Polyhedral and algebraic methods in computational geometry / Michael Joswig, Thorsten Theobald

The book is a revised and updated version of a German textbook the authors wrote for their courses [Algorithmische Geometrie, Vieweg Stud. Aufbaukurs Math., Vieweg, Wiesbaden, 2008]. Assuming only common concepts of calculus and linear algebra, the book offers an introduction to computational geometry (polytopes and polyhedra, linear programming, convex hulls, Voronoi Diagrams, Delone Triangulations) and computational algebraic geometry (resultants, Gröbner bases, solving polynomial systems with elimination). The first seven chapters (the first half of the book) deal with computational geometry. The second part is called "Non-linear Computational Geometry'' and consists of three chapters. In the last three chapters, several applications are presented. Several sections use software: polymake, Maple, and Singular. In addition, Appendix D also mentions CGAL and Sage.
While some undergraduate programs in mathematics and computer science offer students courses in computational geometry and computational algebraic geometry, this textbook provides a nice mix of algorithms in polyhedral and algebraic geometry. (MathSciNet)