Cover image for Pyramid algorithms a dynamic programming approach to curves and surfaces for geometric modeling
Pyramid algorithms a dynamic programming approach to curves and surfaces for geometric modeling
Title:
Pyramid algorithms a dynamic programming approach to curves and surfaces for geometric modeling
Author:
Goldman, Ron, 1952-
ISBN:
9781558603547
Personal Author:
Publication Information:
San Francisco, Calif. : Morgan Kaufmann, 2003.
Physical Description:
xxiii, 551 p. : ill. ; 24 cm.
Series:
Morgan Kaufmann series in computer graphics and geometric modeling
Series Title:
Morgan Kaufmann series in computer graphics and geometric modeling
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.
Abstract:
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.
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