Pyramid Algorithms

1st Edition

A Dynamic Programming Approach to Curves and Surfaces for Geometric Modeling

Print ISBN: 9781493303557
eBook ISBN: 9780080515472
Imprint: Morgan Kaufmann
Published Date: 10th July 2002
Page Count: 576
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Pyramid Algorithms presents a unique approach to understanding, analyzing, and computing the most common polynomial and spline curve and surface schemes used in computer-aided geometric design, employing a dynamic programming method based on recursive pyramids. The recursive pyramid approach offers the distinct advantage of revealing the entire structure of algorithms, as well as relationships between them, at a glance. This book-the only one built around this approach-is certain to change the way you think about CAGD and the way you perform it, and all it requires is a basic background in calculus and linear algebra, and simple programming skills.

Key Features

  • Written by one of the world's most eminent CAGD researchers
  • Designed for use as both a professional reference and a textbook, and addressed to computer scientists, engineers, mathematicians, theoreticians, and students alike
  • Includes chapters on Bezier curves and surfaces, B-splines, blossoming, and multi-sided Bezier patches
  • Relies on an easily understood notation, and concludes each section with both practical and theoretical exercises that enhance and elaborate upon the discussion in the text
  • Foreword by Professor Helmut Pottmann, Vienna University of Technology


mechanical engineers, computer scientists, and applied mathematicians; researchers and developers in geometric modeling, computer graphics, and computer-aided geometric design; practitioners in industry who design and implement computer-aided design and computer graphics software; theoreticians in academia interested in exploring and extending the foundations of geometric modeling and computer graphics.

Table of Contents

Chapter 1. Foundations Chapter 2. Lagrange Interpolation and Neville's Algorithm Chapter 3. Hermite Interpolation and the Extended Neville Algorithm Chapter 4. Newton Interpolation and Difference Triangles Chapter 5. Bezier Approximation and Pascal's Triangle Chapter 6. Blossoming Chapter 7. B-Spline Approximation and the de Boor Algorithm Chapter 8. Pyramid Algorithms for Multi-Sided Bezier Patches


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© Morgan Kaufmann 2003
Morgan Kaufmann
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@qu:"Ron Goldman is a leading expert who knows the fundamental concepts and their interconnectedness, as well as the small details. The elegance of the writing and of the methods used to present the material allows us to get a deep understanding of the central concepts of CAGD. In its simplicity and pure beauty, the theory indeed resembles the pyramids." @source:—Helmut Pottman, Vienna University of Technology "A textbook approach to understanding, analyzing and computing common polynomial and spline curves, and surfaces schemes in computer-aided geometric modeling and design. Goldman employs a dynamic programming method based on recursive pyramids for revealing the structure and relationship of algorithms." - Design Issues