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First comprehensive treatment of the theory of regular triangulations, secondary polytopes and related topics appearing in book form
Discusses the geometric structure behind the algorithms and shows new emerging applications
Theory discusses high-dimensional situations, an area that is not always covered in computational geometry
Step-by-step introduction assuming very little background
Hundreds of illustrations, examples, and exercises
Triangulations appear everywhere, from volume computations and meshing
to algebra and topology. This book studies the subdivisions and
triangulations of polyhedral regions and point sets and presents the
first comprehensive treatment of the theory of secondary polytopes and
A central theme of the book is the use of the rich structure of the
space of triangulations to solve computational problems (e.g., counting
the number of triangulations or finding optimal triangulations with
respect to various criteria), and to establish connections to
applications in algebra, computer science, combinatorics, and
With many examples and exercises, and with nearly five hundred
illustrations, the book gently guides readers through the properties
of the spaces of triangulations of "structured" (e.g., cubes, cyclic
polytopes, lattice polytopes) and "pathological" (e.g., disconnected
spaces of triangulations) situations using only elementary principles.