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.
 Abstract:             
              Going beyond, yet thoroughly rooted to theory, this book provides a comprehensive look at the algorithms that can produce quality Delaunay meshes through a paradigm called the Delaunay refinement. It describes meshing algorithms that can be built on the Delaunay refinement paradigm along with the involved mathematical analysis.                 Read more...