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Designing Fair Curves and Surfaces: Shape Quality in Geometric Modeling and Computer-Aided Design

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Overview

This state-of-the-art study of the techniques used for designing curves and surfaces for computer-aided design applications focuses on the principle that fair shapes are always free of unessential features and are simple in design. The authors define fairness mathematically, demonstrate how newly developed curve and surface schemes guarantee fairness, and assist the user in identifying and removing shape aberrations in a surface model without destroying the principal shape characteristics of the model. Aesthetic aspects of geometric modeling are of vital importance in industrial design and modeling, particularly in the automobile and aerospace industries. Any engineer working in computer-aided design, computer-aided manufacturing, or computer-aided engineering will want to add this volume to his or her library. Researchers who have a familiarity with basic techniques in computer-aided graphic design and some knowledge of differential geometry will find this book a helpful reference.
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Editorial Reviews

Booknews
A collection of papers focusing on the aesthetic aspects of geometric modeling and the problem of visually pleasing curve/surface construction in industrial design and styling. Papers deal with issues of mathematically defined fairness or shape quality, developing new curve and surface schemes that guarantee fairness, and assisting users in identifying shape aberrations in a surface model and removing them without destroying the principal shape characteristics. A common theme to all of the papers is the principle of the simplest shape. Annotation c. Book News, Inc., Portland, OR (booknews.com)
Weston Meyer
This volume, the seventh in a series of geometric design publications from SIAM, focuses on the problem of "visually appealing" line/surface construction. Its twelve chapters explore various ways of (i) defining "fairness" or "shape quality" mathematically, (ii) developing new curve and surface schemes that guarantee fairness, (iii) enabling a user to identify and remove local shape aberrations without global disturbance. A common thread is the use of differential geometry constructs to express fairness.
Mathematics of Computation
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Product Details

  • ISBN-13: 9780898713329
  • Publisher: SIAM
  • Publication date: 1/28/1987
  • Series: Miscellaneous Bks.
  • Pages: 318
  • Product dimensions: 5.98 (w) x 8.98 (h) x 0.71 (d)

Table of Contents

Part I. Fairing Point Sets and Curves. 1. Approximation with Aesthetic Constraints H. G. Burchard, J. A. Ayers, W. H. Frey and N. S. Sapidis; 2. Curvature Integration through Constrained Optimization Alan K. Jones; 3. Automatic Fairing of Point Sets M. Eck and R. Jaspert; 4. Tight String Method to Fair Piecewise Linear Curves Mark Feldman; Part II. Designing Fair Surfaces: 5. Measures of Fairness for Curves and Surfaces John Roulier and Thomas Rando; 6. Minimum Variation Curves and Surfaces for Computer-Aided Geometric Design Henry P. Moreton and Carlo H. S‚quin; 7. Convexity Preserving Surface Interpolation Tim Gallagher and Bruce Piper; Part III. Interactive Techniques for Aesthetic Surface Design: 8. The Highlight Band, a Simplified Reflection Model for Interactive Smoothness Evaluation K .P. Beier and Y. Chen; 9. Interactive Design Using Partial Differential Equations M. I. G. Bloor and M. J. Wilson; 10. Polynomial Splines of Nonuniform Degree: Controlling Convexity and Fairness A. I. Ginnis, P. D. Kaklis, and N. S. Sapidis; Part IV. Special Applications: 11. Constructing C1 Surfaces of Arbitrary Topology Using Biquadratic and Bicubic Splines Jorg Peters; 12. A Convolution Approach to N-Sided Patches and Vertex Blending Yan Zhao and Alyn Rockwood.
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