Computer Animation: Algorithms and Techniques (The Morgan Kaufmann Series in Computer Graphics)

551 Pages·2001·6.33 MB·English

by  Rick Parent

Computer Animation
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The Morgan Kaufmann Series in Computer Graphics
and Geometric Modeling
Series Editor: Brian A. Barsky, University of California, Berkeley
Computer Animation: Algorithms Introduction to Implicit Surfaces User Interface Management
and Techniques Edited by Jules Bloomenthal Systems: Models and Algorithms
Rick Parent Dan R. Olsen, Jr.
Jim Blinn’s Corner: A Trip Down
Advanced RenderMan: Creating the Graphics Pipeline Making Them Move: Mechanics,
CGI for Motion Pictures Jim Blinn Control, and Animation of
Anthony A. Apodaca and Articulated Figures
Larry Gritz Interactive Curves and Surfaces: Edited by Norman I. Badler,
A Multimedia Tutorial on Brian A. Barsky, and David
Curves and Surfaces in Geometric CAGD Zeltzer
Modeling: Theory and Algorithms Alyn Rockwood and Peter
Jean Gallier Chambers Geometric and Solid Modeling:
An Introduction
Andrew Glassner’s Notebook: Wavelets for Computer Graphics: Christoph M. Hoffmann
Recreational Computer Graphics Theory and Applications
Andrew S. Glassner Eric J. Stollnitz, Tony D. An Introduction to Splines for
DeRose, and David H. Salesin Use in Computer Graphics and
Warping and Morphing of Geometric Modeling
Graphical Objects Principles of Digital Image Syn- Richard H. Bartels, John C.
Jonas Gomes, Lucia Darsa, thesis Beatty, and Brian A. Barsky
Bruno Costa, and Luis Velho Andrew S. Glassner
Jim Blinn’s Corner: Dirty Pixels Radiosity & Global Illumination
Jim Blinn François X. Sillion and Claude
Puech
Rendering with Radiance: The
Art and Science of Lighting Knotty: A B-Spline Visualization
Visualization Program
Greg Ward Larson and Rob Jonathan Yen
Shakespeare
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Computer
Animation
Algorithms and
Techniques
Rick Parent

