This book covers combinatorial data structures and algorithms, algebraic issues in geometric computing, approximation of curves and surfaces, and computational topology. Each chapter fully details and provides a tutorial introduction to important concepts and results. The focus is on methods which are both well founded mathematically and efficient in practice. Coverage includes references to open source software and discussion of potential applications of the presented techniques.

This book covers combinatorial data structures and algorithms, algebraic issues in geometric computing, approximation of curves and surfaces, and computational topology. Each chapter fully details and provides a tutorial introduction to important concepts and results. The focus is on methods which are both well founded mathematically and efficient in practice. Coverage includes references to open source software and discussion of potential applications of the presented techniques.

Computational geometry concerns itself with designing and analyzing algorithms for solving geometric problems. The field has reached a high level of sophistication, and very complicated algorithms have been designed.However, it is also useful to develop more practical algorithms, so long as they are based on rigorous methods. One such method is the use of randomized algorithms. These algorithms have become more and more popular, turning into one of the hottest areas of recent years. Dynamic algorithms are particularly interesting because in practice the data of a problem are often acquired progressively. In this monograph the author studies the theoretical complexity and practical efficiency of randomized dynamic algorithms.