Subdivision Methods for Geometric Design: A Constructive Approach / Edition 1

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Overview

"The authors of this book have been on the forefront of these advances, and this book represents the first comprehensive description of subdivision methods. However, the book is not simply a collection of material that can be found in the open literature. Rather, it offers a deep and unique perspective into the world of subdivision. I learned a tremendous amount from reading this book. I'm sure you will, too."
—Tony DeRose, Pixar Animation Studios

The world's leading animation houses rely increasingly on subdivision methods for creating realistic-looking complex shapes. However, until now there was no one book devoted to this powerful geometric modeling technique. Subdivision Methods for Geometric Design does the job with authority and precision, providing all that is needed to understand how subdivision works its magic, and how to make that magic work.

Throughout the book, icons cue readers to visit a companion website loaded with interactive exercises, implementations of the book's images, and supplementary material. Rich in theory, analysis, and practical information, this book is the complete resource for subdivision methods.

Features:

*The result of a collaboration between a leading university researcher and an industry practitioner

*The only book devoted exclusively and comprehensively to this important new technology

*Provides solid background and theoretical analysis of subdivision as well as a wide variety of specific applications

*Addresses algorithms for Bezier and uniform B-Spline curves, Catmull-Clark subdivision for quad meshes, and regularity tests for polyhedral meshes

*The companion website(www.subdivision.org) provides opportunities for readers to experiment hands-on with implementations in a richly interactive environment

*Includes a foreword by Tony DeRose, recipient of the 1999 ACM Computer Graphics Achievement Award for his seminal work in subdivision methods

Audience: Software developers for CAD and CAM systems, geometric modeling researchers, mathematicians, and engineers, and graphics programmers.

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Product Details

Meet the Author


Joe Warren, Professor of Computer Science at Rice University since 1986, is one of the world's leading experts on subdivision. Of his nearly 50 computer science papers-published in prestigious forums such as SIGGRAPH, Transactions on Graphics, Computer-Aided Geometric Design, and The Visual Computer-a dozen specifically address subdivision and its applications to computer graphics. Prof. Warren received both his M.S. and Ph.D. in Computer Science at Cornell University. His research interests focus on mathematical methods for representing geometric shape.

Henrik Weimer is a research scientist at the DaimlerChrysler Corporate Research Center in Berlin, where he works on knowledge-based support for the design and creation of engineering products. Dr. Weimer obtained his Ph.D. in Computer Science from Rice University.

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Table of Contents

Foreword
Preface
Table of Symbols
Ch. 1 Subdivision: Functions as Fractals
1.1 Functions
1.2 Fractals
1.3 Subdivision
Ch. 2 An Integral Approach to Uniform Subdivision
2.1 A Subdivision Scheme for B-splines
2.2 A Subdivision Scheme for Box Splines
2.3 B-splines and Box Splines as Piecewise Polynomials
Ch. 3 Convergence Analysis for Uniform Subdivision Schemes
3.1 Convergence of a Sequence of Functions
3.2 Analysis of Univariate Schemes
3.3 Analysis of Bivariate Schemes
Ch. 4 A Differential Approach to Uniform Subdivision
4.1 Subdivision for B-splines
4.2 Subdivision for Box Splines
4.3 Subdivision for Exponential B-splines
4.4 A Smooth Subdivision Scheme with Circular Precision
Ch. 5 Local Approximation of Global Differential Schemes
5.1 Subdivision for Polyharmonic Splines
5.2 Local Approximations to Polyharmonic Splines
5.3 Subdivision for Linear Flows
Ch. 6 Variational Schemes for Bounded Domains
6.1 Inner Products for Stationary Subdivision Schemes
6.2 Subdivision for Natural Cubic Splines
6.3 Minimization of the Variational Scheme
6.4 Subdivision for Bounded Harmonic Splines
Ch. 7 Averaging Schemes for Polyhedral Meshes
7.1 Linear Subdivision for Polyhedral Meshes
7.2 Smooth Subdivision for Quad Meshes
7.3 Smooth Subdivision for Triangle Meshes
7.4 Other Types of Polyhedral Schemes
Ch. 8 Spectral Analysis at an Extraordinary Vertex
8.1 Convergence Analysis at an Extraordinary Vertex
8.2 Smoothness Analysis at an Extraordinary Vertex
8.3 Verifying the Smoothness Conditions for a Given Scheme
8.4 Future Trends in Subdivision
References
Index
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