Delaunay Mesh Generation

Delaunay Mesh Generation

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Description

Written by authors at the forefront of modern algorithms research, Delaunay Mesh Generation demonstrates the power and versatility of Delaunay meshers in tackling complex geometric domains ranging from polyhedra with internal boundaries to piecewise smooth surfaces. Covering both volume and surface meshes, the authors fully explain how and why these meshing algorithms work. The book is one of the first to integrate a vast amount of cutting-edge material on Delaunay triangulations. It begins with introducing the problem of mesh generation and describing algorithms for constructing Delaunay triangulations. The authors then present algorithms for generating high-quality meshes in polygonal and polyhedral domains. They also illustrate how to use restricted Delaunay triangulations to extend the algorithms to surfaces with ridges and patches and volumes with smooth surfaces. For researchers and graduate students, the book offers a rigorous theoretical analysis of mesh generation methods. It provides the necessary mathematical foundations and core theoretical results upon which researchers can build even better algorithms in the future. For engineers, the book shows how the algorithms work well in practice. It explains how to effectively implement them in the design and programming of mesh generation software.show more

Product details

  • Electronic book text | 410 pages
  • Taylor & Francis Ltd
  • Chapman & Hall/CRC
  • London, United Kingdom
  • 173 Illustrations, black and white
  • 1584887311
  • 9781584887317

Table of contents

IntroductionMeshes 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 timeA proof of termination and good grading Refining slivers away Constrained Delaunay tetrahedral refinement Weighted Delaunay Refinement for PLCs with Small AnglesThe 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 spacesMaps, 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 ε-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.show more

About Siu-Wing Cheng

Siu-Wing Cheng is a professor in the Department of Computer Science and Engineering at the Hong Kong University of Science and Technology. Professor Cheng is an advisory committee member of the International Symposium on Algorithms and Computation and a board member of the Asian Association for Algorithms and Computation. His research interests include computational geometry, mesh generation, manifold reconstruction, and algorithms. He earned a Ph.D. in computer science from the University of Minnesota, Twin Cities. Tamal K. Dey is a professor of computer science at Ohio State University, where he leads the Jyamiti group, which develops software such as the well-known Cocone software for surface reconstruction and DelPSC software for mesh generation. He previously held faculty positions at Indiana University-Purdue University and IIT Kharagpur and research positions at the University of Illinois and Max-Planck Institute. His research interests include computational geometry and topology and their applications in graphics and geometric modeling. He earned a Ph.D. from Purdue University. Jonathan Shewchuk is a professor in the Department of Electrical Engineering and Computer Sciences at the University of California, Berkeley. He is best known for his Triangle software for high-quality triangular mesh generation, which won the 2003 James Hardy Wilkinson Prize in Numerical Software, and his paper "Introduction to the Conjugate Gradient Method without the Agonizing Pain." He received his Ph.D. in computer science from Carnegie Mellon University.show more