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

331 Pages·1987·32.93 MB·English

by  Nickolas S. Sapidis

Designing
Fair Curves
and Surfaces
Geometric Design Publications
Editor
Gerald E. Farin
Arizona State University
Farin, Gerald E., editor, Geometric Modeling: Algorithms and New Trends (1987)
Farin, Gerald E., editor, NURBS for Curve and Surface Design (1991)
Barnhill, Robert E., editor, Geometry Processing for Design and Manufacturing (1992)
Hagen, Hans, editor, Curve and Surface Design (1992)
Hagen, Hans, editor, Topics in Surface Modeling (1992)
Goldman, Ronald N., and Lyche, Tom, editors, Knot Insertion and Deletion Algorithms for
B-Spline Curves and Surfaces (1993)
Sapidis, Nickolas S., editor, Designing Fair Curves and Surfaces: Shape Quality in Geometric
Modeling and Computer-Aided Design (1994)
Designing
Fair Curves
and Surfaces
Shape Quality in
Geometric Modeling
and Computer-Aided Design
Edited by
Nickolas S. Sapidis
National Technical University
of Athens
Eiam.
Philadelphia
Society for Industrial and Applied Mathematics
Library of Congress Cataloging-in-Publication Data
Designing fair curves and surfaces : shape quality in geometric
modeling and computer-aided design / edited by Nickloas S. Sapidis.
p. cm. — (Geometric design publications)
Includes bibliographical references and index.
ISBN 0-89871-332-3
1. Curves, Algebraic—Data processing. 2. Surfaces—Data
processing. 3. Computer-aided design. I. Sapidis, Nickolas S.
II. Series.
QA567.D47 1994
745.4'01'516352—dc20 94-26850
Cover art reprinted with permission from K. G. Pigounakis and P. D. Kaklis, created at the
Ship-Design Laboratory of the National Technical University of Athens, Greece.
Sponsored by SI AM Activity Group on Geometric Design.
All rights reserved. Printed in the United States of America. No part of this book may be
reproduced, stored, or transmitted in any manner without the written permission of the
Publisher. For information, write the Society for Industrial and Applied Mathematics,
3600 University City Science Center, Philadelphia, PA 19104-2688.
Copyright © 1994 by the Society for Industrial and Applied Mathematics.
Siam.
is a registered trademark.
To Robert Barnhill
and
the Computer-Aided Geometric Design Research Group
This page intentionally left blank
List of Contributors
J.A. Ayers, Mathematics Department, General Motors Research Laboratory, Warren, MI
48090-9055.
Klaus-Peter Beier, Department of Naval Architecture and Marine Engineering,
University of Michigan, 2600 Draper, NA & ME Bldg., Ann Arbor, MI 48109-2145.
Malcolm I. G. Bloor, Department of Applied Mathematical Studies, The University of
Leeds, Leeds LS2 9JT, United Kingdom.
H.G. Burchard, Department of Mathematics, Oklahoma State University, Stillwater, OK
74078-0613.
Yifan Chen, Ford Motor Company, P.O. Box 2053/MD3135, Room 3135, SRL, Dearborn,
MI 48121.
Matthias Eck, Department of Computer Science and Engineering, University of
Washington, 423 Sieg Hall, FR-35, Seattle, WA 98195.
Mark Feldman, CAMAX Corporation, 7851 Metro Parkway, Minneapolis, MN 55425.
W.H. Frey, Mathematics Department, General Motors Research Laboratory, Warren. MI
48090-9055.
Tim Gallagher, 48 Nottinghill Road, Brighton, MA 02135.
Alexandros I. Ginnis, Department of Naval Architecture and Marine Engineering, Nationa
Technical University of Athens, Heroon Polytechneiou 9, Zografou 157 73, Athens, Greece.
Rainer Jaspert, Department of Mathematics, University of Science and Technology,
AG 3, Schlossgartenstr. 7 D-64289, Darmstadt, Germany.
Alan K. Jones, Geometry and Optimization, Orgn. G-6413, M/S 7L-21,
Boeing Computer Services, Seattle, WA 98124-0346.
Panagiotis D. Kaklis, Department of Naval Architecture and Marine Engineering, National
Technical University of Athens, Heroon Polytechneiou 9, Zografou 157 73, Athens, Greece.
Henry P. Moreton, MS 6L-005, Silicon Graphics, 2011 N. Shoreline Blvd.. Mountain
View, CA 94039-7311.
Jorg Peters, Department of Computer Science, Purdue University, West Lafayette, IN
47907-1398.
Bruce Piper, Department of Mathematical Sciences, Rensselaer Polytechnic
Institute, Troy, NY 12180.
Thomas Rando, 11 Bush Hill Drive, Niantic, CT 06357
Alyn Rockwood, Department of Computer Science and Engineering, Arizona State
University, Tempe, AZ 85287.
John Roulier, Computer Science and Engineering Department, University of Connecticut,
U155, Storrs, CT 06269-0001.
Nickolas S. Sapidis, Department of Naval Architecture and Marine Engineering, National
Technical University of Athens, Heroon Polytechneiou 9, Zografou 157 73, Athens, Greece.
Carlo H. Sequin, Computer Science Division, Department of Electrical
Engineering and Computer Science, University of California, Berkeley, CA 94720.
Michael J. Wilson, Department of Applied Mathematical Studies, The
University of Leeds, Leeds LS2, United Kingdom.
Van Zhao, Santa Teresa Laboratory, IBM Corporation, L53/F423, San Jose, CA 95141.
Contents
xi Preface
Part 1 Fairing Point Sets and Curves
3 Chapter 1 Approximation with Aesthetic Constraints
H. G. Burchard, J. A. Ayers, W. H. Frey, and N. S. Sapidis
29 Chapter 2 Curvature Integration through Constrained Optimization
Alan K. Jones
45 Chapter 3 Automatic Fairing of Point Sets
Matthias Eck and Rainer .laspert
61 Chapter 4 Tight String Method to Fair Piecewise Linear Curves
Mark Feldman
Part 2 Designing Fair Surfaces
75 Chapter 5 Measures of Fairness for Curves and Surfaces
John Roulier and Thomas Rando
123 Chapter 6 Minimum Variation Curves and Surfaces for Computer-Aided
Geometric Design
Henry P. Moreton and Carlo H. Sequin
161 Chapter 7 Convexity Preserving Surface Interpolation
Tim Gallagher and Rntce Piper
Part 3 Interactive Techniques for Aesthetic Surface Design
213 Chapter 8 The Highlight Band, a Simplified Reflection Model for
Interactive Smoothness Evaluation
Klaus-Peter Beier and Yifan Chen
231 Chapter 9 Interactive Design Using Partial Differential Equations
Malcolm l.G. Bloor and Michael J. Wilson
253 Chapter 10 Polynomial Splines of Nonuniform Degree: Controlling
Convexity and Fairness
Alexandras I. Ginnis, Panagiotis D. Kaklis, and Nicholas S. Sapidis
Part 4 Special Applications
277 Chapter 11 Constructing C] Surfaces of Arbitrary Topology Using
Biquadratic and Bicubic Splines
Jorg Peters
295 Chapter 12 A Convolution Approach to /V-Sided Patches and Vertex Blending
Van Zhao and Alyn Rockwood
315 Index