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 leading-edge. 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 computer-aided geometric design applications
- Covers all significant CAGD curve and surface design techniques-from 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 Point-Normal 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: B-Spline 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 B-Spline 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 B-Spline Curves
- 13.8 Interpolation with Rational Cubics
- 13.9 Rational B-Splines 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 B-Spline Surfaces
- 16.3 Twist Estimation
- 16.4 Bicubic Spline Interpolation
- 16.5 Finding Knot Sequences
- 16.6 Rational Bézier and B-Spline 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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