Pyramid Algorithms: A Dynamic Programming Approach to Curves and Surfaces for Geometric Modeling

Ron Goldman

574 pages, parution le 05/11/2002

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Résumé

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.

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

Contents

Foundations I- Interpolation

Lagrange Interpolation and Neville's Algorithm
Hermite Interpolation and the Extended Neville Algorithm
Newton Interpolation and Difference Triangles

II- Approximation

Bezier Approximation and Pascal's Triangle
Blossoming
B-Spline Approximation and the de Boor Algorithm
Pyramid Algorithms for Multisided Bezier Patches

L'auteur - Ron Goldman

Ron Goldman has worked in industry as a mathematician, design engineer, and principal consultant solving practical problems in computer graphics, geometric modeling, and computer-aided design. Professor of Computer Science at Rice University since 1990, Dr. Goldman holds a B.S. from M.I.T., and an M.A. and Ph.D. from Johns Hopkins University, all in mathematics. His current work includes research in computer-aided geometric design, solid modeling, computer graphics, computer algebra, elimination theory, and splines, and he has published over 100 research articles on these and related topics.

Caractéristiques techniques

	PAPIER
Éditeur(s)	Morgan Kaufmann
Auteur(s)	Ron Goldman
Parution	05/11/2002
Nb. de pages	574
Format	19 x 24
Couverture	Relié
Poids	1176g
Intérieur	Noir et Blanc
EAN13	9781558603547
ISBN13	978-1-55860-354-7