Pyramid algorithms : a dynamic programming approach to curves and surfaces for geometric modeling / Ron Goldman.

Format:

Book

Author/Creator:

Goldman, Ron, 1947-

Series:

Morgan Kaufmann series in computer graphics and geometric modeling.

Morgan Kaufmann series in computer graphics and geometric modeling

Language:

English

Subjects (All):

Computer graphics.

Geometrical models--Data processing.

Geometrical models.

Physical Description:

1 online resource (577 p.)

Edition:

1st edition

Place of Publication:

Amsterdam ; Boston : Morgan Kaufmann Publishers, c2003.

Language Note:

English

System Details:

text file

Summary:

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 b

Contents:

Front Cover; Pyramid Algorithms: A Dynamic Programming Approach to Curves and Surfaces for Geometric Modeling; Copyright Page; Contents; Foreword; Preface; Chapter 1. Introduction: Foundations; 1.1 Ambient Spaces; 1.2 Coordinates; 1.3 Curve and Surface Representations; 1.4 Summary; Part I: Interpolation; Chapter 2. Lagrange Interpolation and Neville's Algorithm; 2.1 Linear Interpolation; 2.2 Neville's Algorithm; 2.3 The Structure of Neville's Algorithm; 2.4 Uniqueness of Polynomial Interpolants and Taylor's Theorem; 2.5 Lagrange Basis Functions

2.6 Computational Techniques for Lagrange Interpolation2.7 Rational Lagrange Curves; 2.8 Fast Fourier Transform; 2.9 Recapitulation; 2.10 Surface Interpolation; 2.11 Rectangular Tensor Product Lagrange Surfaces; 2.12 Triangular Lagrange Patches; 2.13 Uniqueness of the Bivariate Lagrange Interpolant; 214 Rational Lagrange Surfaces; 2.15 Ruled, Lofted, and Boolean Sum Surfaces; 2.16 Summary; Chapter 3. Hermite Interpolation and the Extended Neville Algorithm; 3.1 Cubic Hermite Interpolation; 3.2 Neville's Algorithm for General Hermite Interpolation; 3.3 The Hermite Basis Functions

3.4 Rational Hermite Curves3.5 Hermite Surfaces; 3.6 Summary; Chapter 4. Newton Interpolation and Difference Triangles; 4.1 The Newton Basis; 4.2 Divided Differences; 4.3 Properties of Divided Differences; 4.4 An Axiomatic Approach to Divided Difference; 4.5 Forward Differencing; 4.6 Summary; Part II: Approximation; Chapter 5. Bezier Approximation and Pascal's Triangle; 5.1 De Casteljau's Algorithm; 5.2 Elementary Properties of Bezier Curves; 5.3 The Bernstein Basis Functions and Pascal's Triangle; 5.4 More Properties of Bernstein/Bezier Curves

5.5 Change of Basis Procedures and Principles of Duality5.6 Differentiation and Integration; 5.7 Rational Bezier Curves; 5.8 Bezier Surfaces; 5.9 Summary; Chapter 6. Blossoming; 6.1 Blossoming the de Casteljau Algorithm; 6.2 Existence and Uniqueness of the Blossom; 6.3 Change of Basis Algorithms; 6.4 Differentiation and the Homogeneous Blossom; 6.5 Blossoming Bezier Patches; 6.6 Summary; Chapter 7. B-Spline Approximation and the de Boor Algorithm; 7.1 The de Boor Algorithm; 7.2 Progressive Polynomial Bases Generated by Progressive Knot Sequences; 7.3 B-Spline Curves

7.4 Elementary Properties of B-Spline Curves7.5 All Splines Are B-Splines; 7.6 Knot Insertion Algorithms; 7.7 The B-Spline Basis Functions; 7.8 Uniform B-Splines; 7.9 Rational B-Splines; 7.10 Catmull-Rom Splines; 7.11 Tensor Product B-Spline Surfaces; 7.12 Pyramid Algorithms and Triangular B-Patches; 7.13 Summary; Chapter 8. Pyramid Algorithms for Multisided Bezier Patches; 8.1 Barycentric Coordinates for Convex Polygons; 8.2 Polygonal Arrays; 8.3 Neville's Pyramid Algorithm and Multisided Grids; 8.4 S-Patches; 8.5 Pyramid Patches and the General Pyramid Algorithm; 8.6 C-Patches

8.7 Toric Bezier Patches

Notes:

Description based upon print version of record.

ISBN:

1-281-07801-8

9786611078010

0-08-051547-9

OCLC:

228497626