bibliography Index Notes and Exercises appear at the end of each chapter.
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