Polyhedral and Algebraic Methods in Computational Geometry

The first part of the book studies classical problems and techniques that refer to polyhedral structures. The authors include a study on algorithms for computing convex hulls as well as the construction of Voronoi diagrams and Delone triangulations.  

Throughout the book, interconnections between computational geometry and other disciplines (such as algebraic geometry, optimization and numerical mathematics) are established. 

Introduction and Overview
Geometric Fundamentals
Polytopes and Polyhedra
Linear Programming
Computation of Convex Hulls
Voronoi Diagrams
Delone Triangulations
Algebraic and Geometric Foundations
Gröbner Bases and Buchberger’s Algorithm
Solving Systems of Polynomial Equations Using Gröbner Bases
Reconstruction of Curves
Plücker Coordinates and Lines in Space
Applications of Non-Linear Computational Geometry
Algebraic Structures
Separation Theorems
Algorithms and Complexity
Software
Notation