Computational Geometry: Algorithms and Applications: 2nd Edition

Author: (Dutch) Berg M.
Publisher:
Publishing Date: 2005-09-01
Features: Computational geometry is an important branch of computer theory science. Since it became independent from algorithm design and analysis in the late 1970s, the field has undergone tremendous development in less than 30 years, producing a series of significant theoretical achievements and finding wide applications in numerous practical fields. The first four chapters of this book discuss geometric algorithms, including geometric intersection, triangulation, and linear programming, among which the random algorithms involved are a distinctive feature of the book. Chapters 5 to 10 introduce various geometric structures, including geometric search, kd-trees, region trees, trapezoidal graphs, Voronoi diagrams, permutations, Delaunay triangulation, interval trees, priority search trees, and segment trees, among others. Chapters 11 to 16 continue to discuss several geometric algorithms and their data structures in the context of practical problems, including high-dimensional convex hulls, spatial bisection and BSP trees, motion planning, mesh generation and quad trees, shortest path search and visibility graphs, simplex region search and partition trees and split trees, among others, which further deepen the content of the previous ten chapters. The book is not only comprehensive in content but also closely tied to practical applications, with a clear focus. It provides in-depth explanations while each chapter includes "Notes and Comments" and "Exercises," offering readers the opportunity for a deeper understanding. As a result, it has been widely used as a textbook in many university campuses around the world in recent years. China's research in computational geometry started relatively late, and it is believed that the publication of this book will help promote the development of teaching in this field domestically. Computational geometry is an important branch of computer theory science. Since it became independent from algorithm design and analysis in the late 1970s, the field has undergone tremendous development in less than 30 years, producing a series of significant theoretical achievements and finding wide applications in numerous practical fields. The first four chapters of this book discuss geometric algorithms, including geometric intersection, triangulation, and linear programming, among which the random algorithms involved are a distinctive feature of the book. Chapters 5 to 10 introduce various geometric structures, including geometric search, kd-trees, region trees, trapezoidal graphs, Voronoi diagrams, permutations, Delaunay triangulation, interval trees, priority search trees, and segment trees, among others. Chapters 11 to 16 continue to discuss several geometric algorithms and their data structures in the context of practical problems, including high-dimensional convex hulls, spatial bisection and BSP trees, motion planning, mesh generation and quad trees, shortest path search and visibility graphs, simplex region search and partition trees and split trees, among others, which further deepen the content of the previous ten chapters. The book is not only comprehensive in content but also closely tied to practical applications, with a clear focus. It provides in-depth explanations while each chapter includes "Notes and Comments" and "Exercises," offering readers the opportunity for a deeper understanding. As a result, it has been widely used as a textbook in many university campuses around the world in recent years. China's research in computational geometry started relatively late, and it is believed that the publication of this book will help promote the development of teaching in this field domestically.