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

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Subdivision Methods for Geometric Design provides computer graphics students and designers with a comprehensive guide to subdivision methods, including the background information required to grasp underlying concepts, techniques for manipulating subdivision algorithms to achieve specific effects, and a wide array of digital resources on a dynamic companion Web site. Subdivision Methods promises to be a groundbreaking book, important for both advanced students and working professionals in the field of computer graphics.

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

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Product Details

  • ISBN-13: 9781558604469
  • Publisher: Elsevier Science & Technology Books
  • Publication date: 10/28/2001
  • Series: The Morgan Kaufmann Series in Computer Graphics Series
  • Edition description: New Edition
  • Edition number: 1
  • Pages: 320
  • Product dimensions: 7.62 (w) x 9.54 (h) x 0.92 (d)

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

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
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