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

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

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