Computer Animation. Algorithms and Techniques. Rick Parent. Team LRN

Transcription

1 Computer Animation Algorithms and Techniques Rick Parent

2 Executive Editor Publishing Services Manager Assistant Developmental Editor Editorial Assistant Cover Design Text Design Supplementary Technical Illustration Composition Copyeditor Proofreader Indexer Printer Diane D. Cerra Scott Norton Belinda Breyer Ramona Buehler Ross Carron Design Mark Ong, Side by Side Studios Tom Webster, LineWorks Nancy Logan Sheila Berg Karen Stough Ty Koontz 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, courtesy 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 , 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 distributed 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 Designations used by companies to distinguish their products are often claimed as trademarks or registered trademarks. In all instances in which Morgan Kaufmann Publishers is aware of a claim, the product names appear in initial capital or all capital letters. Readers, however, should contact the appropriate companies for more complete information regarding trademarks and registration. Morgan Kaufmann Publishers 340 Pine Street, Sixth Floor, San Francisco, CA , USA ACADEMIC PRESS A Harcourt Science and Technology Company 525 B Street, Suite 1900, San Diego, CA , USA Academic Press Harcourt Place, 32 Jamestown Road, London, NW1 7BY, United Kingdom by Academic Press All rights reserved Printed in the United States of America No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means electronic, mechanical, photocopying, or otherwise without the prior written permission of the publisher. Library of Congress Control Number: ISBN: This book is printed on acid-free paper.

3 To Mom and Dad To John and Kim for teaching me to keep things in perspective

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5 Foreword... Preface... Overview... Organization of the Book... Acknowledgments... References... xv xvii xvii xx xxi xxii 1 Introduction... 1 Perception... 2 The Heritage of Animation... 4 Early Devices... 4 The Early Days of ˇConventional Animation... 6 Disney... 7 Contributions of Others... 9 Other Media for Animation... 9 Principles of Computer Animation Animation Production Computer Animation Production Tasks Digital Editing Digital Video A Brief History of Computer Animation Early Activity The Middle Years Chapter Summary References Spaces and Transformations Technical Background The Display Pipeline Homogeneous Coordinates and the Transformation Matrix... 36

6 Compounding Transformations: Multiplying Transformation Matrices Basic Transformations Representing an Arbitrary Orientation Extracting Transformations from a Matrix Description of Transformations in the Display Pipeline Round-off Error Considerations Orientation Representation Fixed Angle Representation Euler Angle Representation Angle and Axis Quaternions Chapter Summary References Interpolation Interpolation and Basic Techniques The Appropriate Function Controlling the Motion Along a Curve Computing Arc Length Speed Control Ease-in/Ease-out Constant Acceleration: Parabolic Ease-In/Ease-Out General Distance-Time Functions Curve Fitting to Position-Time Pairs Interpolation of Rotations Represented by Quaternions Path Following Orientation along a Path Smoothing a Path Determining a Path along a Surface Key-Frame Systems Animation Languages

7 Artist-Oriented Animation Languages Articulation Variables Graphical Languages Actor-Based Animation Languages Deforming Objects Warping an Object Coordinate Grid Deformation Morphing (2D) Coordinate Grid Approach Feature-Based Morphing D Shape Interpolation Matching Topology Star-Shaped Polyhedra Axial Slices Map to Sphere Recursive Subdivision Summary Chapter Summary References Advanced Algorithms Automatic Camera Control Hierarchical Kinematic Modeling Representing Hierarchical Models Forward Kinematics Local Coordinate Frames Inverse Kinematics Summary Rigid Body Simulation Bodies in Free Fall Bodies in Contact Enforcing Soft and Hard Constraints Flexible Objects Virtual Springs Energy Minimization

