Synopses & Reviews
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.
x Written by one of the world's most eminent CAGD researchers
x Designed for use as both a professional reference and a textbook, and addressed to computer scientists, engineers, mathematicians, theoreticians, and students alike
x Includes chapters on Bezier curves and surfaces, B-splines, blossoming, and multi-sided Bezier patches
x 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
x Foreword by Professor Helmut Pottmann, Vienna University of Technology
Review
olynomial 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
Review
"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."
—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
Review
rstanding, 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
Synopsis
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
Synopsis
derstood 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
Synopsis
nd 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
Synopsis
Pottmann, Vienna University of Technology
Synopsis
Ideal as a comprehensive introduction to fundamental algorithms for basic curves and surfaces, or for a deeper understanding of entities with which readers may be familiar, this book presents a simple approach to the entire structure of algorithms.
About the Author
Ron Goldman is a researcher at Sun Microsystems Laboratories in California working on alternative software development methodologies and new software architectures inspired by biology. He has been working with open source since hacking on GDB at Lucid, Inc. back in 1992. Since 1998 he has been helping groups at Sun Microsystems understand open source and advising them on how to build successful communities around their open source projects. Prior to Sun he developed a program to generate and manipulate visual representations of complex data for use by social scientists as part of a collaboration between NYNEX Science & Technology and the Institute for Research on Learning. He has worked on programming language design, programming environments, user interface design, and data visualization. He has a PhD in computer science from Stanford University where he was a member of the robotics group.
Sun Microsystems, Inc., Santa Clara, California, U.S.A.
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