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

  • Foreword
  • Introduction—Foundations
  • Lagrange Interpolation and Neville's Algorithm
  • Hermite Interpolation and the Extended Neville Algorithm
  • Newton Interpolation and Difference Triangles
  • Bezier Approximation and Pascal's Triangle
  • Blossoming
  • B-Spline Approximation and the de Boor Algorithm
  • Pyramid Algorithms for Multisided Bezier Patches