Boissonnat J.D., Yvinet M. Algorithmic Geometry

CUP, 1998. - 544 p.
Geometric data structures and their systematic analysis guided the layout of this text. We have dedicated a part to each of the fundamental geometric structures: polytopes, triangulations, arrangements, and Voronoi diagrams.
Combinatorial geometry plays an essential role in this book and the first chapters of each part lay the mathematical grounds and prove the basic combinatorial properties verified by the corresponding geometric structures.
This book assumes no particular knowledge from the reader and should be accessible to any enthusiastic geometer. Its contents has been taught in several graduate courses both in mathematics and in computer science- It is aimed both at mathematicians interested in a constructive approach to geometry, and at computer scientists in need for an accurate treatment of computational geometry. Students, researchers, and engineers in more practical fields will find here a useful methodology and practical algorithms.