Computer Graphics & Geometric Modelling: Volume 2: Mathematics

Description

Possibly the most comprehensive overview of computer graphics as seen in the context of geometric modelling, this two volume work covers implementation and theory in a thorough and systematic fashion. Computer Graphics and Geometric Modelling: Mathematics , contains the mathematical background needed for the geometric modeling topics in computer graphics covered in the first volume. This volume begins with material from linear algebra and a discussion of the transformations in affine & projective geometry, followed by topics from advanced calculus & chapters on general topology, combinatorial topology, algebraic topology, differential topology, differential geometry, and finally algebraic geometry.Two important goals throughout were to explain the material thoroughly, and to make it self-contained. This volume by itself would make a good mathematics reference book, in particular for practitioners in the field of geometric modelling. Due to its broad coverage and emphasis on explanation it could be used as a text for introductory mathematics courses on some of the covered topics, such as topology (general, combinatorial, algebraic, and differential) and geometry (differential & algebraic).


Contents:

Linear Algebra Topics Affine Geometry Projective Geometry Advanced Calculus Topics Point Set Topology Combinatorial Topology Algebraic Topology Differential Topology Differential Geometry Algebraic Geometry Appendices: Basic Algebra Basic Linear Algebra Basic Calculus & Analysis Basic Complex Analysis A Bit of Numerical Analysis