Book description
This fifth edition has been fully updated to cover the many advances made in CAGD and curve and surface theory since 1997, when the fourth edition appeared. Material has been restructured into theory and applications chapters. The theory material has been streamlined using the blossoming approach; the applications material includes least squares techniques in addition to the traditional interpolation methods. In all other respects, it is, thankfully, the same. This means you get the informal, friendly style and unique approach that has made Curves and Surfaces for CAGD: A Practical Guide a true classic.
The book's unified treatment of all significant methods of curve and surface design is heavily focused on the movement from theory to application. The author provides complete C implementations of many of the theories he discusses, ranging from the traditional to the leadingedge. You'll gain a deep, practical understanding of their advantages, disadvantages, and interrelationships, and in the process you'll see why this book has emerged as a proven resource for thousands of other professionals and academics.
 Provides authoritative and accessible information for those working with or developing computeraided geometric design applications
 Covers all significant CAGD curve and surface design techniquesfrom the traditional to the experimental
 Includes a new chapter on recursive subdivision and triangular meshes
 Presents topical programming exercises useful to professionals and students alike
Table of contents
 Cover image
 Title page
 Table of Contents
 The Morgan Kaufmann Series in Computer Graphics and Geometric Modeling
 Copyright
 Dedication
 Preface
 Chapter 1: P. Bézier: How a Simple System Was Born
 Chapter 2: Introductory Material
 Chapter 3: Linear Interpolation
 Chapter 4: The de Casteljau Algorithm
 Chapter 5: The Bernstein Form of a Bézier Curve

Chapter 6: Bézier Curve Topics
 6.1 Degree Elevation
 6.2 Repeated Degree Elevation
 6.3 The Variation Diminishing Property
 6.4 Degree Reduction
 6.5 Nonparametric Curves
 6.6 Cross Plots
 6.7 Integrals
 6.8 The Bézier Form of a Bézier Curve
 6.9 The Weierstrass Approximation Theorem
 6.10 Formulas for Bernstein Polynomials
 6.11 Implementation
 6.12 Problems

Chapter 7: Polynomial Curve Constructions
 7.1 Aitken’s Algorithm
 7.2 Lagrange Polynomials
 7.3 The Vandermonde Approach
 7.4 Limits of Lagrange Interpolation
 7.5 Cubic Hermite Interpolation
 7.6 Quintic Hermite Interpolation
 7.7 PointNormal Interpolation
 7.8 Least Squares Approximation
 7.9 Smoothing Equations
 7.10 Designing with Bézier Curves
 7.11 The Newton Form and Forward Differencing
 7.12 Implementation
 7.13 Problems
 Chapter 8: BSpline Curves
 Chapter 9: Constructing Spline Curves
 Chapter 10: W. Boehm: Differential Geometry I
 Chapter 11: Geometric Continuity
 Chapter 12: Conic Sections

Chapter 13: Rational Bézier and BSpline Curves
 13.1 Rational Bézier Curves
 13.2 The de Casteljau Algorithm
 13.3 Derivatives
 13.4 Osculatory Interpolation
 13.5 Reparametrization and Degree Elevation
 13.6 Control Vectors
 13.7 Rational Cubic BSpline Curves
 13.8 Interpolation with Rational Cubics
 13.9 Rational BSplines of Arbitrary Degree
 13.10 Implementation
 13.11 Problems

Chapter 14: Tensor Product Patches
 14.1 Bilinear Interpolation
 14.2 The Direct de Casteljau Algorithm
 14.3 The Tensor Product Approach
 14.4 Properties
 14.5 Degree Elevation
 14.6 Derivatives
 14.7 Blossoms
 14.8 Curves on a Surface
 14.9 Normal Vectors
 14.10 Twists
 14.11 The Matrix Form of a Bézier Patch
 14.12 Nonparametric Patches
 14.13 Problems
 Chapter 15: Constructing Polynomial Patches

Chapter 16: Composite Surfaces
 16.1 Smoothness and Subdivision
 16.2 Tensor Product BSpline Surfaces
 16.3 Twist Estimation
 16.4 Bicubic Spline Interpolation
 16.5 Finding Knot Sequences
 16.6 Rational Bézier and BSpline Surfaces
 16.7 Surfaces of Revolution
 16.8 Volume Deformations
 16.9 CONS and Trimmed Surfaces
 16.10 Implementation
 16.11 Problems
 Chapter 17: Bézier Triangles
 Chapter 18: Practical Aspects of Bézier Triangles

Chapter 19: W. Boehm: Differential Geometry II
 19.1 Parametric Surfaces and Arc Element
 19.2 The Local Frame
 19.3 The Curvature of a Surface Curve
 19.4 Meusnier’s Theorem
 19.5 Lines of Curvature
 19.6 Gaussian and Mean Curvature
 19.7 Euler’s Theorem
 19.8 Dupin’s Indicatrix
 19.9 Asymptotic Lines and Conjugate Directions
 19.10 Ruled Surfaces and Developables
 19.11 Nonparametric Surfaces
 19.12 Composite Surfaces
 Chapter 20: Geometric Continuity for Surfaces
 Chapter 21: Surfaces with Arbitrary Topology
 Chapter 22: Coons Patches
 Chapter 23: Shape
 Chapter 24: Evaluation of Some Methods
 Quick Reference of Curve and Surface Terms
 List of Programs
 Notation
 References
 Index
Product information
 Title: Curves and Surfaces for CAGD, 5th Edition
 Author(s):
 Release date: November 2001
 Publisher(s): Morgan Kaufmann
 ISBN: 9780080503547
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