Polyhedral and algebraic methods in computational geometry
The authors discuss in the book a selection of linear and non-linear topics in computational geometry. The first part of the book, devoted to linear computational geometry, starts with an introduction to projective geometry to proceed to study polytopes, linear programming problemas, convex hulls, Voronoi diagrams and Delaunay triangulations. The software program polymake is used to illustrate and visualize the concepts that are discussed.
The second part of the book focuses on non-linear computational geometry techniques, being the main tool the use of Groebner bases to solve systems of polynomial equations. Examples are provided using software programs Maple and Singular.
Finally, the third part of the book is devoted to a selection of applications, including the reconstruction of curves using Delaunay triangulation as a tool and an application of Groebner bases to geolocalization using GPS satellites.
The book's audience is made up of mathematicians interested in applications of geometry and algebra as well as computer scientists and engineers with good mathematical background.