The first part of this book introduces the most popular tools in computational geometry. These tools will be put to use throughout the rest of the book.

The first chapter gives a framework for the analysis of algorithms. The concept of complexity of an algorithm is reviewed. The underlying model of computation is made clear and unambiguous.

The second chapter reviews the fundamentals of data structures: lists, heaps, queues, dictionaries, and priority queues. These structures are mostly implemented as balanced trees. To serve as an example, red–black trees are fully described and their performances are evaluated.

The third chapter illustrates the main algorithmic techniques used to solve geometric problems: the incremental method, the divide-and-conquer method, the sweep method, and the decomposition method which subdivides a complex object into elementary geometric objects.

Finally, chapters 4, 5, and 6 introduce the randomization methods which have recently made a distinguished appearance on the stage of computational geometry. Only the incremental randomized method is introduced and used in this book, as opposed to the randomized divide-and-conquer method.