8 Space-Time Constraints Controlling Groups of Objects Particle Systems Flocking Behavior Autonomous Behavior Implicit Surfaces Basic Implicit Surface Formulation Animation Using Implicitly Defined Objects Collision Detection Deforming the Implicit Surface as a Result of Collision Summary Chapter Summary References Natural Phenomena Plants A Little Bit of Botany L-Systems Animating Plant Growth Summary Water Still Waters and Small-Amplitude Waves The Anatomy of Waves Modeling Ocean Waves Finding Its Way Downhill Summary Gaseous Phenomena General Approaches to Modeling Gas Computational Fluid Dynamics Clouds Fire Summary Chapter Summary References

9 6 Modeling and Animating Articulated Figures Reaching and Grasping Modeling the Arm The Shoulder Joint The Hand Coordinated Movement Reaching Around Obstacles Strength Walking The Mechanics of Locomotion The Kinematics of the Walk Using Dynamics to Help Produce Realistic Motion Forward Dynamic Control Summary Facial Animation Types of Facial Models Creating the Model Textures Approaches to Animating the Face Overview of Virtual Human Representation Representing Body Geometry Geometry Data Acquisition Geometry Deformation Clothing Hair Surface Detail Layered Approach to Human Figure Modeling Cloth and Clothing Simple Draping Getting into Clothes Motion Capture Processing the Images Camera Calibration D Position Reconstruction Fitting to the Skeleton

10 Modifying Motion Capture Summary Chapter Summary References A Rendering Issues A.1 Double Buffering A.2 Compositing A.2.1 Compositing without Pixel Depth Information A.2.2 Compositing with Pixel Depth Information A.3 Displaying Moving Objects: Motion Blur A.4 Drop Shadows A.5 Summary References B Background Information and Techniques B.1 Vectors and Matrices B.1.1 Inverse Matrix and Solving Linear Systems B.1.2 Singular Value Decomposition B.2 Geometric Computations B.2.1 Components of a Vector B.2.2 Length of a Vector B.2.3 Dot Product of Two Vectors B.2.4 Cross Product of Two Vectors B.2.5 Vector and Matrix Routines B.2.6 Closest Point between Two Lines in Three-Space B.2.7 Area Calculations B.2.8 The Cosine Rule B.2.9 Barycentric Coordinates B.2.10 Computing Bounding Shapes B.3 Transformations B.3.1 Transforming a Point Using Vector-Matrix Multiplication

11 B.3.2 Transforming a Vector Using Vector-Matrix Multiplication B.3.3 Axis-Angle Rotations B.3.4 Quaternions B.4 Interpolating and Approximating Curves B.4.1 Equations: Some Basic Terms B.4.2 Simple Linear Interpolation: Geometric and Algebraic Forms B.4.3 Parameterization by Arc Length B.4.4 Computing Derivatives B.4.5 Hermite Interpolation B.4.6 Catmull-Rom Spline B.4.7 Four-Point Form B.4.8 Blended Parabolas B.4.9 Bezier Interpolation/Approximation B.4.10 De Casteljau Construction of Bezier Curves B.4.11 Tension, Continuity, and Bias Control B.4.12 B-Splines B.4.13 Fitting Curves to a Given Set of Points B.5 Randomness B.5.1 Noise B.5.2 Turbulence B.5.3 Random Number Generator B.6 Physics Primer B.6.1 Position, Velocity, and Acceleration B.6.2 Circular Motion B.6.3 Newton s Laws of Motion B.6.4 Inertia and Inertial Reference Frames B.6.5 Center of Mass B.6.6 Torque B.6.7 Equilibrium: Balancing Forces B.6.8 Gravity B.6.9 Centripetal force B.6.10 Contact Forces B.6.11 Centrifugal Force B.6.12 Work and Potential Energy B.6.13 Kinetic Energy

12 B.6.14 Conservation of Energy B.6.15 Conservation of Momentum B.6.16 Oscillatory Motion B.6.17 Damping B.6.18 Angular Momentum B.6.19 Inertia Tensors B.7 Numerical Integration Techniques B.7.1 Function Integration B.7.2 Integrating Ordinary Differential Equations B.8 Standards for Moving Pictures B.8.1 In the Beginning, There Was Analog B.8.2 In the Digital World B.9 Camera Calibration References Index About the Author