Curves and Surfaces for CAGD: A Practical Guide

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Elsevier, Nov 1, 2001 - Computers - 520 pages

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.
 

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Contents

How a Simple System Was Born
1
Chapter 2 Introductory Material
13
Chapter 3 Linear Interpolation
25
Chapter 4 The de Casteljau Algorithm
43
Chapter 5 The Bernstein Form of a Bézier Curve
57
Chapter 6 Bézier Curve Topics
81
Chapter 7 Polynomial Curve Constructions
95
Chapter 8 BSpline Curves
119
Chapter 17 Bézier Triangles
309
Chapter 18 Practical Aspects of Bézier Triangles
335
Differential Geometry II
349
Chapter 20 Geometric Continuity for Surfaces
367
Chapter 21 Surfaces with Arbitrary Topology
377
Chapter 22 Coons Patches
399
Chapter 23 Shape
419
Chapter 24 Evaluation of Some Methods
431

Chapter 9 Constructing Spline Curves
147
Differential Geometry I
179
Chapter 11 Geometric Continuity
191
Chapter 12 Conic Sections
205
Chapter 13 Rational Bézier and BSpline Curves
227
Chapter 14 Tensor Product Patches
245
Chapter 15 Constructing Polynomial Patches
269
Chapter 16 Composite Surfaces
285
Appendix A Quick Reference of Curve and Surface Terms
437
Appendix B List of Programs
445
Appendix C Notation
447
References
449
Index
491
Color Plate Section
501
Copyright

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About the author (2001)

Professor Gerald Farin currently teaches in the computer science and engineering department at Arizona State University. He received his doctoral degree in mathematics from the University of Braunschweig, Germany, in 1979. His extensive CAGD experience includes working as a research mathematician in a computer-aided development for Daimler-Benz, serving on the executive committee of the ASU PRISM project, and speaking at a multitude of symposia and conferences. Farin has authored and edited several books and papers, and he is editor-in-chief of Computer Aided Geometric Design.

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