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

Nickolas S. Sapidis



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. It is essential reading for statisticians working on approximation or smoothing of data with mathematical curves or surfaces.

Contents

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

1994 / xii + 318 pages / Softcover / ISBN-13: 978-0-898713-32-9 / ISBN-10: 0-89871-332-3 /
List Price $113.50 / SIAM Member Price $79.45 / Order Code OT44
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