Subdivision Methods for Geometric Design: A Constructive Approach

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Morgan Kaufmann, 2002 - Computers - 299 pages
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
A Differential Approach to Uniform Subdivision
91
Local Approximation of Global Differential Schemes
120
Basis
127
Variational Schemes for Bounded Domains
157
Averaging Schemes for Polyhedral Meshes
198
Spectral Analysis at an Extraordinary Vertex
239
129
259
141
276
157
284
Index
287
198
298
Copyright

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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.

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