Pyramid Algorithms: A Dynamic Programming Approach to Curves and Surfaces for Geometric Modeling
- 8h 42m
- Ron Goldman
- Elsevier Science and Technology Books, Inc.
- 2003
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.
- 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
In this Book
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Foreword
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Introduction—Foundations
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Lagrange Interpolation and Neville's Algorithm
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Hermite Interpolation and the Extended Neville Algorithm
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Newton Interpolation and Difference Triangles
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Bezier Approximation and Pascal's Triangle
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Blossoming
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B-Spline Approximation and the de Boor Algorithm
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Pyramid Algorithms for Multisided Bezier Patches
