Introduction to the Mathematics of Subdivision Surfaces

Overview

This is an introduction to the mathematical theory which underlies subdivision surfaces, as it is used in computer graphics and animation. Subdivision surfaces enable a designer to specify the approximate form of a surface that defines an object and then to refine it to get a more useful or attractive version. A considerable amount of mathematical theory is needed to understand the characteristics of the resulting surfaces, and this book explains the material carefully and rigorously. The text is highly ...
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Overview

This is an introduction to the mathematical theory which underlies subdivision surfaces, as it is used in computer graphics and animation. Subdivision surfaces enable a designer to specify the approximate form of a surface that defines an object and then to refine it to get a more useful or attractive version. A considerable amount of mathematical theory is needed to understand the characteristics of the resulting surfaces, and this book explains the material carefully and rigorously. The text is highly accessible, organising subdivision methods in a unique and unambiguous hierarchy which builds insight and understanding. The material is not restricted to questions related to regularity of subdivision surfaces at so-called extraordinary points, but gives a broad discussion of the various methods. It is therefore an excellent preparation for more advanced texts that delve more deeply into special questions of regularity.
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Product Details

  • ISBN-13: 9780898716979
  • Publisher: SIAM
  • Publication date: 5/13/2010
  • Pages: 378
  • Product dimensions: 7.01 (w) x 10.00 (h) x 0.79 (d)

Meet the Author

Lars-Erik Andersson took his Ph.D. in applied mathematics at Linköping University, Sweden. He is Professor and former Chair of the Department of Mathematics at that university. During 1989–1999 Andersson was Adjoint Director of Research at the Swedish National Defense Research Establishment. He is the author of about 60 publications in various fields: the geometry of Banach spaces, inverse problems, radar imaging, propagation of elastic waves, frictional contact problems in elasticity and computer-aided geometric design. He is a member of SIAM, the Swedish Mathematical Society and EUROMECH.

Neil F. Stewart took his Ph.D. in computer science at the University of Toronto, Canada. He is Professor and former Chair of the Department of Computer Science at the Université de Montréal. He is the author of about 40 publications in operations research and solid modeling.

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Table of Contents

List of figures; List of tables; Preface; Notation, conventions, abbreviations; 1. Introduction; 2. B-spline surfaces; 3. Box-spline surfaces; 4. Generalized-spline surfaces; 5. Convergence and smoothness; 6. Evaluation and estimation of surfaces; 7. Shape control; Appendix; Notes; Bibliography; Index.
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