

Curves and Surfaces in Geometric Modeling: Theory and Algorithms
Jean Gallier, 2000, Morgan Kauffman Publishers, 491 pp., hardcover.
An introduction to geometric concepts and tools needed for solving
problems of a geometric nature with a computer. It offers theoretical
understanding of polynomial curves and surfaces. The focus of
this book is on "blossoming"the process of converting a polynomial to
its polar formas a natural, purely geometric explanation of the behavior
of curves and surfaces. The book covers computer graphics and animation,
robotics, virtual reality, geometric modeling and design, medical imaging,
computer vision, and motion planning.
Chapters include:
Introduction  Basics of Affine Geometry  Introduction to
the Algorithmic Geometry of Polynomial Curves  Multiaffine Maps and Polar
Forms  Polynomial Curves as Bèzier Curves  BSpline Curves

Polynomial Surfaces  Subdivision Algorithms for Polynomial Surfaces 
Polynomial Spline Surfaces and Subdivision Surfaces  Embedding an Affine
Space in a Vector Space  Tensor Products and Symmetric Tensor Products 
Appendices
This book is available in the Wolfram Research bookstore.
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