# Subdivision Methods for Geometric Design: A Constructive Approach

Morgan Kaufmann, 2002 - Computers - 299 pages
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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.

The only book devoted exclusively to subdivision techniques
Covers practical topics including uniform Bezier and B-Spline curves, polyhedral meshes, Catmull-Clark subdivision for quad meshes and objects with sharp creases and pointed vertices
A companion website provides example code and concept implementations of subdivision concepts in an interactive Mathematica environment

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### Contents

 Functions as Fractals 1 An Integral Approach to Uniform Subdivision 27 69 39 Convergence Analysis for Uniform Subdivision Schemes 62 A Differential Approach to Uniform Subdivision 91 Local Approximation of Global Differential Schemes 120
 99 230 Spectral Analysis at an Extraordinary Vertex 239 References 276 103 280 Index 287 Copyright

### Popular passages

Page 278 - Banded matrices with banded inverses II: Locally finite decomposition of spline spaces, Constructive Approximation 9 (1993), 263-282.
Page 281 - Multiresolution Analysis for Surfaces of Arbitrary Topological Type," ACM Transactions on Graphics 16(1), pp.
Page 276 - ... the new material. Then, however, this non-conventional method might be even better suited for solving the given problem of deformation than any real material may be. Nevertheless, a task of further work is to design and implement methods of deformation derived from physical laws. References [1] Alfeld, P.: Scattered data interpolation in three or more variables.

### References to this book

 Physically Based Rendering: From Theory to ImplementationLimited preview - 2004
 Digital Modeling of Material AppearanceNo preview available - 2008
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