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Executive Editor Diane D. Cerra
Publishing Services Manager Scott Norton
Assistant Developmental Editor Belinda Breyer
Editorial Assistant Ramona Buehler
Cover Design Ross Carron Design
Text Design Mark Ong, Side by Side Studios
Supplementary Technical Illustration Tom Webster, LineWorks
Composition Nancy Logan
Copyeditor Sheila Berg
Proofreader Karen Stough
Indexer Ty Koontz
Printer Courier Corporation
Cover Images (from top): Detail of still from Geri’s Game, courtesy Pixar Studios; simulation of volcano spitting fire, courtesy
Katie Boner and Barb Olsafsky; simulation of waves hitting shore, courtesy Arun Somasundaram; “Bragger in Beantown,” cour-
tesy John Chadwick; robot, courtesy Jessica Hodgins; facial model, courtesy Scott King; driving simulation, courtesy Norm
Badler
Interior Images: Figures 5.26 and 5.27 (plates 4 and 5), courtesy David S. Ebert; Figure 5.28 (plate 6) courtesy Ruchir Gatha and
David S. Ebert; figure 6.26, courtesy David S. Ebert; figures 6.28 and 6.31, courtesy Frederic I. Parke; figure 6.39, “Face and 2d
Mesh,” reprinted from Signal Processing: Image Communication 15, nos. 4-5 (Tekalp, 2000): pp. 387-421, by permission of
Elsevier Science; figure A.3 (plate 11), courtesy Disney Enterprises, Inc.; figure A.11 (plate 12), courtesy Pixar Studios, all rights
reserved; figure A.12 (plate 13), courtesy Disney Enterprises, Inc..
The Random Number Generator discussed in appendix section B.5.3 is free software that can be redistributed and/or modified
under the terms of the GNU Library General Public License as published by the Free Software Foundation. This library is distrib-
uted free of charge but without warranty, even the implied warranties of merchantability or fitness for a particular purpose. For
details, see the GNU Library General Public License posted at http://www.fsf.org/copyleft/library.txt.
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instances in which Morgan Kaufmann Publishers is aware of a claim, the product names appear in initial capital or all capital let-
ters. Readers, however, should contact the appropriate companies for more complete information regarding trademarks and regis-
tration.
Morgan Kaufmann Publishers
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Academic Press
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© 2002 by Academic Press
All rights reserved
Printed in the United States of America
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No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means—elec-
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Library of Congress Control Number: 2001090620
ISBN: 1-55860-579-7
This book is printed on acid-free paper.
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To Mom and Dad
To John and Kim for teaching me to keep things in perspective
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Foreword........................................................................... xv
Preface.............................................................................. xvii
Overview..................................................................................... xvii
Organization of the Book.......................................................... xx
Acknowledgments..................................................................... xxi
References ................................................................................. xxii
1 Introduction................................................................... 1
Perception.................................................................................. 2
The Heritage of Animation........................................................ 4
Early Devices ......................................................................... 4
The Early Days of ˇConventional(cid:211) Animation .......................... 6
Disney .................................................................................... 7
Contributions of Others .......................................................... 9
Other Media for Animation ..................................................... 9
Principles of Computer Animation.......................................... 10
Animation Production............................................................... 12
Computer Animation Production Tasks.................................. 15
Digital Editing ......................................................................... 17
Digital Video........................................................................... 20
A Brief History of Computer Animation................................... 21
Early Activity........................................................................... 21
The Middle Years................................................................... 24
Chapter Summary...................................................................... 29
References ................................................................................. 29
Spaces and Transformations ................................................... 31
2 Technical Background ................................................. 31
The Display Pipeline.................................................................. 32
Homogeneous Coordinates and the Transformation
Matrix.......................................................................................... 36
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Compounding Transformations: Multiplying
Transformation Matrices........................................................... 39
Basic Transformations.............................................................. 40
Representing an Arbitrary Orientation.................................... 42
Extracting Transformations from a Matrix.............................. 45
Description of Transformations in the Display Pipeline........ 46
Round-off Error Considerations............................................... 48
Orientation Representation ...................................................... 51
Fixed Angle Representation................................................... 53
Euler Angle Representation ................................................... 56
Angle and Axis ....................................................................... 57
Quaternions............................................................................ 58
Chapter Summary...................................................................... 61
References ................................................................................. 61
Interpolation............................................................................... 63
3 Interpolation and Basic Techniques........................... 63
The Appropriate Function......................................................... 64
Controlling the Motion Along a Curve..................................... 68
Computing Arc Length............................................................ 69
Speed Control ........................................................................ 84
Ease-in/Ease-out.................................................................... 86
Constant Acceleration: Parabolic Ease-In/Ease-Out.............. 89
General Distance-Time Functions.......................................... 92
Curve Fitting to Position-Time Pairs....................................... 94
Interpolation of Rotations Represented by Quaternions....... 97
Path Following........................................................................... 102
Orientation along a Path......................................................... 102
Smoothing a Path................................................................... 108
Determining a Path along a Surface ...................................... 114
Key-Frame Systems .................................................................. 116
Animation Languages............................................................... 120
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Artist-Oriented Animation Languages .................................... 121
Articulation Variables.............................................................. 122
Graphical Languages............................................................. 123
Actor-Based Animation Languages........................................ 123
Deforming Objects..................................................................... 124
Warping an Object.................................................................. 125
Coordinate Grid Deformation ................................................. 125
Morphing (2D) ............................................................................ 143
Coordinate Grid Approach...................................................... 143
Feature-Based Morphing........................................................ 148
3D Shape Interpolation.............................................................. 153
Matching Topology................................................................. 157
Star-Shaped Polyhedra.......................................................... 157
Axial Slices............................................................................. 159
Map to Sphere........................................................................ 160
Recursive Subdivision............................................................ 166
Summary................................................................................ 169
Chapter Summary...................................................................... 169
References ................................................................................. 170
4 Advanced Algorithms................................................... 173
Automatic Camera Control....................................................... 174
Hierarchical Kinematic Modeling............................................. 175
Representing Hierarchical Models ......................................... 177
Forward Kinematics................................................................ 184
Local Coordinate Frames....................................................... 185
Inverse Kinematics................................................................. 192
Summary................................................................................ 203
Rigid Body Simulation .............................................................. 203
Bodies in Free Fall ................................................................. 204
Bodies in Contact................................................................... 216
Enforcing Soft and Hard Constraints ...................................... 231
Flexible Objects...................................................................... 232
Virtual Springs........................................................................ 235
Energy Minimization............................................................... 236
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