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 form--as 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.
Introduction | Basics of Affine Geometry | Introduction to
the Algorithmic Geometry of Polynomial Curves | Multiaffine Maps and Polar
Forms | Polynomial Curves as Bèzier Curves | B-Spline 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 |
This book is available in the Wolfram Research bookstore.
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